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Old 01-23-2013, 02:51 PM   #39
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Originally Posted by jmnk View Post
I'm not exactly sure what you mean by 'ELO (in its pure form) is binary' - but the concept of ELO method makes no assumption about win and loss. in plain language ELO method is based on a concept of an 'expected result between two sides'. What the expected result is? Well, that varies depending on the ranking difference between two sides. For example, in tennis, the expected result between 4.35 and 4.12 players may be 2:0 (in sets), or 2:1(in sets) or 5 games difference - that depends on who is designing the formula. There's no 'right' way to do it - what works the best is based on experience, empirical data, etc.
Now let's assume that whoever designed the system decided that the expected result between 4.35 and 4.12 (or any other two sides where ranking difference is 0.23) is 5 games difference. Now the 4.35 player won 7:6, 6:4. So while he won, he 'lost' per ELO formula since he was expected to win by 5 games while he won by only 3. The formula now will give you number of ranking points that each player gained/lost. that may be further adjusted by the 'importance' of the match - the designer may want to give more weight to sectional matches vs. everyday league match.
The system is very non-linear. Meaning if you perform better than expected while playing a player with similar ranking you will gain a lot. But performing better than expected vs. a player with vastly lower ranking will barely earn you any points. Eventually, at some point (in tennis maybe when players are like more than 1.5 ranking points apart), you do not really gain anything no matter how much you win.
In that sense USTA algorithm --is-- ELO based. BTW - so is FIFA ranking, and FIFA also uses goal differential (and not just win/loss) when calculating ranking points. But Canada Rogers tennis ranking uses win/loss only.

Again, there's no 'right' method. using games differential gives you more granularity, which helps if your data pool is somewhat limited. how many matches does one play during one year? 10? - that is not that many for statistical purposes.
I think you are mistaken about what ELO is. ELO determines the probability of win/lose between two opponents of different ratings, and provides the formula for adjusting the players' ratings based on their starting ratings and the actual win/lose result. ELO does not attempt to predict partial results (i.e. a score in tennis).

No doubt there are other algorithms that use some of ELO as a basis, and then do consider scores rather than absolute results, but there are no longer the pure ELO algorithm. If you are interested, there is a lot of material about ELO on the web, specifically as originally developed and currently implemented for chess.

The rest of your post is correct, in terms of describing how the current algorithm, and an expected-score based system in general, works, but is orthogonal to the discussion on ELO.

The example in your post does highlight one of the major flaws of the current algorithm: Let's take a similar example of a 4.35 vs a 4.20, and let's say the expected difference is 4 games. And let's say the outcome is 6-0, 6-7, 0-1 . Now the 4.35 has won 12 games and the 4.20 has won 8, such that this result is exactly consistent with the expectation, and neither player's rating is adjusted. This is clearly not representative of the reality that the 4.20 beat a higher-rated 4.35.
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