Elo ratings: questions and answers
What is Elo rating and how does it work?
Elo is a widespread rating system, which allows to determine particular players skill level. Elo rating is mostly used in 2 player board games such as chess and backgammon.
What does my rating indicate?
What affects my rating?
– Wins and losses. When you win your rating increases, when you lose – it drops
– Rounds in the match. Winning a long match yields more points than winning a short match. The reason is that in a long match skill plays a bigger role than lucky dice rolls
– Difference in ratings. Beating a player with a higher rating yields more points than beating a player with a lower rating
– Amount of matches played. “Warm up” mode is enabled for new players with less than 500 experience points
What does not affect my rating?
– Number of wins and losses during one match. It does not matter how many rounds you won or lost. If you ended the winning match with score 13-12, then your rating will increase. It does not matter with what score you won the match, a win is a win
How is rating calculated in result of a win/loss?
Rating is calculated by the following formula:
W = (1 – P) * M * S
L = P * M * S , where:
W – number by which the players rating changed as a result of a win
L – number by which players rating changed as a result of a loss
P – probability of the player winning the match. Probability is calculated by the following formula:
P = 1 / (1 + pow(10,(-D * sqrt(n) / 2000))) , where:
pow – 10 to the power of …
D – rating difference between two players. This is calculated for every player seperately. One player will have a positive D (indicating that the player has a higher rating than the opponent), the other player – a negative. For example, D for first player is calculated in the following manner:
D1 = R1 – R2 , where R1 – first players Elo rating, R2 – second players Elo rating
N – match length, i.e. up to how many points the game lasts in the match.
M – “boost” modifier for rating change. This is required for new players to quickly acquire rating which corresponds to their skill level. “Boost” modifier formula is the following:
M = (500 – E)/100 , if E is less than 400
M = 1 , if E is more than 400 , where E – players experience.
Experience (e) is the sum of length of all previous matches. For example, if the player has played 5 matches with 3 points in each, then the experience is 15.
This way experience is used when calculating the “boost” modifier. The less experience, the bigger the “boost” modifier and the quicker Elo score will change. Once experience goes over 400 the “boost” modifier is set to 1 and Elo rating changes normally.
S – number of rating points at stake during the match. This is a basic parameter, indicating how many points a player will gain upon winning or losing.
S = 4 * sqrt(n) , where N – the length of the match, sqrt – square root
This parameter directly affects the amount of points gained upon a win or loss.
Can you give an example?
Imagine a game between “Player A” and “Player B”. “Player A” has Elo of 1100, “Player B” has an Elo rating of 1500. “Player A” has 675 experience points and “Player B” has 950. “Player B” is more experienced, however “Player A” won the match. Match was until 3 points. Let’s calculate what “Player A” gets as the result of a win and how many points “Player B” loses.
The Elo difference is the following: D1 = 1100 – 1500 = -400, D2 = 400
Let’s calculate probability of win for first and second players accordingly:
P1 = 0.31 P2 = 0.69
Let’s calculate number of rating points at stake:
S = 4 * sqrt(3) = 6.92
“Boost” modifier for both players is equal to M = 1, since both players have more than 400 experience points.
Now you have all parameters required to calculate the final result.
Points gained by “Player A” are equal to:
W = (1 – P) * M * S = (1 – 0.31) * 1 * 6.92 = 4.77
Points lost by “Player B” are equal to:
L = P * M * S = 0.69 * 6.92 = 4.77. If “Player B” won, he would get W = 2.14, since he is a more experienced player comparing to “Player A” and his Elo rating is much higher.
This way to get more Elo points the player has to win other players of equal or higher Elo score. Game against players of lower Elo will not add many points to the rating.
What are ways to manipulate rating?
Most backgammon players will do whatever they can to win the game. It is interesting to observe how your overall place in rating changes, as you gradually improve your play skill. However, there are players who don’t focus on backgammon, but on rating instead and try to increase it in any way possible.&br;We will explain ways how a player can “manipulate” rating.
1) Increasing the rating by creating a second account on another device. The user plays against himself and increases rating on one account. Naturally, this is against the rules of “Backgammon Masters” and can become a reason for blocking of both user accounts by device.
2) Regular games in 1 point matches. If the user plays 1 match points regularly, luck will overcome the skill. Meaning that winning a match with only one point relies more on luck than player skill.
3) Playing against beginners. Game against beginners will not yield a lot of rating points, but it will still increase gradually.
4) Playing against inexperienced players, which have temporarily acquired a high rating. Each users rating is under constant change and can swing up and down. Finding such users allows the player to increase his rating. How to find such players? One has to follow ratings of particular players and look for sudden upswings.
What are “quitters”?
“Quitters” are players who leave the game before an obvious loss or upon a high chance of getting a gammon loss. In order to timely escape a gammon, the player leaves the match. To avoid similar cases we have created a special algorithm which calculates the chance of gammon upon quitting. Naturally, gammon cannot be guaranteed, however if such a chance persists, then the player who stays will get two points instead of one.
How to see rating of top 100 players?
Firstly, click on “Online game”. Then log in with your account. Once you are logged in click on the green “View Statistics” button. Afterwards click on the “Rating” button. The header will indicate your place in the overall Elo rating and your Elo score.