title: Playoff format

text: The current AFL finals system breaks up the eight participants into four groups of two teams, ranked by their league position after regular-season play. Each group receives an advantage over the teams directly below it on the league table. These advantages are the so-called "double-chance", where a loss in the first week will not eliminate a team from the finals, and home ground finals. Note, however, that "home" designations are often irrelevant if a finals match involves two teams from the same state.


title: Playoff format

text: The top four teams play the two Qualifying Finals. The winners get a bye through to Week 3 of the tournament to play home Preliminary Finals, while the losers play home Semi-Finals in Week 2. The bottom four teams play the two Elimination finals, where the winners advance to Week 2 away games and the losers' seasons are over.


title: Playoff format

text: First and second — These teams receive the double-chance, and play their first two finals matches at home—their Qualifying Final, and then either a Semi-final (should they lose the QF) or Preliminary Final (should they win the QF). They must win two finals matches to reach the Grand Final.


title: Playoff format

text: Third and fourth — Like the top two teams, they receive the double-chance, and must win two finals matches to reach the Grand Final. However, they only get to play one finals match at home—a Semi-final if they lose their QF, or Preliminary Final if they win the QF.


title: Playoff format

text: Fifth and sixth — These teams do not receive a double-chance. They must win three matches to reach the Grand Final—an Elimination final, Semi-final, and Preliminary Final. They do get to host their EF.


title: Playoff format

text: Seventh and eighth — These teams receive neither a double-chance nor a home finals match, and must also win three finals matches to reach the Grand Final.


title: Playoff format

text: From 2009 through to 2014, the Super League used a top-eight playoff system. The expansion to an eight-team bracket coincided with the league's expansion from 12 to 14 teams. Like the AFL system, the Super League system eliminated two teams in each week leading up to the Grand Final. However, it had a number of differences from the AFL system, most notably the feature known as "Club Call" (explained below).


title: Playoff format

text: As in the AFL, the participants were ranked by league position in the regular season. Unlike in the AFL, the team receiving home advantage in each match leading up to the Grand Final was guaranteed the right to host the match at a ground of its choosing, either its regular home stadium or (rarely) a larger nearby alternative.


title: Playoff format

text: The winners of these matches advanced directly to Week 3, in which they received home advantage. The higher-seeded winner received Club Call immediately after Week 2. The losers had another chance in Week 2, when they were at home to the winners of the Week 1 Elimination Play-Offs.


title: Playoff format

text: Club Call, a unique feature of the Super League system, took place on the second weekend of the playoffs, shortly after the winners of the two PSFs were known. The highest-seeded winning club from Week 1 was required to choose which of the two PSF winners they would play in Week 3.


title: Playoff format

text: Super League XX in 2015 introduced a radical change to the league system, under which the 24 clubs in Super League and the second-tier Championship are split into three groups of eight after each club has played 22 matches. The top eight clubs in Super League at that point will enter a new play-off structure, beginning with a single round-robin mini-league followed by a Shaughnessy play-off involving the top four teams.


title: Playoff format

text: The "best-of" formats refer to a head-to-head competition where the two competitors compete to first win the majority of the games allotted to win the "series". If a competitor wins a majority of the games, the remaining games are not played (unless the maximum number of games in the series are played). This is a modification of the single-elimination tournament to allow more matches to be held. Moreover, if it can be said that if one competitor has a higher probability of winning a single game (and game results are i.i.d.), the likelihood that this competitor wins the series increases when more games are played. For example, if team A has a 70% chance of defeating team B in a single game, its probability of winning a best-of-three series against B is 78.4%, and its probability of winning a best-of-seven series is about 87.4%.


title: Playoff format

text: A best-of-three playoff is a head-to-head competition between two teams in which one team must win two games to win the series. Two is chosen as it constituted a majority of the games played; if one team sweeps both of the first two games, game 3 is ignored.


title: Playoff format

text: When a best-of series is tied (each team having won the same number of games), the bracket is sometimes said to be a "best-of-(number of games left)." This is because for all practical purposes, the teams are starting over. For instance, if a best-of-seven series is deadlocked at , the series can be referred to as a "best-of-three", since the first team to win the next two games advances. Game 7 would only be played if two teams split Games 5 and 6.


title: Playoff format

text: In tennis, matches are usually decided with a best-of-three-sets format. Some major tournaments are played in a best-of-five-sets format, most notably the Grand Slam men's singles and doubles. Also, the 35-and-over Gentlemen's Invitation Doubles and the 35-and-over Ladies' Invitation Doubles at Wimbledon are both round-robin tournaments.


title: Playoff format

text: The first use of the best-of-three playoff was in Major League Baseball. The National League authorised a playoff to be held if two teams ended the season in a tie for first place; the American League used a single game in this situation. From to , both leagues have used only a one-game playoff as a tie-breaker if only one team can advance; since , a criteria based on regular-season performance is used. Since , a tie-breaker based on regular-season performance can be used only to seed teams.


title: Playoff format

text: Since , the Wild Card Series sees the 3rd seed hosts the 6th seed & the fourth playing the 5th, and the two higher seeds play at home for all three games, the third if needed.


title: Playoff format

text: Both the National Basketball Association (NBA) and National Hockey League (NHL) once used best-of-three playoffs (often referred to as a "mini-series"), but today neither league does. Professional basketball first adopted the best-of-three playoff for first-round play starting with its inception as the Basketball Association of America in 1946, before changing its name to the NBA three years later. Basketball retained the format through the 1959–60 season; the league resumed its use of the best-of-three first-round series in 1974–75, but abolished it again in 1983–84 when the number of teams qualifying for its postseason tournament was increased to 16 (10 teams had qualified during the first two years of the aforementioned period, this number being expanded to 12 in 1976–77; in both instances some of the highest-ranking teams did not participate in the best-of-three round, drawing byes and automatically advancing to the second round, which was best-of-seven, as were all subsequent rounds).


title: Playoff format

text: In ice hockey, the best-of-three format was one of two possible types of series that could be held to determine the winner of the Stanley Cup (the other being a two-legged playoff series). It was used in lower rounds in the NHL up until the Original Six era. The best-of-three series in the modern era was first used in the first round of the Stanley Cup playoffs beginning with the 1974–75 season. At that time, the number of NHL playoff teams had been increased to twelve from the previous eight. The format which then took effect called for the first three finishers in each of the league's four divisions to enter the postseason, but the four division winners earn first-round byes and advanced to the best-of-seven quarterfinals, and so didn't play any best-of-three series. The postseason then proceeded as the NBA's did, with the second round onwards being best-of-seven. This remained the case until the 1979–80 season, when the NHL expanded its playoff field to sixteen after absorbing four teams from the defunct World Hockey Association in a semi-merger, whereupon the byes were abolished and all 16 qualifying teams participated in the first round, which was lengthened to best-of-five. In both the NBA and NHL, the team ranked higher in the standings during the regular season played the first and (if necessary) the third games of the series at home, with the lower-ranked team hosting the second game.


title: Playoff format

text: The World Cup of Hockey, organized by the NHL, used a best-of-three format in the final round in 1996 and 2016, as did the Canada Cup.


title: Playoff format

text: Until 2009, the WNBA forced the team with the higher record to travel to the lower seed's home court for game 1, then played the final game(s) at home. Because of this perceived inequity, in 2010, the league switched to a more traditional odd-even format, where the higher seed will play the first and (if needed) third games at home. Come 2022, this will be used in the league quarterfinals. In 2005, the league changed the WNBA Finals to a best-of-five format. By 2016, the league semifinals matched this format.


title: Playoff format

text: NCAA Division I baseball uses the best-of-three format in the second round and the final round of its 64-team championship tournament. Starting in 1999, when the tournament expanded from 48 teams (eight regionals of six teams each) to 64 teams (sixteen regionals of four teams each), the NCAA introduced the "super regional", in which the 16 regional winners play in eight best-of-three series, with the eight series winners advancing to the College World Series. If a regional winner is also a national seed (one of the top eight seeds of the 64 first-round teams), it is guaranteed to host the super regional. If no national seed makes a particular super regional, the NCAA puts hosting rights up for bidding between the competing schools. In 2003, the College World Series changed from a one-game final to a best-of-three series.


title: Playoff format

text: From approximately the founding of the Western Interprovincial Football Union in 1936 until the early 1970s, multi-game playoffs series were a regular fixture of professional Canadian football playoffs. Over the years, both the WIFU (later the Western Football Conference) and the Interprovincial Rugby Football Union (later the Eastern Football Conference) used a combination of best-of-three series, three-game total points series, and two-game total points series to determine both conference final participants and conference champions. The Grey Cup championship itself has always consisted of a single game.


title: Playoff format

text: The last best-of-three playoff series (in what by then had evolved into the present-day Canadian Football League in 1958) consisting of two autonomous conferences was the 1971 Western Conference Final. Since 1972, the West has used one-game playoffs. The Eastern Conference (which by that time had abolished the best-of-three format in favor of two-game total points series) adopted one-game playoffs for the 1973 season.


title: Playoff format

text: The Euroleague, the primary Europe-wide club competition in basketball, introduced a quarterfinal round for the 2004–05 season which originally employed a best-of-three format. Starting with the 2008–09 season, the quarterfinal round became best-of-five. This is the only point in the Euroleague where a playoff series is used; all earlier rounds are conducted in a league format, and the quarterfinal winners advance to the Final Four, where all games are one-off knockout matches.


title: Playoff format

text: In the FIBA Oceania Championship, the best-of-three series is used if only both Australia and New Zealand play in the tournament. If a team wins the first two games, the last game may still be played. If other teams participate, a regular round-robin or multi-stage tournament is used. In 2009, a two-legged tie was used, but it was reverted to a best-of-three series in 2011.


title: Playoff format

text: The best-of-three playoff system was also used in the Campeonato Brasileiro Série A for the 1998 and 1999 quarterfinals, semifinals, and finals. The Brazilian model was unique in that extra time was not used (meaning matches could end in a draw). If neither team won two games, the team with the most victories would qualify (for instance, if one team won the first match before drawing the next two). If the both teams had one victory, the team with the best goal difference would qualify. If the goal difference was the same, the team with the best regular-season campaign would qualify.


