Elo

> The **Elo rating system** is a method for calculating the relative skill levels of players in zero-sum games such as chess. It is named after its creator Arpad Elo, a Hungarian-American physics professor.
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Elo is seen in two forms in *War Brokers*: games Elo and kills Elo. The former is based on a player's wins vs losses, while the latter is decided off of kills and deaths. Many players confuse Elo in *War Brokers* to be an accurate measure of player skill, not realizing that Elo is designed for zero-sum games—which *War Brokers* is not and therefore incompatible with Elo's design. It is normally an invisible statistic that is used in Monte Carlo simulations to help balance teams. Players may view this information through the POMP's Mod setting or the shortcut P to toggle the side menus. It is not visible on the player statistics website. While incompatible with the design of the Elo rating system, there is still small value in it as a variable to consider in judging one's skill; ultimately a lower skilled player will still have a low score while better players will have higher score, the system just can't properly rank players. Elo should be used alongside other statistics to weigh up a player's skill.

Bots and starting out Guests do not have an Elo score. In Elo calculations against them, there is no Elo loss/gain. When running the Monte Carlo simulation, they are treated as 1300 kills Elo. Once a guest has played long enough and cookies begin to track a temporary save file of stats—or once a player creates an account—that player will be started off on 1500 kills Elo and 1500 games Elo and begin to count to Elo calculations.

At present (Sep 6, 2023), Elo only takes effect in Classic (excluding Gun Game). Players tracking Elo changes with POMP's Mod enabled may notice that their Elo is changing when they play other modes like Competitive 4v4; however these changes are temporary and purely visual. All changes reset upon changing server or reopening the game. Gun Game interestingly will lock Elo progress in Classic to its value before the match initiates, and then keep it there even in matches following regardless of the mode. For a player to regain access to normal Elo changes, they would need to reopen the game or change server to valid Classic mode.

Games Elo was the primary Elo of choice for balancing rounds; however due to issues with smurfing and the slow nature of games Elo, the switch to kills Elo was made. At this time Elo was still visible naturally in the kill feed and round results card. Elo score visibility was removed after discussion in late August 2019 where game developer JoJa15 asked players for their input on how Elo should be treated. He voiced concern that some players were playing the game too seriously because of Elo. While some players enjoyed ranking up their Elo, many argued that the system should be removed or at least hidden. Eventually the development team decided that Elo should be hidden.

Kills Elo would be visible again in the round results of 2020's Competitive mode, before the mode was ultimately removed before the year end. Come v470 (May 25, 2022), the introduction of POMP's Mod in the settings would be the first official way to view both Elo scores in years. Visibility has not been made available on the player statistics website, though many have wanted it to be—especially following POMP's Mod.

### Synergy between the two Elo scores

Kills Elo and games Elo play inverse roles to one another to some degree. Players who put in the effort to work as a team and complete objectives are more-likely to win rounds and increase games Elo, but may disadvantage themselves in fights when defusing/arming bombs or doing similar tasks that take up a player's actions. This would result in lowering their kills Elo. Players who choose to preserve their kills Elo at the cost of not helping in objectives instead now jeopardize their team's victory and are more-likely to lose rounds and consequently lose games Elo.

This can lead to a case of a player generally gaining in one and losing in the other. The extent of this is limited however. Players should be careful not to exaggerate this effect to support their arguments in why their stats do not appear to reflect skill (which it cannot accurately measure to begin with regardless). Even with modes with objectives that take up player actions, teams take turns for attacking and defending. As a player plays multiple rounds over time, this should generally even out to a roughly 50/50 split on those modes, and therefore lead to evened out scores; deflating their score when busy interacting with an objective and inflating when getting the easier kills on enemies interacting with objectives. Players can also play in ways that minimize the deaths they get while interacting with objectives, especially with good teamwork. Between the two Elo scores, a player is likely to have a higher games Elo to kills Elo based upon how often even good players should realistically be dying. The exceptions to this tend to come from players who take more individualistic roles rather than team-based ones and/or farming.

