Body: <p>I already looked on several websites but I have not been able to get a clear and thorough answer to this question: </p>
  
  <p>If player <em>A</em> has FIDE rating <strong>x</strong> and player <em>B</em> has FIDE rating
  <strong>y</strong>, how many times, on average, player <em>A</em> should be able to win? In other words, what is the probability for <em>A</em> to beat <em>B</em>?<br>
  Is there a mathematical formula to get such a probability?</p>
  
  <p>Furthermore, what is the amount of points that are added/subtracted to the players if they have a certain difference in Elo rating? Which is the mathematical formula behind it?</p>
  
  <p>For instance, this article <a href="https://thechessworld.com/articles/general-information/all-truth-about-elo-rating-system/" rel="nofollow noreferrer">All truth about ELO rating system</a>
  gives a couple of examples for opponents with a rating difference of 200, 400, 600; but is there a more generic formula?</p>
  
  <p>Could someone give (or point to) a quite decent and thorough explanation? Thanks in advance!</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-06T18:03:05.040Z
Comments.Text: Welcome to [chess.se]! Please have a look at [How to calculate the FIDE Percentage Expectancy Table](https://chess.stackexchange.com/q/19653/7297) which may already answer your question; my answer there includes the exact formula (taken from Wikipedia).
Comments.UserDisplayName: Glorfindel
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-07T00:15:08.067Z
Comments.Text: If winning percentages could really be determined from rating differences, that would mean that if we knew A's winning percentage against B, and B's winning percentage against C, then we could determine A's winning percentage against C. I don't believe this is the case.
Comments.UserDisplayName: bof
Tags: <rating><elo><mathematics>
Title: Probability of winning based on Elo rating
ThreadText: # Probability of winning based on Elo rating
  
  (Asked by: username_0 on 2019-05-06)
  
  I already looked on several websites but I have not been able to get a clear and thorough answer to this question:
  
  If player *A* has FIDE rating **x** and player *B* has FIDE rating
  **y**, how many times, on average, player *A* should be able to win? In other words, what is the probability for *A* to beat *B*?  
  Is there a mathematical formula to get such a probability?
  
  Furthermore, what is the amount of points that are added/subtracted to the players if they have a certain difference in Elo rating? Which is the mathematical formula behind it?
  
  For instance, this article [All truth about ELO rating system](https://thechessworld.com/articles/general-information/all-truth-about-elo-rating-system/)
  gives a couple of examples for opponents with a rating difference of 200, 400, 600; but is there a more generic formula?
  
  Could someone give (or point to) a quite decent and thorough explanation? Thanks in advance!
  
  **Tags:** rating, elo, mathematics
  
  > **Comments:**
  > **username_1**: Welcome to [chess.se]! Please have a look at [How to calculate the FIDE Percentage Expectancy Table](https://chess.stackexchange.com/q/19653/7297) which may already answer your question; my answer there includes the exact formula (taken from Wikipedia).  
  > **username_2**: If winning percentages could really be determined from rating differences, that would mean that if we knew A's winning percentage against B, and B's winning percentage against C, then we could determine A's winning percentage against C. I don't believe this is the case.  
  
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  ## 0 answers
  
  