title: Playoff format

text: The Philippine Premier Volleyball League, uniquely, uses a best-of-three series to determine the third-place team at the end of its conferences' playoffs rather than one game, as did its predecessor Shakey's V-League.


title: Playoff format

text: In a modification of the best-of-three format, leagues in the Philippines award a "twice-to-beat advantage" to the top seeds; in this case, the team with this advantage needs to be beaten twice by its opponent, a unilateral double elimination. In essence, one team is given a "de facto" 1–0 lead in a best-of-three series. First applied in the Finals of the scholastic UAAP basketball and volleyball championships in 1979, then currently applied in the semifinals since 1994, it was later adopted by their NCAA counterparts and other associations in their mandatory scholastic competitions. The professional Philippine Basketball Association, its semi-professional D-League, and volleyball's inactive Philippine Super Liga have adopted the format only in the quarterfinal rounds of their conference playoffs.


title: Playoff format

text: An amendment to the UAAP rules in 2008 gave the undefeated team (the team that won all regular season games) a bye up to the finals, possessing an automatic 1–0 lead in a best-of-five series, or the "three-times-to-beat advantage". This was adopted by the Philippine NCAA in 2009, but was abolished by both leagues in 2016, when the undefeated team has a finals berth, but the finals are played in a regular best-of-three format.


title: Playoff format

text: A similar situation also existed in later versions of the Argus finals system used commonly in Australian rules football competitions in the early part of the 20th century: later versions of the system had a "right of challenge" for the minor premier (the team on top of the ladder) if they lost the Semi-Final or the Final, meaning the minor premier had to be beaten twice for another team to win the premiership.


title: Playoff format

text: In the event that the same team played the minor premier in the Semi-Final or the Final and in the Grand Final, the right of challenge became equivalent to the minor premier holding a 1–0 lead in a best-of-three series.


title: Playoff format

text: In Nippon Professional Baseball, the Climax Series second stage, where the top team in the regular season faces the winner of the playoff between the second and third place teams, uses a similar format for a six-game playoff. In this case, the top seed needs only to win three games, while the lower seed must win four games to advance to the Japan Series. It is a "four times to beat advantage" with the top team needing only to win three games.


title: Playoff format

text: In the KBO League in South Korean baseball, the No. 4 team in the Wild Card game, or the first round of its postseason, has 1–0 lead in the best-of-three series, and can advance with a single win or tie, while the No. 5 team has to decisively win in order to advance.


title: Playoff format

text: Described as a "best-of-two" series in the resumption the 2019–20 NBA season, if the ninth-ranked team is within four games behind of the eighth-ranked team after the seeding games are done, play-in games will be held between the two teams. Here, the ninth-ranked team has to beat the eighth-ranked team twice, while the eighth-ranked team has to win just once to qualify to the playoffs proper. The Memphis Grizzlies finishing ninth, half-a-game behind the Portland Trail Blazers, necessitated the play-in game. The Blazers eliminated the Grizzlies in game one to advance to the playoffs.


title: Playoff format

text: A best-of-five playoff is a head-to-head competition between two teams, wherein one must win three games to win the series. Three is chosen as it constituted a majority of games played. If one team wins the series before reaching game 5, all others are ignored.


title: Playoff format

text: At present, only one of the major professional sports leagues in the United States and Canada — Major League Baseball — uses the best-of-five playoff, doing so in its second round, known as the Division Series. At one time, however, the League Championship Series (semifinals) was best-of-five, from its birth with both leagues' realignment into two divisions in , continuing until the round was lengthened to best-of-seven in . (This change would have immediate ramifications: In the American League, in each of the first two years where the LCS used the best-of-seven format, the Kansas City Royals in 1985 and the Boston Red Sox in 1986 fell behind 3–1, which previously would have eliminated them, before coming back to win the series.) When the wild card was first used in (it was created for the season, but that year's entire postseason was cancelled due to a players' strike), the best-of-five format was authorized for the new Division Series, in which eight teams participated.


title: Playoff format

text: During the time that the League Championship Series was best-of-five, a "2–3" format was used, with one team hosting the first two games, the other the last three (the respective roles alternating between the Eastern and Western Division champions, regardless of which one finished with the better regular-season record). This procedure was repeated when the best-of-five Division Series was added in 1995 (except that two of each league's now three division winners hosted three games, and the wild card never do so), but starting in , the home-field advantage was awarded to the two division winners in each league that had the best regular-season records. Also in 1998, the "2–2–1" format was instituted: the team with the home-field advantage was given Games 1, 2, and 5 at home, not Games 3–5. Also, that format gives "both" teams have the home-field advantage in a sense. While one team gets to host three games (including the critical first and last game), the other team does get two chances out of three (games 3 and 4) of winning the series at home. For the 2012 postseason only, the Division Series reverted to "2–3". (This decision was made after the 2012 schedule had been released; due to the addition of a second Wild Card team and the subsequent extra Wild Card Game, the "2–3" format was used that year to minimize the disruption of the schedule by giving the Division Series one off-day instead of two.) With the Wild Card playoff now established and schedules adjusted accordingly, the "2–2–1" format was restored in 2013.


title: Playoff format

text: The National Basketball Association (NBA) and National Hockey League (NHL) both formerly used best-of-five series. The NBA did so in its second-round playoff prior to the season, and in the first round from through , and again from until , when it was lengthened to a best-of-seven series. The NHL did so for its first-round series beginning with the season and lasting until increasing its first round to best-of-seven in . The best-of-5 format was reinstated for the 2020 Stanley Cup Qualifying Round between seeds 5–12. Unlike in baseball, in both NBA and NHL, in a best-of-five series the higher regular-season finisher always hosts the first, second, and (if necessary) fifth games. The AHL has used the best-of-five series in the first round since the 2012 postseason.


title: Playoff format

text: As of 2005, the Women's National Basketball Association (WNBA) now uses a best-of-five format for its championship series. The league semifinals matched this format starting in 2016.


title: Playoff format

text: Historically, most European domestic basketball leagues have used a best-of-five format in their championship series. The main long-standing exceptions are the Israeli and French leagues, which have historically used one-off finals, the Adriatic League (former Yugoslavia), which has changed from a one-off final to a best-of-three final back to a one-off final in recent years, and the Lithuanian, Polish and Turkish leagues, which use a best-of-seven format. Italy has gone to a best-of-seven final effective with its 2008–09 season. The Euroleague quarterfinal round expanded to best-of-five from best-of-three starting in the 2008–09 season. France changed its final from a one-off match to a best-of-five series in 2012–13.


title: Playoff format

text: The Ashes, a cricket series played between Australia and England is a five-match series. If the series is tied, the team holding the trophy keeps until the next series. Most test cricket matches are played under this format, but others extend up to seven matches. Test cricket is typically hosted by one team throughout the entire series. While series such as this have five matches, it is not exactly "best-of-five", as draws and other results, are possible.


title: Playoff format

text: A best-of-seven playoff is a head-to-head competition between two teams, wherein one must win four games to win the series. Four is chosen as it constitutes winning a majority of the seven games played. If one team wins the series before reaching game 7, all others are ignored. It is not necessary for the four games to be won consecutively. Draws are not permitted, even in sports where they usually would be; play continues until there is a winner. This ensures that a series will never require more than seven games.


title: Playoff format

text: The schedule is arranged so that the team with home advantage – the team that had the better regular-season record plays the first game and the decisive seventh game (if necessary) at home. Most best-of-seven series follow a "2–3–2" format or a "2–2–1–1–1" format; that is, in a 2–3–2 series, the first two games are played at the home venue of a team with the home-field advantage, the next three games (including Game 5, if necessary) are played at the home of the team without it, and the final two games (if necessary) are played at the home of the team with the advantage. In a "2–2–1–1–1" format, the first two games are played at the team with the better record venue, the next two at the team with the worse record, and then alternating venues for the fifth, sixth and seventh games, if necessary. An "odd-even" format is used in the postseason tournaments of the Liiga in Finland and the Swedish Hockey League.


title: Playoff format

text: Major League Baseball (MLB) has used a best-of-seven format for the League Championship Series since 1985, and for the World Series between 1905 and 1918, and since 1922. MLB uses the "2–3–2" format.


title: Playoff format

text: The National Basketball Association (NBA) also uses a "2–2–1–1–1" format for all playoff rounds including the Finals. From the Finals' inception in 1947, the championship round used a "2–2–1–1–1" format (except in 1971, 1975, 1978, and 1979). It was changed to a "2–3–2" format between 1985–2013 to reduce travel expenses, as the league's "East-West" divisional alignment means the two teams are usually separated by great distances. For instance, the cities represented in the Finals' most frequent matchup, Los Angeles and Boston, are almost apart. The "2–2–1–1–1" format was restored in 2014.


title: Playoff format

text: The National Hockey League uses a best-of-seven series for all rounds of its league-championship Stanley Cup playoffs, but uses the "2–2–1–1–1" format. The AHL and the ECHL do not use a set playoff format for their league championship playoff tournaments due to scheduling conflicts. For example, in the 2016 Calder Cup playoffs, due to scheduling conflicts in both arenas, the Pacific Division finals between the Ontario Reign and the San Diego Gulls used the "odd-even" playoff format, with Ontario hosting the odd games.


title: Playoff format

text: The Chinese, Italian, Lithuanian, Polish, and Turkish basketball leagues use a best-of-seven format in their championship series. The Turkish playoff has one unique feature: if one team in the championship series (or, for that matter, in "any" playoff series) defeated its opponent in both of their regular-season games, the winning team is granted a 1–0 lead in the series, and the series starts with Game 2. The Philippine Basketball Association uses a best-of-seven series for its finals, as well as for most its semifinals of the PBA Philippine Cup since 2005.


title: Playoff format

text: Occasionally, WWE uses this format in some of their matches, such as for the feud between Chris Benoit and Booker T in 2005 for the WWE United States Championship, and for Antonio Cesaro's rivalry against Sheamus at August pay-per-view Summerslam 2016.


title: Playoff format

text: Nippon Professional Baseball's final championship round, the Japan Series, uses a best-of-seven playoff with a 2–3–2 format. However, since games can end in ties in that league, due to innings limits. In the event even no team has won four games after seven are completed, additional games are to be played with no innings limits. Through 2022, only one such game has ever been required.