### Tips from the developer

The physics developer for the game, MJD (aka Ponzi Inc.), was the one who implemented the Elo rating system into *War Brokers*. To answer player's questions about what they could expect from the system and how it functioned, they left some comments in the official War Brokers Discord server:

> So, I know what you're thinking "how do I game the Elo system". I'm one step ahead of you :) Quitting a game, you are losing, will NOT help.
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> The kills Elo is easier to game.
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> Steal kills, and avoid dying. But if you have a good kills Elo, and bad games Elo, WE KNOW HOW YOU DID IT.
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> I don't know how to game the games Elo, it is only based on winning games. So, Launch those Missiles, and Deliver those Packages, for the WIN!
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> If you quit a game, don't rejoin the same game. If you rejoin, on the other team, you will automatically lose (since you were on both teams, and the only way to prevent gaming the system, is to give you the worse outcome).
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> Also at the beginning, while the Elo's are changing a lot (and good players still have a low Elo), avoid being on a small team against a good player. Once the Elo's are accurate, it doesn't matter, since you won't go down much if you lose, but you'll go up a lot, if you win.
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## Kills Elo

Of the two Elo scores, kills Elo is the most-commonly used and compared. Should a player kill an enemy with a higher kills Elo to them, the player will gain a large increase to their kills Elo score. Similarly, should a player kill an enemy with a lower kills Elo to them, the player would gain a small increase to their kills Elo score. The inverse is also true, where a player will receive a small deduction to their kills Elo when dying to an enemy with higher kills Elo, and will receive a large deduction when dying to an enemy with lower kills Elo. This calculation does not occur when with BGM or Air Strike, unless from a self-destruct (the player self-destructing will receive a deduction to their kills Elo).

Kills Elo gained popularity starting 2022 when a mod began circulation. Players who previously enjoyed farming K/D ratios were now met with a statistic that was not influenced by bots. This led some players to begin judging others based on their K/D ratio vs kills Elo; those with a low kills Elo score but high K/D were clearly farming bots in empty servers and had inflated stats, while those with higher kills Elo scores must have more "legit" K/D ratios. When the mod was later rendered useless in an update that patched the vulnerability the mod made use of, the creator brought his concerns to the devs and an agreement was reached to bring features from that mod to the game. This was added as the setting: POMP's Mod.

Kills Elo via the mod is made visible in the leaderboard to the right of a player's latency. Many players have taken the stance of comparing one another based on this number, not properly understanding the trivial value the score actually has in a non–zero-sum game. The rough "skill estimation" that players have varies widely between individuals and all share the common issue of relying upon logic of duels and fair gameplay, where realistically a player may easily be thrown into a 2v1, 3v1, or worse—or a player focused on an objective like launching a missile may be more vulnerable to attacks than they normally would be. Player playstyles also differ and can have a rock/paper/scissors effect on one another, with the addition of map/weapon synergy playing into how well a player might perform for that specific round.

In terms of distribution of Elo (June 2023), players with a kills Elo score of 1800 or higher are in the top 1.4% of players, players with a kills Elo score of 1700 or higher are in the top 6% of players, players with a kills Elo score of 1600 or higher are in the top 20% of players, and 56% of players are at the starting 1500 or higher. This only counts the stats of players who had played some time in the last 60 days from the date of analysis. Despite the limit to active players, there is no doubt an influx of new players who create an account to try the game out before leaving after a round or two, sitting at a 1500 or 1400 score. This would lessen the "rarity" of some scores somewhat if they were to be discounted. For example, perhaps 1800+ is actually closer to top 5% and/or 1700+ is closer to top 15%—this is impossible to ascertain however.

## Games Elo

The lesser of the two Elo scores in terms of popularity and use, games Elo is a slower and more stable score that bases itself on wins and losses. This calculation will only include a player if they were present at the initiation of a match (starting a match from the vote screen), and will continue to include players even if they left the match mid-round. Joining mid-way will not include a player in the calculation at all, making it safe for players hopping between servers looking for a server they wish to play in. All valid players from either team have their scores added up for the calculation, and are all granted a change based upon that total. Players who reconnect to a match they started and join the opposite team will end up with a Elo loss no matter what the score is. This is to prevent abuse to the system as players count for both the winning and losing team. With the correct score differences, switching to a winning team from a losing one could mean that a player offsets their losses and gains a small score increase. This is counteracted by the system giving players the worst outcome.

With the renewed interest in Elo in 2022, players began to look down on games Elo as a pointless score. Games Elo has no usage in the team balance algorithm, and doesn't get used anywhere else. It's just a number in the system that counts up and down. Some of these players were in a new wave of farmers who tried to use the features of kills Elo not counting bots as pseudo-evidence that they were skilled with "legit stats" to back it up. As games Elo can be used to help debunk players who farm kills Elo—similar to how kills Elo can debunk K/D farming on bots—these players have tried to put games Elo down to hide their actions.

