ලකුණු ලබා ගැනීමේ වේගය (ක්‍රිකට්)

Net Run Rate(NRR) is a statistical method used in analysing teamwork and/or performance in the sport ofcricket. It is the most commonly used method of ranking teams with equal points inlimited oversleague competitions, analogous togoal differencein association football.
The NRR in a single game is theaverageruns peroverthat a team scores, minus the average runs per over that is scored against them. The NRR in a tournament is the average runs per over that a team scores across the whole tournament, minus the average runs per over that is scored against them across the whole tournament.This is the same as theweighted averageof the run rates scored in each match (weighted by the lengths of the innings batted compared to the other innings batted), minus the weighted average of the run rates conceded in each match (weighted by the lengths of the innings bowled compared to the other innings bowled). This isnotusually the same as the total or average of the NRRs from the individual matches in the tournament.
A positive NRR means a team is scoring faster than its opposition overall, while a negative NRR means a team is scoring slower than the teams it has come up against.It is therefore desirable for the NRR to be as high as possible.
NRR has been criticised as hard to understand, and 'often misunderstood'.Also it doesn't accurately reflect true margins of victory, as it measures how quickly teams score and concede runs, but takes no account of wickets taken or lost, so a team with a narrow victory can have a higher NRR than a team with a comfortable victory. This means a team which progresses in a tournament at the expense of another team, due to a higher NRR, may not have actually had better victories.
A team'srun rate(RR), or runs per over (RPO), is the average number of runs scored per over by the whole team in the whole innings (or the whole innings so far), i.e.run rate=total runs scoredtotal overs faced{\displaystyle {\text{run rate }}={\frac {\text{total runs scored}}{\text{total overs faced}}}}.
So if a team scores 250 runs off 50 overs then their RR is25050=5{\displaystyle {\frac {250}{50}}=5}. Note that as an over is made up of six balls, each ball is 1/6 of an over, despite being normally written in cricket's notation as .1 of an over. So if they got that same score off 47.5 overs, their RR would be2504756=5.23{\displaystyle {\frac {250}{47{\frac {5}{6}}}}=5.23}.
The concept of net run rate involvessubtractingthe opponents' run rate from the team's run rate, i.e.match net run rate=total runs scoredtotal overs faced−total runs concededtotal overs bowled{\displaystyle {\text{match net run rate }}={\frac {\text{total runs scored}}{\text{total overs faced}}}-{\frac {\text{total runs conceded }}{\text{total overs bowled}}}}.
For two teams which have just played, the winning side will have a positive Match NRR, and the losing side will have thenegativeof this (i.e. the Match NRRs will beadditive inverses, summing to zero). A single match's NRR is used very rarely, perhaps only after a team has played one match in a tournament, so their tournament NRR is the same as the match NRR.
Usually, runs and overs are summed together throughout a season to compare teams in a league table. A team's overall NRR for a tournament is not defined as the sum or average of the NRR's from the individual matches, but as:
tournament net run rate=total runs scored in all matchestotal overs faced in all matches−total runs conceded in all matchestotal overs bowled in all matches{\displaystyle {\text{tournament net run rate }}={\frac {\text{total runs scored in all matches}}{\text{total overs faced in all matches}}}-{\frac {\text{total runs conceded in all matches}}{\text{total overs bowled in all matches}}}}
The exceptions to this are:
All scenarios assumeOne Day Internationalrules with 50 overs per side.
Most of the time, in limited overs cricket tournaments, there are round-robin groups among several teams, where each team plays all of the others. Just as explained in the scenarios above, the NRR is not the average of the NRRs of all the matches played, it is calculated considering the overall rate at which runs are scored for and against, within the whole group.
Let's take as an example South Africa's net run rate in the1999 World Cup.
FOR
South Africa scored:
In the case of Zimbabwe, because South Africa were all out before their allotted 50 overs expired, the run rate is calculated as if they had scored their runs over the full 50 overs. Therefore, across the five games, South Africa scored 1016 runs in a total of 238 overs and 2 balls (i.e. 238.333 overs), an average run rate of 1016/238.333 = 4.263.
AGAINST
Teams opposing South Africa scored:
Again, with Sri Lanka, England and Kenya counting as the full 50 overs as they were all out, the run rate scored against South Africa across the five games is calculated on the basis of 851 runs in a total of 250 overs, an average run rate of 851/250 = 3.404.
NET RUN RATE
South Africa's final tournament NRR is therefore 4.263 − 3.404 = +0.859.
