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Questions tagged [elo]

"The Elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games such as chess" (Wikipedia)

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Modeling player interactions in multi-dimensional rating systems

In traditional rating systems (such as Elo), a player's strength is represented by a single scalar value, which is assumed to be consistent across different opponents. However, in some games, the ...
mb1's user avatar
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Elo rating: how many comparisons necessary to achieve accurate rating with n players given no prior knowledge?

If I have n participants in a two-player-game league, whose initial ratings are unknown, is there a good heuristic for how many games/comparisons/pair-faceoffs are required to achieve an accurate ...
2080's user avatar
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7 votes
3 answers
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On the cradle of the Elo Rating System, and how to find it

A definitive proposal can be found in: Elo, Arpad E. (August, 1967). The Proposed USCF Rating System, Its Development, Theory, and Applications. Chess Life XXII (8): 242-247. How exactly are THE ...
clp's user avatar
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124 views

A multidimensional ELO rating with rock paper scissors playing styles: how to estimate

Consider the following latent variable model for a potential Elo rating with additional player type. Each player has a performance level $r$ and a playing type $\theta$. Assume that a game between two ...
Sextus Empiricus's user avatar
3 votes
1 answer
296 views

Skill score/Rating systems that take into consideration margin of victory

I am trying to create ratings/skill scores using ranking systems like Elo, TrueSkill, and OpenSkill. All of these systems are similar in that they have a distribution that represents players' skill ...
GBPU's user avatar
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6 votes
2 answers
740 views

Obtain ranking from pairwise comparison with continuous outcome

I have some data of pairwise comparisons between players with a continuous value as outcome, for instance like this: ...
a_gdevr's user avatar
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3 votes
0 answers
67 views

Elo rating with additional player type

When rating players using Elo system, sometimes we have additional associated player type that may affect the game result, this additional player type information in some cases may help predicting ...
WiSaGaN's user avatar
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0 answers
289 views

Rating system for zero-sum games that has good theoretical properties compared to Elo rating?

The Elo rating system is widely used in two-player zero-sum games/sports like Chess. It is not obvious to me that the Elo rating system is has the "nicest" theoretical properties out of all ...
user56834's user avatar
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1 vote
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Deriving distribution for multiplayer game results from pairwise probabilities

Suppose there is a game with three participants: Player A, Player B, and Player C. One player will finish in first place, another in second place, and another in third place (no ties allowed). I know ...
djcunningham0's user avatar
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50 views

Is the Elo "rule of 400" a variation on EWMA?

tldr: The Elo rule looks like an ewma-style running average to me. Is that right? Details: The Elo rule of 400 (here) could be expressed this way: $$ rating_{N} = \frac{1}{N} \Sigma_{i=1}^{N}\left( ...
EngrStudent's user avatar
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Building a Ranking Model for Junior Golf

So, I'm trying to figure out the best way to build a model for Junior Golf Rankings. The best system out there currently uses a Sagarin type methodology that compares head-to-head records of ...
curious golfer's user avatar
3 votes
3 answers
1k views

Does the Elo system work with different expected value functions?

In many Elo rating systems, the expected value for player A with rating $R_A$ against an opponent with rating $R_B$ is $$E_A = \frac1{1+10^{(R_B - R_A)/c}}$$ The original Elo system is based on a ...
Victor's user avatar
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3 votes
2 answers
273 views

Winning probability in multiplayer game with variable number of players

In a multiplayer game up to 10 players can play against each other and only 1 player can win. There can be no collaboration between players. Let's assume that the 10 players are called: A, B, C, D, E,...
Newbie's user avatar
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3 votes
1 answer
326 views

Does the Elo K-factor affect winning probabilities?

Per the Wikipedia article on Elo ratings: The difference in the ratings between two players serves as a predictor of the outcome of a match. Two players with equal ratings who play against each ...
cb7's user avatar
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What are the Elo formulas when assuming performance to be logistically distributed?

I'm struggling to find a definite source on the Elo rating system but from what I understand: it originally assumes players performance to be normally distributed with $\sigma = 1$ the expected ...
user2740's user avatar
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2 votes
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224 views

Is the difference between two MSEs significant?

I developed several Elo rankings and used MSEs to compare them on their predictive capacity of the 2018 World Cup. I've been asked to use a statistical test to find if the difference between two of my ...
Thib008's user avatar
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4 votes
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129 views

Autocorrelation in Elo ratings

FiveThirtyEight uses the following formula for their NFL Elo ratings: $$ R_i^{k+1} = R_i^k + K \cdot M(z) \cdot A(x) \cdot (S_{ij} - \sigma(x)) $$ where $z$ is the game's margin of victory, $x=R_i^k - ...
stevemo's user avatar
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2 votes
1 answer
116 views

Using a generalised linear model for tennis winning probability

I have a dataset of historical tennis matches, one row per match. Each row has the ELO points of each player, and a calculated ELO difference. And of course a column to indicate if Player 1 won as a 1 ...
Steven Gao's user avatar
9 votes
0 answers
155 views

In sports modelling, are hot simulations better or cold simulations?