Games Elo is only visible to the account owner via the POMP's Mod side menu (shortcut toggle is P). It is likely that its hidden nature makes it easier for players to sacrifice this score in order to focus on the visible kills Elo which is easy to compare in the leaderboard. As games Elo changes very slowly to be accurate (only being influenced at the end of an entire round), it is the most-accurate of the two scores. Its higher accuracy comes down to number of variables that are in winning versus losing a round as opposed to any kill or death experienced on the field, as well as the stability that comes with slow changes instead of the turbulent and ever changing kills Elo which can easily jump up and down large amounts around a rough range.

In terms of distribution of Elo (June 2023), players with a games Elo score of 2100 or higher are in the top 1.46% of players, a score of 2000 or higher are top 2.18%, a score of 1900 or higher are top 3.5%, a score of 1800 or higher are top 5.66%, a score of 1700 or higher are top 9.6%, a score of 1600 or higher are top 17.4%, and a games Elo score of 1500 or higher (at the starting point or above) places a player in the top 63%. Only ~37% of players are below a 1500 games Elo score, with 29.4% of them being in the 1400 range. Opposed to kills Elo, the range of games Elo is much higher with players reaching much lower and much higher scores across the board. The playerbase generally has a higher games Elo compared to their kills Elo. Part of this comes down to the value of players working together as a team vs what the individual can do on their own. Even a player with a Kill/Death ratio of 3/5 in a match could be providing the support required for their team to win, and consequently earn a games Elo increase. If new accounts that joined to try the game out and then left shortly are removed, these values may shift somewhat. The spread of games Elo compared to kills Elo is more normal, which is to be expected from the higher accuracy of games Elo.

## Team Balance

The reason games Elo was cast aside as the score to balance teams and replaced with kills Elo was due to smurfs. These are players who sign out to play as a guest or make an alternate account to appear weaker than they are and not be recognized. As these new accounts are set at 1500 games Elo when they start out, a player who might perform at a really high 2500 games Elo would be treated as someone much weaker than they are. While smurfs would gain Elo and start to be judged in the balance more accurately over time, this process would be very slow thanks to small incremental changes only at the end of full rounds. As kills Elo is quick to change, the game moved to the lower accuracy option to allow team balancing equations to have more accurate Elo scores faster, and consequently reduce the amount of time a smurf has to effectively affect rounds.

The system is of course not perfect. Team balancing is a hot topic in the community. A large downside to the use of the low accuracy kills Elo is found in players who deflate their scores playing the game more naturally (as teamwork to reach victory can lead to many needed sacrifices to take control of the battle) will end up making teams too strong, while players who are more individualistic in their ways and/or farm with inflated scores will make their teams too weak. To a degree, the two sides of inaccuracy lead to a mix of deflated/inflated players that roughly equalize one another; however this is very limited. Elo scores cannot account for if a player is good or bad on a specific map. It cannot account for if teams will have more players who are better at weapons more suited to a map (for example, more snipers on a large map). It cannot account for the internet quality of the user in that server. The region of the player may have a different level of Elo in an "economy" as opposed to other regions—there is more Elo to go around in the US servers, but less in one like the India servers; a player with 1700 Elo in the US may only have 1600 Elo playing at the same level of skill in India. The balancing algorithm also cannot account for if a player leaves right after the teams were balanced (immediately throwing off the balance) or if a player joins after the balancing. Many variables effect what kind of kills Elo a player may have, and many more variables effect how relevant that score actually is to how a player can perform in a match.

In the fight for helping even out teams, suggestions to change the default Elo in the Monte Carlo simulation led to the default 1500 kills Elo being changed to 1300 kills Elo for the bots and Elo-less guests. The fact that there is no Elo on those accounts did not change. Only the value they would be treated as specific to the team balance algorithm. Players have generally felt like teams have been better following this; however this drastically affected the effects of smurfing on fresh guest accounts by treating these smurfs at an all time low value. This means that where a 1800 kills Elo player could be smurfing and treated as 1500 in the old system, the gap of 1800 to 1300 kills Elo in the new system introduces large much larger power gaps and hurts team balance badly.