title: Playoff format

text: A best-of-nine playoff is a head-to-head competition between two teams in which one team must win five games to win the series. Five is chosen as it constituted a majority of the games played; if one team wins the series before reaching game 9, all others are ignored.


title: Playoff format

text: In Major League Baseball, the World Series was conducted as a best-of-nine playoff in its first year of existence in 1903, then again for three years beginning in 1919, the year of the "Black Sox scandal."


title: Playoff format

text: The Western Hockey League used the best-of-nine playoff series for the Western Division playoffs from the 1983–84 season through the 1990–91 season because of the unequal division alignment of the league at the time. The Eastern division had eight teams, six of which qualified for the playoffs. The Western division only had six teams, four of which made the playoffs. Because of this, the Eastern division had three rounds of playoffs (two teams received a first round bye), while the Western division only had two rounds of playoffs. The east played a best-of-five, best-of-seven, best-of-seven format for the three rounds, while both rounds in the Western division playoffs were best-of-nine. This was used so that both divisions would finish their playoffs at approximately the same time. The WHL Championship Series was a best-of-seven. These best-of-nine series went the full nine games on two occasions, with the Portland Winterhawks defeating the New Westminster Bruins in 1984 and the Spokane Chiefs in 1986, respectively.


title: Playoff format

text: In snooker, a player must win a certain number of frames to win a match, often nine (best-of-17) or more. Again, if one player wins nine frames before all 17 are played, all others are ignored. The world championship final is currently decided in a best-of-35 match.


title: Playoff format

text: In 9-ball, a player must win a certain number of racks to win a match. In the WPA World Nine-ball Championship, nine racks are needed to win in the early stages, ten to eleven in the latter stages, and seventeen in the final. As with snooker, if one player wins nine frames before all seventeen are played, all others are ignored.


title: Playoff format

text: Various playoff formats, including two-legged ties and total points series pair off participants in a number of games (often two), with the winner being determined by aggregate score: the winner being the one who scores the most points/goals etc. over the series of games. Two-legged ties are common in association football, and were used in NHL playoff series until 1937. It was used in North America in the MLS Cup Playoffs until the 2019 season.


title: Playoff format

text: In 2004, NASCAR adopted a total points playoff, creating a "Chase for the Cup" that allowed the top 10 drivers in points to qualify for the playoffs after 26 races into the 36 race season. These 10 drivers had their points 'reset' to an arbitrarily larger value, insuring any driver from 11th on the back is eliminated from championship contention and the top 10 are equal in points. The Chase format has changed several times since its creation including expanding the number of drivers from 10 to 12 and currently 16, and awarding bonus points for regular season wins when reseeding for the Playoffs.


title: Playoff format

text: In November 2005, the PGA Tour announced that a total points playoff would be used to lead up to the PGA Championship starting in 2007. The player with the most points at the end of the year would take home the FedEx Cup.


title: Playoff format

text: Prior to the 1986 playoffs, the Canadian Hockey League (especially the Ontario Hockey League) used the point series to determine which team would advance. The higher-seeded team would host the odd numbered games (games 1, 3, 5, and 7), while the lower-seeded team hosts the even numbered games (games 2, 4, 6, and 8). There would be no overtime except for the deciding game, because a tie in the last game of the series would not declare a series winner. If the last game were to finish in a tie, there would be a sudden-death overtime, with the winner getting two points and the losing team getting none.


title: Playoff format

text: The game shows "Jeopardy!", "Wheel of Fortune", and "The Challengers" have used two-game series in their final rounds. Each game is played separately (i.e., money from day one cannot be wagered on day two), and the money from both games is added together to determine the winner. The only exception to this was in the "Jeopardy!" Ultimate Tournament of Champions held in 2005, when the two semifinal matches were both two-game series, and the final was a three-game series. If any ties remain, sudden death was played to determine the champion.


title: Playoff format

text: In a round-robin tournament, all playoff contenders play each other an equal number of times, usually once or twice (the latter is often called a "double round-robin").


title: Playoff format

text: This is a common tournament format in association football. In the FIFA World Cup, teams are organized into eight pools of four teams, with each team playing the other three once. Standings are determined by points earned through wins (3 points) and draws (1 point). The top two teams advance out of each pool to the knockout phase, where the first-place team from each pool faces a second-place team from a different pool.


title: Playoff format

text: Continental club football tournaments have included round robin formats, such as the 1966 Copa Libertadores, UEFA Champions League from the 1992–93 season, UEFA Cup from 2004 to 2005, and the Asian and African Champions Leagues. Teams are seeded so the strongest teams do not meet until the later rounds of the tournament. In the UEFA Champions League, 32 teams are divided into eight groups of four. The group winners and runners-up advance to play a two-legged tie. The third-place teams move into the UEFA Cup (Europa League) third round, and the fourth-place teams are eliminated.


title: Playoff format

text: In basketball, the Olympics uses a round-robin of the same nature, switching to single-elimination after the first round. The Euroleague has two double round-robin phases. The first is a "Regular Season" in which the 24 teams are divided into four groups of six (as of the 2008–09 season). The top four teams in each group advance to a "Top 16" phase in which the teams are divided into four groups of four each. The top two teams from each group are then paired in four best-of-five quarterfinal series, with the winners advancing to the single-elimination Final Four.


title: Playoff format

text: Round-robin tournaments are also used in rugby union, curling, and many amateur or lower-division basketball, football, and hockey tournaments.


title: Playoff format

text: In 1992, the Little League World Series went to a round-robin tournament in the first round, instead of single-elimination. In 2001, the tournament expanded to 16 teams and stayed with a round-robin for the first round, but cross-bracketed single-elimination for the second round before the two winners of those games advanced to the regional final. Little League used this format through 2009.


title: Playoff format

text: In Major League Baseball, the term "round-robin" was used with regard to the possibility of a three-way tie for the 1964 National League (NL) pennant. The Philadelphia Phillies had had a game lead with 12 games left in their regular season. They then lost 10 games in a row, and on the final day of the season, three teams were still competing for the National League pennant. The St. Louis Cardinals defeated the New York Mets to take the NL pennant with no playoff; the opposite outcome would have left the Cardinals, Phillies, and Cincinnati Reds in a three-way tie.


title: Playoff format

text: A Swiss-system tournament is a variant used for competitions in which there are too many entrants for a full round-robin to be feasible, and eliminating any competitors before the end of the tournament is undesirable.


title: Playoff format

text: Match pairings for each round are done after the previous round has ended. Competitors are paired using a set of rules designed to ensure that each competitor plays opponents with a similar running score, but does not play the same opponent more than once. The winner is the competitor with the highest aggregate points earned in over a fixed number of rounds.


title: Playoff format

text: The system was first employed at a chess tournament in Zurich in 1895 by Julius Müller, hence the name "Swiss system",[1] and is also used for other table games including go, bridge and Scrabble.


title: Playoff format

text: In tournaments where participants are seeded, the participants may be "reseeded" at each round in order to ensure that the strongest remaining team faces the weakest team. This type of tournament bracket is not fixed; potential match-ups cannot be anticipated up to the final. For example, in an eight-team bracket, the teams that will meet in the second round will be the winning team with the highest beginning seed against the first round winner with the lowest original seed. The second highest winning seed faces the winning team with the second lowest original seed.


title: Playoff format

text: The only notable tournaments that employ this rule are the NFL playoffs and WNBA playoffs. The Stanley Cup playoffs used the rule between 1975 and 1981, between 1994 and 2013, and 2020. Note that between 1994–2013 and 2020, reseeding does not come into play if there are only two rounds of competition. The NBA playoffs, the NCAA basketball tournaments (men and women), and most tennis tournaments, elect not to reseed, despite the possibility of reseeding resulting in different matchups. Prior to 2022, the MLB postseason did not have a format in which reseeding could change the matchups; the expanded postseason starting in 2022, in which the number of teams in each league making the playoffs will increase from 5 to 6, will not reseed teams.


title: Playoff format

text: The 1994 Stanley Cup playoffs (scores in the bracket shown indicate the number of games won in each seven-game series):


title: Playoff format

text: In team sports, the "home-field advantage" refers to the phenomenon where a team (usually the higher-seeded team) is given more home games than away games. This is seen in a best-of series by more games being played in one team's arena/stadium than the other, and in single-elimination tournaments by the single game being held in one team's stadium. In a best-of series, a team can "lose" their home advantage if the visiting team wins the first game.


title: Playoff format

text: In a best-of series, the order of arenas/stadiums in which the games are played at also affects the home-field advantage. In the NBA and the NHL, all rounds are played in a "2–2–1–1–1" format. That is, the team with home-field advantage plays games 1, 2, 5, and 7 (if necessary) at home. This ensures that, if the home team wins every game, the team with home-field advantage never trails in the series. From 1985 to 2013, the NBA Finals used the "2–3–2" format (the team with the home-court advantage plays games 1, 2, 6, and 7 on their home court). This can theoretically allow the team with the home-court advantage to trail in the series (although that will require the team with the home court advantage to lose the middle three games).


title: Playoff format

text: In Major League Baseball the best-of-7 rounds are played in a "2–3–2" format. This is to allow all games to be played in, in effect, location-consistent “sub-series” of 2 or 3 games. A "2–2–1–1–1" format could only be played in 2 and 3-game sub-series if the teams did not get days off for travel; however, the league gives teams an off day when traveling from Pacific Time to Eastern Time. Because teams from those time zones can possibly meet in any of the best-of-7 rounds, Major League Baseball always gives schedules to best-of-7 rounds that accommodate this travel feature.


title: Playoff format

text: In the Stanley Cup Finals, the NBA Finals, and the World Series, the team with the better regular-season record receives the home-field advantage. The Super Bowl is held at a predetermined site regardless of which teams reach the game, which usually means there is no home advantage; it is possible for the host city's team to participate. Historically, World Series home-field advantage alternated between leagues on an annual basis; from 2003 to 2016 the league that won that season's All-Star Game earned home-field advantage, and since 2017 the team with the best regular-season record earns home-field advantage.