After match one
In the above example of South Africa at the 1999 World Cup, after their first match their tournament NRR was25447.33−25350.{\displaystyle {\frac {\mbox{254}}{\mbox{47.33}}}-{\frac {\mbox{253}}{\mbox{50}}}.}
As Run Rate = Runs scored/Overs faced, the runs scored by and against South Africa in each innings can be replaced in this formula by Run Rate x Overs faced. They scored 254 runs from 47.33 overs, a rate of 5.37 runs per over. Therefore, the total of 254 runs can be replaced by 5.37 runs per over x 47.33 overs. Similarly, the total of 253 runs conceded can be replaced by 5.06 runs per over x 50 overs:
(5.37×47.3347.33)−(5.06×5050)=(5.37×100%)−(5.06×100%).{\displaystyle \left(5.37\times {\frac {\mbox{47.33}}{\mbox{47.33}}}\right)-\left(5.06\times {\frac {\mbox{50}}{\mbox{50}}}\right)=\left(5.37\times 100\%\right)-\left(5.06\times 100\%\right).}
After match two
After their second match, tournament NRR was254 + 19947.33 + 50−253 + 11050 + 50,{\displaystyle {\frac {\mbox{254 + 199}}{\mbox{47.33 + 50}}}-{\frac {\mbox{253 + 110}}{\mbox{50 + 50}}},}which is the same as25497.33+19997.33−253100−110100.{\displaystyle {\frac {\mbox{254}}{\mbox{97.33}}}+{\frac {\mbox{199}}{\mbox{97.33}}}-{\frac {\mbox{253}}{\mbox{100}}}-{\frac {\mbox{110}}{\mbox{100}}}.}
Making the same replacements for 254 and 253 as before, and replacing 199 runs scored in match two with 3.98 runs per over x 50 overs, and 110 runs conceded in match two with 2.20 runs per over x 50 overs, this becomes:
(5.37×47.3397.33)+(3.98×5097.33)−(5.06×50100)−(2.20×50100){\displaystyle \left(5.37\times {\frac {\mbox{47.33}}{\mbox{97.33}}}\right)+\left(3.98\times {\frac {\mbox{50}}{\mbox{97.33}}}\right)-\left(5.06\times {\frac {\mbox{50}}{\mbox{100}}}\right)-\left(2.20\times {\frac {\mbox{50}}{\mbox{100}}}\right)}
=(5.37×48.6%)+(3.98×51.4%)−(5.06×50%)−(2.20×50%).{\displaystyle =\left(5.37\times 48.6\%\right)+\left(3.98\times 51.4\%\right)-\left(5.06\times 50\%\right)-\left(2.20\times 50\%\right).}
After match three
After their third match, tournament NRR was254 + 199 + 22547.33 + 50 + 50−253 + 110 + 10350 + 50 + 50,{\displaystyle {\frac {\mbox{254 + 199 + 225}}{\mbox{47.33 + 50 + 50}}}-{\frac {\mbox{253 + 110 + 103}}{\mbox{50 + 50 + 50}}},}i.e.254147.33+199147.33+225147.33−253150−110150−103150.{\displaystyle {\frac {\mbox{254}}{\mbox{147.33}}}+{\frac {\mbox{199}}{\mbox{147.33}}}+{\frac {\mbox{225}}{\mbox{147.33}}}-{\frac {\mbox{253}}{\mbox{150}}}-{\frac {\mbox{110}}{\mbox{150}}}-{\frac {\mbox{103}}{\mbox{150}}}.}
Making the same replacements for 254, 253, 199 and 110 as before, and replacing 225 runs scored in match three with 4.50 runs per over x 50 overs, and 103 runs conceded in match three with 2.06 runs per over x 50 overs, this becomes:
(5.37×47.33147.33)+(3.98×50147.33)+(4.50×50147.33)−(5.06×50150)−(2.20×50150)−(2.06×50150){\displaystyle \left(5.37\times {\frac {\mbox{47.33}}{\mbox{147.33}}}\right)+\left(3.98\times {\frac {\mbox{50}}{\mbox{147.33}}}\right)+\left(4.50\times {\frac {\mbox{50}}{\mbox{147.33}}}\right)-\left(5.06\times {\frac {\mbox{50}}{\mbox{150}}}\right)-\left(2.20\times {\frac {\mbox{50}}{\mbox{150}}}\right)-\left(2.06\times {\frac {\mbox{50}}{\mbox{150}}}\right)}
=(5.37×32.1%)+(3.98×33.9%)+(4.50×33.9%)−(5.06×33.3%)−(2.20×33.3%)−(2.06×33.3%).{\displaystyle =\left(5.37\times 32.1\%\right)+\left(3.98\times 33.9\%\right)+\left(4.50\times 33.9\%\right)-\left(5.06\times 33.3\%\right)-\left(2.20\times 33.3\%\right)-\left(2.06\times 33.3\%\right).}
Tournament NRR as a weighted average
Therefore, tournament NRR can alternatively be thought of as theweighted averageof the run rates scored in each match (weighted by the lengths of the innings batted compared to the other innings batted), minus the weighted average of the run rates conceded in each match (weighted by the lengths of the innings bowled compared to the other innings bowled). Each time another match is played, the weights of the previous innings reduce, and so the contributions of the previous innings to overall NRR reduce.