I'm thinking here largely of the context in which someone has an Elo rating model for a particular sport. To calculate things such as how often the team makes the Finals series, or wins the ...
user1205901 - Слава Україні's user avatar
3 votes
1 answer
209 views

How to regress ELO scores back to the mean in R? [closed]

I am using the elo package in R to calculate college football scores over the course of several decades. But I am having trouble understanding the regression function in the package: This is the ...
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2 votes
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164 views

Skill-based ranking system with individual performance

I am attempting to rank players in an online game and have successfully used TrueSkill to create a good ranking system however I would like to take it a step further and let individual performance ...
EmberZ's user avatar
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10 votes
2 answers
1k views

Elo-type ranking system that incorporates game score

The Elo rating system is used to calculate relative skill levels between individuals or teams. It can be applied to many types of games and sports, but when applied, it only considers wins and losses. ...
Figaro's user avatar
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1 vote
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Estimating hidden rating in games

There are a number of online games (e.g. Overwatch, League of Legends) that use a hidden rating system thats designed to be an estimate of your "true" skill level, and is used to match you with/...
Simon's user avatar
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3 votes
1 answer
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Does Elo rating system address isolated groups of players?

I am looking to apply a flavor of the Elo Rating System to a game that is played all over the world (not chess) and am toying with the idea of adding what I might consider an "enhancement" to it. So ...
smeeb's user avatar
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2 votes
1 answer
164 views

Elo Ranking Expected Scores

I am implementing an Elo ranking system for fun and came across an example on Wikipedia that I can't follow: Suppose Player A has a rating of 1613, and plays in a five-round tournament. He or she ...
mritz_p's user avatar
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4 votes
1 answer
107 views

How to compute global elo ratings when teams mostly play in their own regions?

I'm trying to compute a global elo rating for a popular eSports title, but the problem is that the teams mostly compete in their own regions. Specifically, there are five major regions, and teams ...
Derek Chiang's user avatar
5 votes
1 answer
382 views

Elo ranking for attack and defence seperately

I want to create a simple statistical model for the bowler versus batsman contest in a game of cricket (it's similar to pitcher versus batter in baseball). Let's say the simple the model is this: One ...
Ravi's user avatar
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6 votes
2 answers
5k views

Determining proper K value for Elo rating

For the question I previously posted here with a general question about elo ranking applied to a a bit weird sport. From the ranking POV it's a bit like marathon - you can have up to n players but - ...
nimdil's user avatar
  • 250
3 votes
1 answer
393 views

How can I make Elo ranking system more diversified?

As far as I know, Elo ranking system generates points between 100-2800 generally. However lets say we have 1,000,000 players. Now this range of points is too small. Many players would get the same ...
Furkan Gözükara's user avatar
6 votes
1 answer
727 views

ELO rating for non-pairing sport + serious math

I was considering sport disciplines for which there are multiple players at the event but rather than playing against each other, they do stuff, are assigned points and their final position is based ...
nimdil's user avatar
  • 250
3 votes
1 answer
202 views

How can I calculate expected finishing order in a board game?

I'm tracking stats for my board game group. I'm using a modified ELO system where I consider each game of multiple players be a group of 1v1 matches between all pairs of players as seen here: http://...
FigBug's user avatar
  • 131
9 votes
2 answers
191 views

Distribution for Paired Elo Matches Drawn from Normal Distribution

Is there a nice way (closed form) to represent the distribution of $Z$ that results from taking two independent normal draws $X_1, X_2 \sim N(0,1)$ and determining the outcome using $Y \sim U(0,1)$ ...
Zane Blanton's user avatar
15 votes
3 answers
9k views

Do alternatives to Elo exist for non-team/individual events?

Are there any well-known rating or ranking systems, similar to Elo, for multi-participant events? For example, a system that can rate various forms of racing (auto, downhill, horse etc.) or other ...
TravisVOX's user avatar
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5 votes
1 answer
2k views

Accounting for "autocorrelation" in margin-based Elo ratings

I'm trying to incorporate margin-weighting into a simple Elo rating system for a sports league. Classic Elo only encompasses Win/Draw/Loss data but I want to further reward teams for winning by a ...
Boris Cocker's user avatar
2 votes
0 answers
133 views

Comparing two values in a normal distribution after cutting off the tail of the distribution

I'm doing a sports-related analysis about comparing regular-season performance versus playoff performance, in particular which teams tend to do better during the playoffs. Thus, I'm making a "regular ...
Liam B's user avatar
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1 vote
0 answers
76 views

ELO Rating for players that do not learn

Lately there are some AI competitions online, where the bot has no capability to "learn/adapt" (ironically) over games. Thus, each uploaded version of a bot by a player is static. On the website, ...
PascalVKooten's user avatar
19 votes
4 answers
6k views

How to get started with rating and ranking based on pairwise competition data?

I'm interesting in learning about how to rate and rank individuals in a group who only interact/compete in a pairwise fashion (i.e., systems like the ELO rating system for chess). Are there are any ...
dcl's user avatar
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