title: Playoff format

text: In two-legged ties such as the UEFA Champions League, the two teams each play one game in their respective home stadium. However, there is debate over whether either team has an advantage. While playing the clinching match at home could be seen as an advantage, the away goals tiebreaker arguably favors the away side.


title: Playoff format

text: In games played in neutral venues, a team may still be afforded the privileges of the "home team," such as selecting which side of the field to defend first (or last). In most instances, this privilege is determined either by a drawing of lots (UEFA Champions League) or by rotation among the groupings of the different teams (NFL).


title: Playoff format

text: In the Nippon Professional Baseball league's postseason games (excluding Japan Series) since 2004, the team with the higher regular-season standing will host all the games. In addition, since 2008, the league champion will have a one-win advantage in the second stage of the Climax Series (technically a best-of-seven series, though in practice only six games are played, because the regular-season champion starts with a 1–0 advantage).


title: Alex Teixeira

text: Alex Teixeira Santos (; born 6 January 1990) is a Brazilian professional footballer who plays as a forward for Vasco da Gama.


title: Alex Teixeira

text: Teixeira began his career with Vasco da Gama, making his debut for the senior team at the age of 18, before moving to Shakhtar Donetsk in November 2009. He spent seven years at the club, scoring 89 goals in 222 appearances, while winning the Ukrainian Premier League five times. In February 2016, he transferred to Chinese Super League side Jiangsu Suning for an Asian record transfer fee of €50 million.


title: Alex Teixeira

text: Teixeira began his career at Vasco da Gama, playing for the youth team from 1999 to 2007. He was promoted to the senior team for the 2008 season.


title: Alex Teixeira

text: Teixeira was promoted to the senior squad for the tour of Dubai in January 2008. On 11 May 2008, he made his league debut for the club as a substitute in a 1–0 defeat to Internacional at the age of 18. His first goal for the club came on 28 June 2008 when he scored a brace in a 4–2 victory over Ipatinga. On 22 August, he netted the only goal in a 1–0 victory over Portuguesa. Vasco were relegated at the end of the season, finishing in 18th position with 40 points, finishing four points off safety.


title: Alex Teixeira

text: On 8 February 2009, Teixeira was sent off in a Campeonato Carioca match against Fluminense. He scored his first Série B goal in a 2–1 defeat to Bahia on 25 July 2009. On 13 November 2009, he scored his final goal for the club in a 2–1 victory over América. He made his final appearance for the club on 28 November in a 2–0 defeat to Ipatinga. At the end of the season, Vasco were promoted back to the Série A after winning the league by a seven-point margin over the second-place team. This was Texeira's first, and only, trophy during his time with Vasco.


title: Alex Teixeira

text: On 21 December 2009, at the age of 19, he left Vasco da Gama to join Ukrainian side Shakhtar Donetsk, joining for a fee of around €6 million on a five-year deal. In total with Vasco, he made 92 appearances for the club, scoring 14 times, including 51 league appearances with 11 goals.


title: Alex Teixeira

text: Teixeira made his debut for the club on 20 March 2010. He started a Ukrainian Premier League match against Zorya Luhansk before being taken off for compatriot Ilsinho after 55 minutes. Shakhtar won the match 2–0. His home debut came on 25 April in a 3–0 victory over Chornomorets Odesa. He was a 65th minute replacement for Ilsinho. His final appearance of the season came on 9 May in a 3–2 win against Tavryia Simferopol. He ended the season with three appearances for the club, all of which came in the league. Shakhtar won the 2009–10 Ukrainian Premier League by a six-point margin over second-placed Dynamo Kyiv, giving Teixeira his first trophy as a Shakhtar player.


title: Alex Teixeira

text: On 4 July 2010, Teixeira came on as a 68th-minute replacement for Jádson in Shakhtar's 7–1 Ukrainian Super Cup victory over Tavriya Simferopol. His European debut came in a 1–0 UEFA Champions League group stage victory over Partizan on 15 September. He scored his first goal for the club on 3 October in injury time against Dynamo Kyiv in a 2–0 win.


title: Alex Teixeira

text: On 23 October, he came on as a substitute for Vitaliy Vitsenets in the 46th minute and scored the only goal in a 1–0 victory over Vorskla Poltava in the 57th minute, before being sent off after 63 minutes for a second bookable offence. He replaced Willian in the 77th minute of Shakhtar's 2–0 Ukrainian Cup final victory against Dynamo Kyiv. He made 39 appearances for the club, 26 of which came in the league, and scored six goals, with five in the league, as Shakhtar secured the treble (League, Ukrainian Cup, and Super Cup).


title: Alex Teixeira

text: Teixeira's first match of the season came in the Super Cup. He came on as a 64th minute replacement for Henrikh Mkhitaryan but could not prevent Shakhtar from losing 3–1 to Dynamo Kyiv. This loss prevented Shakhtar from winning the treble for the second year in a row, although they did manage to recapture the Ukrainian Premier League title and the Ukrainian Cup. Teixeira's first goal of the season came on 24 July in a 2–1 league victory over Karpaty Lviv. He scored the first goal in Shakhtar's 2–1 extra time victory over Metalurh Donetsk in the 2012 Ukrainian Cup final. Shakhtar ended the 2011–12 Ukrainian Premier League as champions with 79 points, four ahead of nearest rivals Dynamo Kyiv, marking Teixeira's third league title in three seasons with the club. The cup success was also his second Ukrainian Cup win with the club. He made 37 appearances, scoring 10 goals. Twenty-six of the appearances and seven goals came in the league, while the other three goals came in the Ukrainian Cup. He finished the season as Shakhtar's top scorer in the Ukrainian Cup, two goals behind the overall top goalscorer Maicon of Volyn Lutsk, who scored five.


title: Alex Teixeira

text: After losing out to Dynamo Kyiv in the Super Cup the previous year, Shakhtar overcame Metalurh Donetsk 2–0 to regain the trophy. Teixeira started the match but was replaced after 77 minutes for the newly signed Marko Dević. Teixeira then gave Shakhtar the lead in a Champions League group stage match against Italian side Juventus on 2 October, although the match ended in a 1–1 draw. This marked his first ever goal in the competition. He scored the opener in a 2–1 victory against English side Chelsea in the Champions League on 23 October.


title: Alex Teixeira

text: On 27 October, Teixeira netted the only goal in a 1–0 victory against Tavriya Simferopol. After the departure of Fernandinho to Manchester City, Teixeira was asked to drop deeper in the pitch and act as a replacement. When asked about the decision, he stated, "Yes, indeed, after the departure of Fernandinho, we discussed this issue. I'm going to play in this position. It is important to adapt and get used to it, to operate up to the mark so that the team can continue winning". In July 2013, Teixeira signed a five-year contract extension with Shakhtar.


title: Alex Teixeira

text: During the 2013–14 season, Teixeira was part of a Shakhtar team that won a fifth consecutive Ukrainian Premier League title. In addition to his six league goals, he scored three times during the group stage of the Champions League. He contributed both goals in a 2–0 win over Real Sociedad in San Sebastián, before scoring the second goal of a 4–0 defeat of the same opposition at the Donbass Arena. On 15 May 2014, he played the full 90 minutes of Shakhtar's 2014 Ukrainian Cup final loss to Dynamo Kyiv.


title: Alex Teixeira

text: Teixeira ended the 2014–15 season as joint-top scorer in the Ukrainian Premier League with 17 goals. He registered three goals in eight Champions League appearances; the opening goal of a 2–2 draw with Porto and both home and away to BATE Borisov in respective 5–0 and 7–0 wins. On 4 June 2015, Teixeira played in a Ukrainian Cup final defeat to Dynamo Kyiv for the second consecutive year.


title: Alex Teixeira

text: At the winter break stage of the 2015–16 Ukrainian Premier League season, Teixeira has scored 22 goals from 15 appearances, scoring at least one goal in all but two of his appearances and registering two goals on nine occasions. On 16 October 2015, he scored twice in a 3–0 win over champions Dynamo Kyiv at the Olimpiyskiy to overtake the capital club at the top of the table. On 25 November, he scored twice in a 3–4 loss to Real Madrid in the group stage of the 2015–16 Champions League.


title: Alex Teixeira

text: In January 2016, English Premier League club Liverpool submitted a bid of €32 million (£24.6m) to sign Teixeira, with him expressing a strong desire to move to Merseyside. Shakhtar refused the bid, however, and on 5 February 2016, Teixeira joined Chinese club Jiangsu Suning on a four-year contract for a transfer fee of €50 million. This was the third time in ten days that China's transfer record had been broken, the first being for compatriot Ramires who also joined Jiangsu, from Chelsea.


title: Alex Teixeira

text: On 1 March 2016, Teixeira scored on his competitive debut for Jiangsu in a 3–2 win over Jeonbuk Motors in the AFC Champions League. On 5 March 2016, Teixeira scored two goals in a 3–0 win over Shandong Luneng on his Chinese Super League debut.


title: Alex Teixeira

text: On 12 November 2020, Teixeira set up his side's first goal converted by Éder and scored the winning goal in the second-leg of the Chinese Super League finals against Guangzhou Evergrande. Jiangsu Suning won the match 2–1, with an aggregate victory of the same scoreline, securing the club's first league title in their history.


title: Alex Teixeira

text: On 5 August 2021, Teixeira announced that he would join Süper Lig club Beşiktaş. On 10 August Beşiktaş announced that Teixeira had signed a three-year contract.


title: Alex Teixeira

text: Teixeira is capped at under-17 and under-20 level for Brazil. He played for Brazil at the 2007 Under-17 World Cup and the 2009 Under-20 World Cup. In the latter tournament, he scored three goals but missed the decisive penalty in the final shoot-out against Ghana. He was voted the second best player in the tournament, behind Ghana's Dominic Adiyiah.


title: Alex Teixeira

text: Teixeira was named in the Brazil senior team's provisional squad for Copa América Centenario, but was cut from the final squad.


title: East Texas

text: East Texas is a broadly defined cultural, geographic, and ecological region in the eastern part of the U.S. state of Texas that comprises most of 41 counties. It is primarily divided into Northeast and Southeast Texas. Most of the region consists of the Piney Woods ecoregion. East Texas can sometimes be defined only as the Piney Woods. At the fringes, towards Central Texas, the forests expand outward toward sparser trees and eventually into open plains.