For example, the 5.37 run rate achieved in match one had 100% weighting after match one, 48.6% weighting after match two, and 32.1% weighting after match three.
In the language ofDuckworth-Lewis, teams have two resources with which to score runs − overs and wickets. However, NRR takes into account only one of these − overs faced; it takes no account of wickets lost. Therefore, a team regarded as having a narrow victory can have a higher NRR than a team regarded as having a comfortable victory. For example, a team which just manages to win a close game with many overs to spare but with only one wicket in hand is likely to have a higher NRR than a team which paces itself to win comfortably with only a few overs in hand but many wickets.
For example, in the2013 Champions Trophy Group A:
This fact can encourage a team to play in an overly aggressive manner, to maximise NRR by batting with next to no regard for preserving wickets, when the required run rate alone seems low, which can then put the team in danger of losing.
A team's batted and bowled overs in a match count differently to tournament NRR
All overs batted in a tournament are given equal weighting when finding tournament NRR, and all overs bowled in a tournament are also given equal weighting. However, when the total number of overs batted is different from the total number of overs bowled, the weight for each over batted is different from the weight for each over bowled. This means that batted overs and bowled overs in the same match count differently towards tournament NRR.
For example, in the2009 World Twenty20 Group D, as New Zealand had batted 6 overs and bowled 7 overs against Scotland, the runs they scored in each of the 20 overs batted against South Africa contributed 1/26th to their tournament NRR, while the runs conceded in each of the 20 overs bowled against South Africa contributed only 1/27th. In fact, the effect of the higher weight for the batting overs was so strong that despite scoring fewer runs than South Africa from the same number of overs, and hence having a negative match NRR and losing the match, the net contribution of this match to New Zealand's tournament NRR was actually positive (127/26 − 128/27 is positive).
Each over in a match counts differently for the two teams
Moreover, if two teams in a tournament have different total numbers of overs batted or bowled, then each innings in the match(es) between them will contribute differently towards their tournament NRRs. For example, in the2009 World Twenty20 Group D, South Africa batted for 40 overs in total in their two matches, so their score of 128 from 20 overs against New Zealand contributed 128/40 = 3.20 to their tournament NRR, whereas New Zealand bowled for 27 overs in total in their two matches, so South Africa's score of 128 from 20 overs against them contributed −128/27 = −4.74 to New Zealand's tournament NRR.
As a team's NRR measures how many more runs it scores per over than it concedes, the NRRs of all the teams in a league table shouldsum to zero. However, because of this fact of each innings usually counting differently to the two teams' tournament NRRs, this rarely happens. If the sum is positive, this implies that overall more runs were scored per over than were conceded, which is obviously impossible. (And if the sum is negative that less were scored than conceded). The teams' tournament NRRs will all sum to zero if all the teams have played one or zero matches, or if every innings had exactly the same number of overs. This happens sometimes with small league tables. For example, Group B in the2009 World Twenty20featured three matches. Five of the six innings had the full complement of 20 overs, and in the sixth innings the team was bowled out, which counts as the full complement of 20 overs.
The same score by two teams counts differently to tournament NRR
If two teams make the same score from the same number of overs (either in the same match or different matches), this will count differently to their respective tournament NRR's if they have different total numbers of overs batted across the whole tournament. For example, in the2007 World Twenty20 Group B, Australia and Zimbabwe each scored 138 from 20 overs in one of their matches. However, as Australia batted for 14.5 overs in their other match, this contributed 138/34.833 = 3.96 to their tournament NRR, whereas as Zimbabwe batted for 19.5 overs in their other match, this contributed 138/39.833 = 3.46 to their tournament NRR.
This is also the case if two teams concede the same score in the same match or different matches, but have different total numbers of overs bowled in the tournament.
Tournament NRR can penalise teams which win batting second rather than first
If one team, batting first, scores 250 from their 50 overs, and another team, batting second, is set a target of 100 which it easily reaches in 20 overs, then both sides have a batting run rate of 5. Therefore, both sides will have the same match NRR, all else being equal, and should have the same contribution to tournament NRR. However, when it comes to calculating tournament NRR, the first team's innings will count more heavily than the second team's as it was longer, even though the second team achieved the same run rate and could potentially have reached the same total if it could have completed its 50 overs.
