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01-23-2013, 06:26 PM   #40
jmnk
Professional

Join Date: Jul 2009
Posts: 978

Quote:
 Originally Posted by OrangePower I think you are mistaken about what ELO is.
Well, we just have to disagree here.

Quote:
 Originally Posted by OrangePower 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).
ELO formula most certainly calculates what the expected score between two sides is based on their respective strength (current ranking) - if you normalize the scoring such that all the outcomes are in 0-1 range, which can be done for any type of competition. Accidentally, it is (almost) exactly the same as saying that it 'determines the probability of win/lose between two opponents'

from Wikipedia http://en.wikipedia.org/wiki/Elo_rating_system:

"Supposing Player A was expected to score E points but actually scored S points. The formula for updating his rating is

A player's expected score is his probability of winning plus half his probability of drawing. Thus an expected score of 0.75 could represent a 75% chance of winning, 25% chance of losing, and 0% chance of drawing. On the other extreme it could represent a 50% chance of winning, 0% chance of losing, and 50% chance of drawing. The probability of drawing, as opposed to having a decisive result, is not specified in the Elo system. Instead a draw is considered half a win and half a loss.
If Player A has true strength Ra and Player B has true strength Rb, the exact formula (using the logistic curve) for the expected score of Player A is

Similarly the expected score for Player B is

"[end quote]

In practice, for USTA tennis you can easily normalize via the following:
'the best possible result' is 12 games difference (6:0, 6:0 score) - so that is '1' in ELO calculations
'the worst possible result' is -12 games difference (0:6, 0:6 score) - so that is '0' for ELO calculations.
'the tie' is 0 game difference.

so now if per ELO the expected score for any two players is for example 0.75 than that means that the game difference in that match should be 0.75*24-12=6 (meaning a routine 6:3, 6:3 type of the score)

if the expected score is 0.35 than the game difference (expected) is 0.4*24-12=-3.6. that means that if a lower ranked player lost like 4:6, 6:7 than he actually 'won' since he performed better than was expected.

Quote:
 Originally Posted by OrangePower 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.
yes, thanks for the suggestion. I'm actually painfully familiar with the algorithm, as I have indeed played tournament chess for quite a while.

The beauty of ELO algorithm is that it can be applied to many, many various scenarios. Individual chess game is in fact not that great for that purpose as it provides only three possible outcomes (win/loss/tie), which is why the formula is applied to a set of chess games - either a match, or a tournament, or multiple games played over a given time period.

That way the opponents ranking can be averaged over multiple opponents, and the overall result from many games can be actually anything in 0 to 1 range (like 5 wins in 15 games = 0.33) - which corresponds much better to the concept of 'expected result' for ELO purposes.

Quote:
 Originally Posted by OrangePower 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.
I agree with you here. You make a good point. This is really due to the way tennis match is scored - you win by winning most sets and not necessarily most games (or points). But I would not call it a 'major flaw'. On average you will find very high correlation between a tennis match win and the game's difference. sure, there are going to be exceptions, as in your example, but they are really rare. the best method would be to make some sort of adjustment to game-difference method such that a winning player (the one that actually won a tennis match) is always assured a positive game difference, regardless of what the actual game difference was. i would vote for that.

Last edited by jmnk; 01-23-2013 at 08:33 PM.