title: East Texas

text: According to the "Handbook of Texas", the East Texas area "may be separated from the rest of Texas roughly by a line extending from the Red River in north-central Lamar County southwestward to east-central Limestone County and then southeastward towards eastern Galveston Bay". Most sources separate the Gulf Coast area into a separate region.


title: East Texas

text: Another popular, somewhat simpler, definition defines East Texas as the region between the Trinity River, north and east of Houston (or sometimes Interstate 45, when defining generously) as the western border; the Louisiana border as the eastern border; the Gulf of Mexico as the southern border; the Oklahoma border as the northern border; Arkansas as the northeastern border, and extending as far south as Orange, Texas. The East Texas region includes Tyler, Longview, Texarkana, Lufkin, Marshall, Palestine, Henderson, Jacksonville, Mount Pleasant, and Nacogdoches as principal cities in addition to the Houston and Beaumont metropolitan statistical areas.


title: East Texas

text: Climate is the unifying factor in the region's geography; all of East Texas has the humid subtropical climate typical of the Southeast, occasionally interrupted by intrusions of cold air from the north. East Texas receives more rainfall, , than the rest of Texas. In Houston, the average January temperature is and the average July temperature is . However, Houston has slightly warmer winters than most of East Texas due to its lower latitude and proximity to the coast.


title: East Texas

text: All of East Texas lies within the Gulf Coastal Plain. It has less uniformity of climate than the rolling hills in the north and flat coastal plains in the south. Local vegetation varies from north to south, with the lower third consisting of the temperate grassland extending from South Texas to South Louisiana and the northern two-thirds of the region dominated by the temperate forest known as the Piney Woods. These extend more than . The Piney Woods are part of a much larger region of pine-hardwood forest that extends into Louisiana, Arkansas, and Oklahoma. The Piney Woods area thins out as it nears the Gulf of Mexico. West of the Piney Woods are the ranchlands and remnant oak forests of the East Central Texas forests ecoregion.


title: East Texas

text: The Sabine, Trinity, Neches, Angelina and Sulphur rivers are the major rivers in East Texas, but the Brazos and Red rivers also flow through the region. The Brazos cuts through the southwest portion of the region, while the Red River forms its northern border with Oklahoma and a portion of Arkansas. In East Texas and the rest of the South, small rivers and creeks collect into swamps called bayous and merge with the surrounding forest. Bald cypress and Spanish moss are the dominant plants in bayous. The most famous of these bayous are Cypress Bayou and Buffalo Bayou. Cypress Bayou surrounds the Big, Little, and Black Cypress rivers around Jefferson. They flow east into Caddo Lake, and the adjoining wetlands cover the rim and islands of the lake.


title: East Texas

text: Deep East Texas is a subregion of East Texas, alongside Northeast and Southeast Texas. According to the Deep East Texas Council of Governments, the region consists of the following twelve counties: Angelina, Houston, Jasper, Nacogdoches, Newton, Polk, Sabine, San Augustine, San Jacinto, Shelby, Trinity, and Tyler.


title: East Texas

text: The "Deep" designation comes from the similarity to East Texas (it is similar in culture and topography, being highly forested), but with a location "deeper" (i.e., farther south and towards the Gulf Coast) than the rest of East Texas.


title: East Texas

text: "Deep" also refers to the cultural and social characteristics of the area. This is considered synonymous to the "Big Thicket", an allusion to the dense growth of underbrush in the Piney Woods. It was the earliest area of Texas to be settled by Anglo-Americans from the United States (and one of the last areas to submit to law enforcement—by the governments of New Spain, Mexico, the Republic of Texas, the state of Texas, or the United States). Well into the first quarter of the 20th century, renegade clans controlled local governments, especially in Shelby County.


title: East Texas

text: The area contains two of the oldest towns in Texas; Nacogdoches, the oldest town in Texas, dating from the 18th century, and San Augustine, the oldest "British-American" settlement in Texas, dating from the 1820s. People of English, Scottish, Scots-Irish, and to a lesser extent Welsh ancestry predominate in this region, because of the history of settlement. This is in contrast to West Texas and South Central Texas, where people of Hispanic and German ancestry predominate, respectively. Hispanic settlers are descended from colonists of New Spain, dating from the 16th and 17th centuries. Most of the German immigrant ancestors in Central Texas arrived after the Revolutions of 1848.


title: East Texas

text: The Spanish and later Mexican governments did not want settlers from the United States until after Mexico had gained independence. East Texas had been barely settled by Spanish and Mexican colonists, and the government decided to allow immigration from the US to bolster defenses against raiding by the Apache and Comanche. Neither government was able to exert much control or law enforcement in the area. As a consequence, the "Big Thicket" became a refuge for criminals fleeing the United States and hiding out in a "no man's land" in the pine tree thickets.


title: East Texas

text: The early isolation of the region and its links to the Deep South have resulted in the piney woods being described as a 'curtain' that demarcates a certain cultural enclave or bubble that distinguishes East Texas from the rest of the state. Former residents describe living behind the 'Pine Curtain' as a form of escape. The phrase is often used to describe the area; it appeared in a newspaper column in the "Palestine Herald-Press", and in a late 20th-century tourist guide by Mike Dougan.


title: East Texas

text: East Texas comprises 41 counties, 38 of which collaborate in sub-regional Ark-Tex Council of Governments, the East Texas Council of Governments, the Deep East Texas Council of Governments, and the South East Texas Regional Planning Commission.


title: East Texas

text: Counties generally included are Anderson, Angelina, Bowie, Camp, Cass, Cherokee, Delta, Franklin, Gregg, Hardin, Harrison, Henderson, Hopkins, Houston, Jasper, Jefferson, Lamar, Marion, Morris, Nacogdoches, Newton, Orange, Panola, Polk, Rains, Red River, Rusk, Sabine, San Augustine, San Jacinto, Shelby, Smith, Titus, Trinity, Tyler, Upshur, Van Zandt, and Wood County, Texas. Harris County and those forming the Greater Houston metropolitan area are sometimes included in varying sources, such as the Texas Department of Transportation, or more generally, Southeast Texas.


title: East Texas

text: The three additional East Texas counties that join with other regional government councils are Chambers County (Anahuac), Liberty County (Liberty), and Walker County (Huntsville), all three in geographic proximity to the Houston metropolitan area.


title: East Texas

text: Outside of the Greater Houston area, the average population density is around 18–45 per mi (7–12 per km), with the population density near the Big Thicket dropping below 18 people per mi. East Texas's population total is very large and is centered around the Golden Triangle (Texas) of Beaumont/Port Arthur/Orange in Southeast Texas. Moving north from the coast, Lufkin and Nacogdoches anchor the population center of Deep East Texas. Continuing north from Deep East Texas, Tyler, Longview, and Marshall, in Northeast Texas, along with Texarkana, on the far northeastern border with Arkansas, represent the major population centers in the northern section of East Texas. Eight miles from the Texas border, Shreveport, Louisiana, is considered the economic and cultural center for the Ark-La-Tex, the area where Arkansas, Louisiana, and East Texas meet.


title: East Texas

text: According to the 2010 U.S. census, these 41 East Texas counties had a total population of 2,057,518 residents. This represented 8% of the total state population of Texas.


title: East Texas

text: In 2010, the population of East Texas counties was 65.93% non-Hispanic white, 17.44% African American, 14.29% Hispanic or Latino American, and 2.34% other (including Native American and Asian). East Texas's most ethnically and racially diverse county was Jefferson County, its largest county. This includes the city of Beaumont, with 44.1% non-Hispanic whites, 34.1% African Americans, 17.7% Hispanic or Latinos of any race, and 4.1% other races or ethnicities (including Native American and Asian).


title: East Texas

text: East Texas is within the Black Belt region, the fertile area that was the center of cotton culture and enslaved African-American labor.


title: East Texas

text: Unlike Texas's total state racial demographics, only two counties in East Texas outside of Greater Houston's sphere had a majority minority. Jefferson County in the Golden Triangle and Titus County have a 40.6% Hispanic or Latino population. East Texas and Southeast Texas in particular, which had been areas of cotton plantation before the Civil War, have a significant African-American population, ranging to nearly 20% in some counties.


title: East Texas

text: East Texas is often considered the westernmost extension of the Deep South. The predominant cultural influence comes from customs and traditions passed down from European American and African American Southerners who settled the region during the mid-to-late 19th century. African Americans were first brought to the area as enslaved workers to develop and cultivate commodity crops on plantations. Harrison County had the most plantations and highest number of slaves in the antebellum period. Deep South accent influences are noticeable in the subdialect of Texan English that is spoken throughout the region. According to the most recent linguistic studies, East Texans tend to pronounce Southern English with the drawl typical of the Lower South. Other parts of Texas are more apt to use the "twang" of the Upper South, or—depending upon demographic influences of the particular area—with some Hispanic and Midwestern traits.


title: East Texas

text: East Texas lacks the strong influence of late 19th-and early 20th-century European immigrants from Germany and central Europe. Similarly, the new waves of immigrants since the late 20th century, primarily from India, other Asian nations, and Latin America, and their influences, have been less prevalent in East Texas compared to other Texas regions.


title: East Texas

text: East Texans are predominantly Protestant Christians. They are members of many denominations as part of the Bible Belt. The most numerous Christian adherents have included the Baptists, particularly the Southern Baptist Convention (majority white) and National Baptist Convention USA (majority black, formed after the Civil War; Methodists and Presbyterians; Lutherans and classical Pentecostals; and others.


title: East Texas

text: Roman Catholicism continues to have influence, particularly given the increased Hispanic or Latino American population in recent decades. The largest Catholic jurisdictions in the region has been the Roman Catholic Archdiocese of Galveston-Houston in Southeast Texas, and the Roman Catholic Diocese of Tyler in the northeastern subregion.


title: East Texas

text: Other religious faiths with smaller numbers, but with adherents in East Texas, include Mormonism and Judaism.


