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01-23-2013, 11:46 AM   #37
jmnk
Professional

Join Date: Jul 2009
Posts: 978

Quote:
 Originally Posted by OrangePower Not exactly; ELO (in its pure form) is binary; what would be important is who won the set, and not the set score. So the rating does not set an expectation for the set score, rather the difference in player ratings determines the starting probability of each player winning the set. Ratings adjust after each set based on who won/lost the set. This method would be superior in considering scores such as 7-6, 1-6, 1-0. As I understand it, in the current system adjustments are based on total number of games (perhaps I am wrong?). So in this example, the game score is 9-12, and player A is determined to have 'lost', although of course he won the first match! The binary ELO per set method would recognize this as 2 sets won for player A, and one set for player B. The primary drawback is of course not being able to differentiate between for example 6-1, 6-1, and 7-6, 7-6. ELO can be adjusted to consider margin of set score in addition to won/loss, but I'm not even sure that would be better. I think scores within a set are often not representative of relative strength anyway. Also, comparing with the current algorithm, the current algorithm already has a similar (and actually more significant) flaw in that the third set is just recorded and considered as 1-0. USTA algorithm is not ELO, although of course they share the principle of adjusting ratings after each set/match. I meant actually applying the specific ELO methodology and algorithm. Most significantly as I've noted above, pure ELO is binary and considers win/loss rather than score, and that's what I would implement for starters. I've implemented this for other things and think it would be a good fit for tennis.
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.