Elo difference to win/ draw/ loss percentages

I am aware of the use of Elo difference to calculate win/ loss percentage. This website provides a very useful table

http://www.ascotti.org/programming/chess/elo.htm

Using the table, we can easily determine that a player that is 72 points stronger than his opponent, has a 60% chance of winning a game, and 40% chance of losing it.

However in real life, and especially at the highest level, draws happen very frequently. And therefore this number(0.6) could be

60% win, 0% draw, 40% loss

50% win, 20% draw, 30% loss

40% win, 40% draw, 20% loss

or one of infinite such combinations...

Therefore I  believe that even though Elo difference is extremely informative, it does not provide the complete information.

I have a few thoughts about how to provide the additional information. If two players with > 1000 Elo difference play with each other, the draw percentage will essentially be zero. However, if two players with equal Elo play against each other, they draw approximately around 40% times. This is not true for two 1300s but true for 2700s.

So we can add an extra column of approximate draw percentages at that Elo difference and then the table becomes much more useful.

I am sure hardcore chess players/ and others such as those interested in math and statistics would already know much more about this. So please provide your thoughts.

Thanks

One of the clubs I go to you have to report your results and you get a club rating.  All for fun of course, but there are all that stats right there if you want to look at them.

As expected the higher rated players had a higher percentage of draws, but I found that the 2nd highest rated member had one of the lowest draw percentages of all.

Of course this is just blitz, and for what you're doing it would be more interesting (IMO) to look at only tournament games.  But still, there's one hiccup for your vision of perfect information, that it depends on the individual's style of play.

I suppose you could give ranges, and that's better than a total guess.

Thanks @wafflemaster, interesting thoughts!

I think I found the answer that I was looking for here in this blog post: Although it is not compelling enough, it is the best answer I have seen.

http://www.ncchess.org/wordpress/2012/09/individual-chess-game-probabilities/

  I wrote the article you found in the ncchess.org blog. You are correct that the probabilities are not static for the full range of Chess players, but the are very good for the majority. I researched data for computer programs (they are more likely to play consistently) vs computer programs to test the math I did for the article. For programs (and I believe for humans) with ratings around 2200  to about 1400, the proabilities that I stated held well. For programs rated above 2600, the draw rate increases thus equally shrinking the win rates for both the higher and lower rated programs. I checked for humans above 2600 and the higher draw rate holds there as well.

  For those rated below 2200 to about 1300 (the majority), my probabilites should be a good predictor. For mathces where both players are rated below 800, draw rates are lower and performance is more eratic. 

cool