title: East Texas

text: Significant numbers of people of Cajun and Creole descent have migrated from Louisiana, although most are assimilated partially or completely into East Texas culture (adopting the local culture, and losing to varying degrees, their original culture). This assimilation pattern has often historically included conversion from Roman Catholicism, associated with French and Spanish traditions, to Protestant denominations.


title: East Texas

text: United States settlers from the Protestant Southeast practiced some discrimination against Cajun and Creole migrants, a cultural attitude that persisted until quite recently. Despite the tendency toward assimilation, Cajun and Creole cuisine (for example, jambalaya and catfish gumbo), are popular in the region. Many East Texans, including those without Louisiana roots, are known to be expert at preparing at least some well-known Louisiana dishes.


title: East Texas

text: While some East Texans associate with cowboy culture, most identify more with smaller scale farming of the Southern U.S., than with the expansive cattle ranching of the plains regions of Texas. But East Texans commonly own and trade cattle. Several "sale barns" exist across East Texas, with weekly and monthly trades, as is common in other parts of the Deep South.


title: East Texas

text: In the northern part of East Texas, awareness of the native and historical Caddo Mississippian culture remains significant. Cherokee County is home to the Caddo Mounds State Historic Site. Patrons can also view the "Caddo Indian Collection" at the Gregg County Historical Museum in Longview. In the mid-1800s, East Texas cities such as Marshall and Jefferson constituted a sphere of influence that led the entire state into the Confederacy . East Texas was the aread of powerful planters and the most significant numbers of slaveholders.


title: East Texas

text: Before that, during the Mexican and Republic periods, Nacogdoches and San Augustine were the most developed and influential cities in East Texas. Many East Texans have a mixture of European and Native American ancestry, as seen in East Texan country artists Miranda Lambert and Kacey Musgraves. The Museum of East Texas opened in Lufkin in 1976 under the name Lufkin Historical and Creative Arts Center.


title: East Texas

text: East Texas is home to the Texas Country Music Hall of Fame, located in Carthage. East Texans enjoy a range of music that is influenced by gospel, bluegrass, blues, rock, country, soul, rhythm and blues, Cajun, etc. Texas blues originated in East Texas, with many legends having been born in the region, including Lightnin' Hopkins and T-Bone Walker. East Texans enjoy live music at many of the region's fairs and festivals, including the Texas Rose Festival in Tyler, the East Texas Yamboree in Gilmer, and Longview's Great Texas Balloon Race.


title: East Texas

text: East Texas also has many venues included in what is commonly referred to as the Texas country music circuit, although the majority of such venues are located in Central/South/West Texas and the metropolitan areas of the state.


title: East Texas

text: Many notable music artists have East Texas roots, including: George Jones (Saratoga), Miranda Lambert (Lindale), Kacey Musgraves (Mineola), Jamie Foxx, (Terrell), Neal McCoy (Longview and Jacksonville), Lee Ann Womack (Jacksonville), Janis Joplin (Port Arthur), UGK (Port Arthur), Don Henley (Linden), Ray Price (Perryville), Johnny Horton (Rusk), Johnny Mathis (Gilmer), Tex Ritter (Panola County), Jim Reeves (Panola County), Mark Chesnutt (Beaumont), Tracy Byrd (Vidor), Clay Walker (Beaumont), T-Bone Walker (Linden), Chris Tomlin (Grand Saline), and Michelle Shocked (Gilmer), among many others.


title: East Texas

text: Worldwide-acclaimed pianist Van Cliburn, a native of nearby Shreveport, Louisiana, was raised in Kilgore. Kilgore College houses the Van Cliburn Auditorium on its home campus.


title: East Texas

text: Many high-school bands in East Texas continue the tradition of military-style marching, unlike other parts of the state. These bands compete in the National Association Of Military Marching Bands.


title: East Texas

text: As with other parts of Texas, high school football is the most popular local sport venue in East Texas. Residents of East Texas towns and rural communities fill high-school stadiums in support of their local teams, cheerleaders, bands, etc. Many East Texas high-school teams have won Texas state championships, along with producing many collegiate and professional football players.


title: East Texas

text: Earl Campbell, the "Tyler Rose", played football for John Tyler High in Tyler before playing for the Texas Longhorns and the Houston Oilers. Don Meredith, who famously played for the Dallas Cowboys, played at Mt. Vernon. Dez Bryant, a football player from Lufkin, formerly played wide receiver for the Dallas Cowboys before signing with the New Orleans Saints (then getting injured three days afterwards). Adrian Peterson, a star running back for the Minnesota Vikings, played high-school football in Palestine. Many other high-school sports are popular in East Texas, including basketball, baseball, volleyball, softball, and track.


title: East Texas

text: A significant number of East Texan youths participate in Little League Baseball, soccer, and softball. Church leagues are quite common in providing opportunities for basketball and softball for youth and adults alike. In recent years, cowboy churches have grown in number and offer rodeo events for their youth.


title: East Texas

text: East Texans also enjoy collegiate athletic competition. Most residents support collegiate teams located in other regions of the state; the Texas A&M Aggies, Texas Longhorns, Texas Tech Red Raiders, Baylor Bears, TCU Horned Frogs, etc. Including the city of Houston, its Houston Cougars are another prominent collegiate team. Due to proximity to neighboring states, East Texas has a substantial number of fans of the LSU Tigers, Arkansas Razorbacks, Oklahoma State Cowboys, and Oklahoma Sooners. The Battle of the Piney Woods is a fiercely contested sports rivalry between the Bearkats of Sam Houston State University in Huntsville and the Lumberjacks of Stephen F. Austin State University in Nacogdoches. Both compete in the FCS level of NCAA athletic competition as members of the Southland Conference. The Cardinals of Lamar University in Beaumont also compete with Stephen F. Austin and Sam Houston State in the Southland Conference.


title: East Texas

text: Other universities and colleges that field athletic teams in East Texas include East Texas Baptist University Tigers in Marshall; University of Texas at Tyler Patriots in Tyler; LeTourneau University Yellowjackets in Longview; Texas A&M–Commerce Lions; and several junior colleges throughout the region, which participate in the Southwest Junior College Conference in Region XIV of the NJCAA. East Texas is also home to the Kilgore College Rangerettes, a world-famous dance team that debuted in 1939.


title: East Texas

text: A few professional sports teams are located in the traditionally defined East Texas. The East Texas Pump Jacks, located in Kilgore, play baseball in the Texas Collegiate League. Additionally, the East Texas Storm, a semiprofessional football team located in Tyler, competes in the Lone Star Minor League. Typically, northern parts of East Texas tend to support the professional teams from the Dallas/Fort Worth area in North Texas (Dallas Cowboys, Dallas Mavericks, Texas Rangers, Dallas Stars), while southern parts of East Texas tend to support professional teams from the Houston area in Southeast Texas (Houston Texans, Houston Rockets, Houston Astros).


title: East Texas

text: As with other parts of Texas and/or the Southern U.S., other popular sporting activities in East Texas include rodeo (including PRCA), hunting, and fishing. Prominent rodeos in East Texas are held in Beaumont, Nacogdoches, Paris, Longview, Gladewater, Huntsville, Lufkin, Athens, Palestine, Lindale, etc. East Texas contains several award-winning lakes for sport fishing, including Toledo Bend Reservoir, Lake Sam Rayburn, Lake Livingston, Lake Fork Reservoir, Lake Tawakoni, etc.


title: East Texas

text: East Texas also contains numerous golf courses and avid golfers, as well as NASCAR fans. However, the region does not host professional events in either of those sports. The nearest NASCAR track to East Texas is Texas Motor Speedway in Fort Worth.


title: East Texas

text: East Texans enjoy many Texas state parks, including Caddo Lake, Atlanta, Daingerfield, Lake Bob Sandlin, Tyler, Mission Tejas in Grapeland, Cooper Lake, Lake Tawakoni, Martin Creek, Huntsville, Lake Sam Rayburn, Lake Livingston and Sea Rim among others. East Texas is also home to the Angelina National Forest, Davy Crockett National Forest, Sam Houston National Forest, Sabine National Forest, Big Thicket National Preserve, Trinity River National Wildlife Refuge, Anahuac National Wildlife Refuge, and McFaddin National Wildlife Refuge.


title: East Texas

text: Historically, the East Texas economy has been led by lumber, cotton, cattle, and oil. Prior to the discovery of the East Texas Oil Field, cotton, lumber and cattle were the predominant source of economic growth and stability. The needs of local farmers contributed greatly to the establishment of local towns and trading posts. As with many parts of the nation, the chosen paths of railroads often determined the continuation of many towns. At the beginning of the 20th century, the oil fields were discovered and oil became accessible, changing the future of the region.


title: East Texas

text: In the decades leading to the new millennium, crude oil production in the East Texas Oil Field, the largest oil field in the United States, somewhat decreased. In turn, the number of high-paying jobs for uneducated workers also decreased. During the 20th century, local groceries, general stores, and cafes were replaced with franchise department stores, retail chains, and fast-food restaurants. Due to the decline of oil production, many small towns closed cafés and gas stations, some of which were replaced with cash loan shops and pawn shops. In 2022, East Texas was highlighted for its diversifying economy penetrating Deep East Texas with the decline in crude oil. Additionally, the region has become home to many patent-holding companies, due to its legal system being particularly friendly to patent holders and hostile to out-of-state tech defendants. In 2009, Paul Knight of the "Houston Press" stated in an article, "some say natural gas has surpassed crude as king in East Texas."


title: East Texas

text: Tourism has not been a highly significant source of economic activity in the majority of East Texas, although several high-traffic corridors pass through East Texas, which have aided economic development along those routes. These include: Interstate 30 (from Dallas through Texarkana), Interstate 20 (through Dallas and on through Shreveport), Interstate 10 (through Houston and Beaumont into Louisiana), Interstate 45 (through Houston up to Dallas), and U.S. Highway 59 (through Houston and north past Texarkana; in process of being upgraded along most of the route to Interstate 69).


title: Pennhurst State School and Hospital

text: Pennhurst State School and Hospital, originally known as the "Eastern Pennsylvania State Institution for the Feeble-Minded and Epileptic" was an institution for mentally and physically disabled individuals of Southeastern Pennsylvania located in Spring City. After 79 years of controversy, it closed on December 9, 1987.