A team may choose to artificially reduce their margin of victory, as measured by NRR, to gain an additional advantage by not disadvantaging their opponent too much. For example, in the final round of matches in the1999 World Cup Group B, Australia needed to beat West Indies to progress to the Super Six stage, but wanted to carry West Indies through with them to the Super Six, rather than New Zealand. This is because Australia would then have the additional points in the Super Six stage from beating West Indies in the group stage, whereas they had lost to New Zealand in the group stage. It was therefore to Australia's advantage to reduce their scoring rate and reduce their margin of victory, as measured by NRR, to minimise the negative impact of the match on West Indies' NRR, and therefore maximise West Indies' chance of going through with them.
However, this is also likely to be a possibility with alternatives to NRR.
This is similar to the way a narrow victory for one side in a game offootballmay enable both sides to progress to the next stage, e.g.West Germany v Austria in the 1982 World Cup.
NRR can be hard to understand, and is 'often misunderstood'.For example, Tournament NRR has been incorrectly explained as the sum of the NRRs from each match.
A number of alternatives or modifications to NRR have been suggested.
Use Tournament NRR as present, but when a side batting second successfully completes the run chase, use theDuckworth−Lewis methodto predict how many runs they would have scored with a full innings. This means the calculation would be done on the basis of all innings being complete, and so would remove the criticisms of NRR penalising teams which bat second, and NRR not taking into account wickets lost. However, this does nothing to alter the fact that when matches are rain-affected, different matches and even two complete innings in one match, can be different lengths long (in terms of overs), and so does nothing about some of the other criticisms above.
Therefore, alternatively, use Duckworth−Lewis to predict the 50-over total foreveryinnings less than this,even, for example, if a match is reduced to 40 overs each, and a side completes their 40 overs. This would make every innings in the tournament the same length, so would remove all the criticisms above. However, a side will bat differently (less conservatively) in a 40-over innings compared to a 50-over innings, and so it is quite unfair to use their 40-over total to predict how many runs they could have scored in 50 overs.
Either way, using Duckworth−Lewis would mean relying on subjective modelling predictions, which are opinions, rather than actual performances, which are facts.
Calculate tournament NRR as the total or average of the individual match NRRs. This would mean all matches have equal weighting, no matter how long they were, (rather than all batted overs across the tournament having equal weighting, and all bowled overs across the tournament having equal weighting). This would remove the criticisms under the 'Tournament NRR calculation' subheading above. For example, the different teams' tournament NRRs would always sum to zero if the total of the individual match NRRs were used, or if the average of the individual match NRRs were used and all teams had played the same number of games.
An example of when using this would have made a difference was the1999 Cricket World Cup Group B. New Zealand and West Indies finished level on points. Having scored a total of 723 runs from 201 overs, and conceded 746 runs from 240.4 overs, West Indies' tournament NRR was (723/201) − (746/240.6667) =0.50. However, New Zealand had scored 817 runs from 196.1 overs, and conceded 877 runs from 244.2 overs, so their tournament NRR was (817/196.167) − (877/244.333) =0.58. Therefore, New Zealand progressed to the Super Six stage and West Indies were eliminated. However, with individual match NRRs of −0.540, 0.295, 0.444, 5.525 and −0.530, the West Indies' average match NRR was1.04, and with individual match NRRs of 1.225, 0.461, −0.444, −1.240 and 4.477, New Zealand's average match NRR was0.90. Therefore, West Indies' average NRR was better than New Zealand's.
Ball difference (BD) is the number of balls remaining at the point of victory.For a team winning batting second, BD would be the number of balls remaining. For a team winning having batted first, BD would be the number of balls between the precise delivery when the beaten team was outscored and the end of their innings (either the end of the overs or until the team were all out).For the losing team, BD is the negative of the winning team's BD.
However, like the current NRR calculation, BD takes no account of wickets lost, so can produce similarly unjust results. In the example above from the 2013 Champions Trophy Group A, New Zealand's narrow victory over Sri Lanka would have a BD of +81, whereas Sri Lanka's comfortable victory over England would have a BD of only +17.
Also, if a match is affected by the weather, a side batting first can win having scored fewer runs, if Duckworth-Lewis increases the target for the team batting second, and they overtake the first team's score, but fail to reach the target. It's not clear what BD would be in this scenario.
Split teams level on points using the results from the matches between them. However, this unfairly increases the importance of that one match and reduces the importance of other matches in the league, when all matches in a league should be of equal value − the team with the better head-to-head record will have a worse record against other teams. Also, the head-to-head record will not decide it if the game between them was a No result, or if they played each other twice, and won one game each.
Alternatively, stage a play-off match between the teams level on points. However, organising this at very short notice may be difficult, or the teams may be in the middle of a league table with no promotion or relegation or progression at stake, so there may be no appetite for a play-off match.
These two methods both also run into difficulties when three or more teams are level on points.