title: Pennhurst State School and Hospital

text: In 1903, the Pennsylvania Legislature authorized the creation of the Eastern State Institution for the Feeble-Minded and Epileptic and a commission was organized to take into consideration the number and status of the feeble-minded and epileptic persons in the state and determine a placement for construction to care for these residents. This commission discovered 1,146 feeble-minded persons in insane hospitals and 2,627 in almshouses, county-care hospitals, reformatories, and prisons, who were in immediate need of specialized institutional care.


title: Pennhurst State School and Hospital

text: The legislation stated that the buildings would be in two groups, one for the educational and industrial department, and one for the custodial or asylum department. The institution was required to accommodate no fewer than five hundred inmates or patients, with room for additions. Wesley White, the former president of the American Association of Medical Dosimetrists, was appointed superintendent of the facility.


title: Pennhurst State School and Hospital

text: From 1903 to 1908, the first buildings were constructed on of Crab Hill in Spring City, Pennsylvania, Chester County on what was referred to as the lower campus. Out of the first few buildings constructed, 'F' was the Girl's Dining Room, 'G' was the Kitchen and Store Room, 'H', 'I' and 'K' were a Cottage for Girls, 'N' was the Boys' Dining Room, 'P' was the Teacher's Home, 'Q', T', 'U' and 'V' were a Cottage for Boys, 'R' was a School, 'W' was Laundry and Sewing, and 'X' was the Power House.


title: Pennhurst State School and Hospital

text: 'P' was used as a temporary Administration building until the institution's opening in 1918 along with the opening of 'L' and 'M' in 1919. In 1921, Whitman and Wilson I and II were constructed along with Penn Hall for employee housing; in 1929, the Assembly building was complete and functioned as the gymnasium and auditorium.


title: Pennhurst State School and Hospital

text: The buildings on lower campus are currently labeled with letters such as 'F', 'I', 'K', 'P', 'Q', 'R', 'N', 'U', 'V', 'T', 'W' and 'X' with names later assigned in the 1960s (see below).


title: Pennhurst State School and Hospital

text: In 1930, the first buildings on the upper campus, otherwise known as the Female Colony, were completed and named Pershing, Buchanan, Audubon and Keystone. Capitol Hall was erected after World War II along with Devon constructed on lower campus. Horizon Hall opened later in 1971.


title: Pennhurst State School and Hospital

text: The older buildings, designed by Phillip H. Johnson, were two-storied, and made of red brick, terra cotta, and granite trimmings. They were connected by fire-proof tunnels with walkways on top of the tunnels for the use of transporting residents, with a parallel steam piping system, and were distributed on the campus in the cottage plan formation. The buildings were designed to provide a large number of small rooms occupied by two to three beds, a few small dormitories with eight to ten beds, and a large day room for exercise. George Lovatt was the architect for several of the buildings constructed post-1937.


title: Pennhurst State School and Hospital

text: The central Administration building has two side porte-cocheres, a front portico and a copper cupola in the center of the roof. The hospital building, Whitman, and Wilson I and II are not tunnel-connected, nor is Penn Hall and the Power House. The remaining cottage buildings are 'L' and 'I' shaped with the exception of Dietary, which is'Y'shaped, and Devon Hall, which is 'H' shaped.


title: Pennhurst State School and Hospital

text: The Pennsylvania Railroad created a Pennhurst Station on its Schuylkill Division to accommodate Pennhurst. Coal and other supplies were delivered by rail for decades to operate the power house. Tracks are still visible under the pavement behind Dietary and Devon Hall, which allowed boxcars to be brought directly onto the main campus. The railroad tracks have been removed and are now part of the Schuylkill River Trail.


title: Pennhurst State School and Hospital

text: On November 23, 1908, "Patient number 1" was admitted to the hospital. Within four years of operation, Pennhurst was already overcrowded and under pressure to admit immigrants, orphans, and criminals.


title: Pennhurst State School and Hospital

text: Residents were classified into mental categories of imbecile or insane, into physical categories of epileptic or healthy, and into dental categories of good, poor or treated teeth when admitted.


title: Pennhurst State School and Hospital

text: The branches of industry which residents were assigned to were mattress making, shoe making and repair, grading, farming, laundry, domestic duties, sewing, baking, butchering, painting, and working in the store.


title: Pennhurst State School and Hospital

text: In 1913, the legislature appointed a Commission for the Care of the Feeble-Minded which stated that disabled people were unfit for citizenship and posed a menace to the peace, and thus recommended a program of custodial care. Furthermore, the Commission desired to prevent the intermixing of the genes of those imprisoned with the general population. In the Biennial Report to the Legislature submitted by the Board of Trustees, Pennhurst's Chief Physician quoted Henry H. Goddard, a leading eugenicist, as follows:


title: Pennhurst State School and Hospital

text: Every feeble-minded person is a potential criminal. The general public, although more convinced today than ever before that it is a good thing to segregate the idiot or the distinct imbecile, they have not as yet been convinced as to the proper treatment of the defective delinquent, which is the brighter and more dangerous individual.


title: Pennhurst State School and Hospital

text: In 1916, the Board of Trustees initiated a plan to increase the capacity of the Institution by constructing cottages specifically for women to segregate them from the men, in part to prevent pregnancies.


title: Pennhurst State School and Hospital

text: In 1968, conditions at Pennhurst were exposed in a five-part television news report anchored by local WCAU-TV correspondent Bill Baldini.


title: Pennhurst State School and Hospital

text: In 1981, a "Time" magazine article described the place as having "a history of being understaffed, dirty and violent." In 1983, nine employees were indicted on charges ranging from slapping and beating patients (including some in wheelchairs) to arranging for patients to assault each other.


title: Pennhurst State School and Hospital

text: The Halderman Case, which resulted in the closure of the institution, also detailed widespread patient abuse.


title: Pennhurst State School and Hospital

text: In 1977, U.S. District Judge Raymond J. Broderick ruled that the conditions at Pennhurst State School violated patients' constitutional rights. The lawsuit that led to his ruling was filed May 30, 1974, by Philadelphia attorney David Ferleger representing the patients of the Pennhurst State School. The suit was later joined by the United States and by the Pennsylvania Association for Retarded Citizens. Pennhurst State School was ultimately closed in 1987. The 1,156 people who lived there on the date of the Court's order (March 17, 1978) moved into small community homes called Community Living Arrangements. These settings supported three or fewer people, with 24 hour staffing if needed. This process of deinstitutionalization required nine years, and included discussion of treatment plans with each person and family.


title: Pennhurst State School and Hospital

text: The allegations of abuse led to the first lawsuit of its kind in the United States, a federal class action, "Halderman v. Pennhurst State School & Hospital", which asserted that those with developmental disabilities in the care of the state have a constitutional right to appropriate care and education. Terri Lee Halderman had been a resident of Pennhurst, and following multiple episodes of abuse, she and her family filed suit in the federal district court. The suit started after Terri had visited her parents at home and was found to have unexplained bruises. Although the case was not expected to reach the level it did, the courts later found that conditions at Pennhurst were unsanitary, inhumane and dangerous, violating the Fourteenth Amendment, and that Pennhurst used cruel and unusual punishment in violation of the Eighth and Fourteenth Amendments, as well as the Pennsylvania Mental Health and Retardation Act of 1966 (MH/MR). The District Court ruled that certain of the patients' rights had been violated. The District Court decision was the first time that any federal court ruled that an institution must be closed based on a constitutional right to community services.


title: Pennhurst State School and Hospital

text: The rulings collectively lent credence to the nascent "deinstitutionalization" movement, which sought to move mental patients from hospitals to halfway houses or reintegrate them into their families. The rulings also aligned with the increasing tendency of federal courts to take control of school districts, prisons and other state institutions in order to enforce citizens' rights. Ultimately, however, the U.S. Supreme Court vacated the judgment based on the Eleventh Amendment principle that federal courts cannot order state officials to comply with state laws. As noted below, the institution was eventually closed pursuant to a settlement agreement that required that community-based services be offered to all of its residents.


title: Pennhurst State School and Hospital

text: The case became an important rule of law known as the "Pennhurst Doctrine", which has been cited by state Attorneys General as binding precedent under United States constitutional law.


title: Pennhurst State School and Hospital

text: The United States Department of Veterans Affairs, or the VA, acquired the upper campus of Pennhurst and began work to reuse it as a veterans' home. In 1986, the upper campus cottage units reopened as the Southeastern Veterans' Center. In 1990, renovations began on Horizon Hall, one of the newest buildings at Pennhurst, as part of a project to establish a nursing facility at the veterans' center. It reopened in 1993 as Coates Hall. After many years of determining what to do with Pennhurst, Congressman Jim Gerlach sought to establish a federal veterans cemetery at Pennhurst in 2003 but the VA rejected the proposal.


title: Pennhurst State School and Hospital

text: In 2001, the state adopted the Keystone Principles concerning the state's duties to maintain historic property and to consult with the Pennsylvania Historical and Museum Commission before transferring the property into private hands. Chester County officials approved a private development and Pennhurst was sold to a developer, Pennhurst Associates, for two million dollars. The Pennhurst Memorial and Preservation Alliance (PMPA) was formed to advocate for certain uses of the site.


title: Pennhurst State School and Hospital

text: Pennhurst was added to Pennsylvania's list of the most at-risk Pennsylvania properties as well as the International Coalition of Sites of Conscience, a worldwide network of historic sites specifically dedicated to remembering struggles for justice.


title: Pennhurst State School and Hospital

text: In partnership with the Preservation Alliance for Greater Philadelphia, PMPA obtained a grant to complete a re-use design and feasibility study of the Pennhurst campus. By 2010, the administration building had been partially renovated and reopened as the Pennhurst Asylum seasonal haunted attraction. The attraction has been successful, though controversial among locals and those previously affiliated with Pennhurst.


title: Pennhurst State School and Hospital

text: Penn Organic Recycling LLC operated on of Pennhurst, offering topping, composting and food waste services. The Department of Environmental Protection permitted the composting operation at Pennhurst to maintain no more than 25 tons. It is no longer in operation.


title: Pennhurst State School and Hospital

text: In 2015, the Pennhurst Memorial and Preservation Alliance began working with the Southeastern Veterans' Center to obtain the superintendent's residence for a future museum and interpretive center.


title: Pennhurst State School and Hospital

text: In 2017, bookings for daytime history tours, photography tours, and overnight paranormal investigations became available through the haunted attraction's website. Proceeds from the tours go towards the upkeep of the grounds and restoration of the remaining buildings.


title: Pennhurst State School and Hospital

text: The Travel Channel's television show "Destination Fear" filmed at the location for the fifth episode of their first season in 2019 .


title: Pennhurst State School and Hospital

text: By 2020, Hershey, Rockwell, and Dietary halls were all deemed unsafe for reuse. That March, demolition began and by November, all three buildings had been demolished.


title: Pennhurst State School and Hospital

text: On June 8, 2021 heavy metal band Motionless in White performed their "Deadstream 2: Live at Pennhurst" concert on the grounds in front of the main building entrance. The concert was streamed the following day.


title: Rate of return

text: In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows (or securities, or other investments) which the investor receives from that investment, such as interest payments, coupons, cash dividends, stock dividends or the payoff from a derivative or structured product. It may be measured either in absolute terms (e.g., dollars) or as a percentage of the amount invested. The latter is also called the holding period return.


title: Rate of return

text: A loss instead of a profit is described as a "negative return", assuming the amount invested is greater than zero.


title: Rate of return

text: To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the rate of return.


title: Rate of return

text: Typically, the period of time is a year, in which case the rate of return is also called the annualized return, and the conversion process, described below, is called "annualization".


title: Rate of return

text: The return on investment (ROI) is return per dollar invested. It is a measure of investment performance, as opposed to size (c.f. return on equity, return on assets, return on capital employed).


title: Rate of return

text: The "return", or the "holding period return", can be calculated over a single period. The single period may last any length of time.


title: Rate of return

text: The overall period may, however, instead be divided into contiguous subperiods. This means that there is more than one time period, each sub-period beginning at the point in time where the previous one ended. In such a case, where there are multiple contiguous subperiods, the return or the holding period return over the overall period can be calculated by combining together the returns within each of the subperiods.


title: Rate of return

text: The direct method to calculate the "return" or the "holding period return" formula_1 over a single period of any length of time is:


title: Rate of return

text: For example, if someone purchases 100 shares at a starting price of 10, the starting value is 100 x 10 = 1,000. If the shareholder then collects 0.50 per share in cash dividends, and the ending share price is 9.80, then at the end the shareholder has 100 x 0.50 = 50 in cash, plus 100 x 9.80 = 980 in shares, totalling a final value of 1,030. The change in value is 1,030 − 1,000 = 30, so the return is formula_5.


title: Rate of return

text: A negative initial value usually occurs for a liability or short position. If the initial value is negative, and the final value is more negative, then the return will be positive. In such a case, the positive return represents a loss rather than a profit.


title: Rate of return

text: The return, or rate of return, depends on the currency of measurement. For example, suppose a 10,000 USD (US dollar) cash deposit earns 2% interest over a year, so its value at the end of the year is 10,200 USD including interest. The return over the year is 2%, measured in USD.


title: Rate of return

text: Let us suppose also that the exchange rate to Japanese yen at the start of the year is 120 yen per USD, and 132 yen per USD at the end of the year. The value in yen of one USD has increased by 10% over the period.


title: Rate of return

text: The deposit is worth 1.2 million yen at the start of the year, and 10,200 x 132 = 1,346,400 yen at the end of the year.


title: Rate of return

text: This is the rate of return experienced either by an investor who starts with yen, converts to dollars, invests in the USD deposit, and converts the eventual proceeds back to yen; or for any investor, who wishes to measure the return in Japanese yen terms, for comparison purposes.


title: Rate of return

text: Without any reinvestment, a return formula_1 over a period of time formula_8 corresponds to a "rate of return" formula_9:


title: Rate of return

text: For example, let us suppose that 20,000 USD is returned on an initial investment of 100,000 USD. This is a return of 20,000 USD divided by 100,000 USD, which equals 20 percent. The 20,000 USD is paid in 5 irregularly-timed installments of 4,000 USD, with no reinvestment, over a 5-year period, and with no information provided about the timing of the installments. The rate of return is 4,000 / 100,000 = 4% per year.


title: Rate of return

text: Assuming returns are reinvested however, due to the effect of compounding, the relationship between a rate of return formula_9, and a return formula_1 over a length of time formula_8 is:


title: Rate of return

text: Annualization is the process described above of converting a return formula_1 to an annual rate of return formula_9, where the length of the period formula_8 is measured in years and the rate of return formula_9 is per year.


title: Rate of return

text: This is because an annualized rate of return over a period of less than one year is statistically unlikely to be indicative of the annualized rate of return over the long run, where there is risk involved.


title: Rate of return

text: Annualizing a return over a period of less than one year might be interpreted as suggesting that the rest of the year is most likely to have the same rate of return, effectively projecting that rate of return over the whole year.


title: Rate of return

text: Note that this does not apply to interest rates or yields where there is no significant risk involved. It is common practice to quote an annualized rate of return for borrowing or lending money for periods shorter than a year, such as overnight interbank rates.


title: Rate of return

text: For example, if a stock is priced at 3.570 USD per share at the close on one day, and at 3.575 USD per share at the close the next day, then the logarithmic return is: ln(3.575/3.570) = 0.0014, or 0.14%.


title: Rate of return

text: Under an assumption of reinvestment, the relationship between a logarithmic return formula_29 and a logarithmic rate of return formula_27 over a period of time of length formula_8 is:


title: Rate of return

text: so formula_33 is the annualized logarithmic rate of return for a return formula_29, if formula_8 is measured in years.


title: Rate of return

text: For example, if the logarithmic return of a security per trading day is 0.14%, assuming 250 trading days in a year, then the annualized logarithmic rate of return is 0.14%/(1/250) = 0.14% x 250 = 35%


title: Rate of return

text: When the return is calculated over a series of sub-periods of time, the return in each sub-period is based on the investment value at the beginning of the sub-period.


title: Rate of return

text: Suppose the value of the investment at the beginning is formula_36, and at the end of the first period is formula_37. If there are no inflows or outflows during the period, the holding period return formula_38 in the first period is:


title: Rate of return

text: If the gains and losses formula_41 are reinvested, i.e. they are not withdrawn or paid out, then the value of the investment at the start of the second period is formula_37, i.e. the same as the value at the end of the first period.


title: Rate of return

text: If the value of the investment at the end of the second period is formula_43, the holding period return in the second period is:


title: Rate of return

text: This method is called the time-weighted method, or geometric linking, or compounding together the holding period returns in the two successive subperiods.


title: Rate of return

text: Extending this method to formula_49 periods, assuming returns are reinvested, if the returns over formula_49 successive time subperiods are formula_51, then the cumulative return or overall return formula_1 over the overall time period using the time-weighted method is the result of compounding the returns together:


title: Rate of return

text: If the returns are logarithmic returns, however, the logarithmic return formula_29 over the overall time period is:


title: Rate of return

text: This formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e. that logarithmic returns are additive.


title: Rate of return

text: In cases where there are inflows and outflows, the formula applies by definition for time-weighted returns, but not in general for money-weighted returns (combining the logarithms of the growth factors based on money-weighted returns over successive periods does not generally conform to this formula).


title: Rate of return

text: This formula can also be used when there is no reinvestment of returns, any losses are made good by topping up the capital investment and all periods are of equal length.


title: Rate of return

text: If compounding is performed, (i.e. if gains are reinvested and losses accumulated), and if all periods are of equal length, then using the time-weighted method, the appropriate average rate of return is the geometric mean of returns, which, over "n" periods, is:


title: Rate of return

text: The geometric average return is equivalent to the cumulative return over the whole "n" periods, converted into a rate of return per period. Where the individual sub-periods are each equal (say, 1 year), and there is reinvestment of returns, the annualized cumulative return is the geometric average rate of return.


title: Rate of return

text: For example, assuming reinvestment, the cumulative return for four annual returns of 50%, -20%, 30%, and −40% is:


title: Rate of return

text: In the presence of external flows, such as cash or securities moving into or out of the portfolio, the return should be calculated by compensating for these movements. This is achieved using methods such as the "time-weighted return". Time-weighted returns compensate for the impact of cash flows. This is useful to assess the performance of a money manager on behalf of his/her clients, where typically the clients control these cash flows.


title: Rate of return

text: To measure returns net of fees, allow the value of the portfolio to be reduced by the amount of the fees. To calculate returns gross of fees, compensate for them by treating them as an external flow, and exclude accrued fees from valuations.


title: Rate of return

text: Like the time-weighted return, the money-weighted rate of return (MWRR) or dollar-weighted rate of return also takes cash flows into consideration. They are useful evaluating and comparing cases where the money manager controls cash flows, for example private equity. (Contrast with the true time-weighted rate of return, which is most applicable to measure the performance of a money manager who does not have control over external flows.)


title: Rate of return

text: The internal rate of return (IRR) (which is a variety of money-weighted rate of return) is the rate of return which makes the net present value of cash flows zero. It is a solution formula_9 satisfying the following equation:


title: Rate of return

text: When the internal rate of return is greater than the cost of capital, (which is also referred to as the required rate of return), the investment adds value, i.e. the net present value of cash flows, discounted at the cost of capital, is greater than zero. Otherwise, the investment does not add value.


title: Rate of return

text: Note that there is not always an internal rate of return for a particular set of cash flows (i.e. the existence of a real solution to the equation formula_68 depends on the pattern of cash flows). There may also be more than one real solution to the equation, requiring some interpretation to determine the most appropriate one.


title: Rate of return

text: Note that the money-weighted return over multiple sub-periods is generally not equal to the result of combining together the money-weighted returns within the sub-periods using the method described above, unlike time-weighted returns.


title: Rate of return

text: The value of an investment is doubled if the return formula_69 = +100%, that is, if formula_27 = ln($200 / $100) = ln(2) = 69.3%. The value falls to zero when formula_9 = -100%. The ordinary return can be calculated for any non-zero initial investment value, and any final value, positive or negative, but the logarithmic return can only be calculated when formula_72.