# Rating Calculation Modification. Use Ratings of...

Phillidor
Site Ideas 04 May '08 16:32
1. 04 May '08 16:32
I propose that the "OpponentRating" variable and the "YourRating" variables be determined by the respective ratings AT THE START OF THE GAME. (See formula calculation at the bottom of this post)

I propose this in order to discourage players from using the clock to delay losing a game in order to lose the least number of rating points.

EXAMPLE:
Player A begins the game rated at 1500 & Player B is rated at 1700

During the course of the game (2 weeks), Player A increases his rating to 1650

Player B is one move from checkmate and has 2 weeks of timebank left.

Player B acting rationally expects player A to continue increasing his/her rating so Player B may delay resigning as long as possible so that at the time of resignation or checkmate, Player A is now rated (assuming linear rating growth) at 1800.

Now Player B (still rated at 1700) loses far less rating points to Player A who is rated at 1800 than had ratings been based upon the original ratings of 1500 and 1700.

This will also help players who have a low rating and agree to play a similarly low rated opponent (1300 vs 1300) to a very long time control game. Over the course of the year that may go by before the original game was completed, either player may substantially increase his/her rating based upon acquiring chess playing skills.

(A 1300 level beginner (Player A) to chess, makes a mistake against a low rated opponent (Player B). Over the course of a year, Player A become a chess whiz and increases his/her rating to 1900. When Player A eventually loses to player B due to the beginners mistake made 1 year ago when Player A first learned to play and started the very long time control game, Player A loses a lot of chess rating points (1900 vs 1300).

The formula assumes skill levels are constant throughout the course of the game.

I believe the formula should only base rating changes upon the ratings and the level of chess playing ability at the beginning of the game.

So, when the 1900 level player loses to the 1300 player, because original ratings were similar, the rating change should be based off of 1300 vs. 1300.

NOTE:
Players are rated using the following formula:
New Rating = Old Rating + K * (Score - Win Expectancy)
K is a constant (32 for 0-2099, 24 for 2100-2399, 16 for 2400 and above)
Score is 1 for a win, 0.5 for a draw and 0 for a loss.
The Win Expectancy is calculated using the following formula :
Win Expectancy = 1 / (10^((OpponentRating-YourRating)/400)+1)
2. 04 May '08 16:48
At the very least, the Average of the beginning rating and end rating should be used. (Begin the game rated 1300; End the game at 1600; Use 1450 to determine rating points won or lost)

Perhaps the danger of using only the beginning ratings would be if a player (of 2000 ELO strength) purposefully plays pitiful games during the provisional period to establish a very low non-provisional rating (Say 900). Then the 900 ELO player (who is really 2000) proceeds to start 500 games against other players rated similarly and win them all. This player would then have an ELO VERY VERY high. Using the average, however, would help eliminate this perverse incentive.
3. 04 May '08 17:11
Perhaps a Weighted Average would be an alternative to using the simple average.

Player A begins a game rated at 1000 with Player B rated 1000. (GAME ZERO)

While GAME ZERO is being played, Player A wins 5 games and increases his/her rating 20 points each time.
Now player A is rated at 1100.
Player A (rated 1100) then checkmates Player B (still rated 1000).

Player A's rating could be calculated using a weighting system such as:
For the 6 ratings that Player A held during the course of GAME ZERO,
(1000 * 6) + (1020 * 5) + (1040 * 4) + (1060 * 3) + (1080 * 2) + (1100 * 1) / (6 + 5 + 4 + 3 + 2 + 1)

(6000 + 5100 + 4160 + 3180 + 2160 + 1100) / 21

21700 / 21 = 1033.33

The simple average would be 1050 for Player A's rating.

Use 1033 as Player A's rating for calculation purposes when Player A wins against Player B (still rated at 1000).
4. Ragnorak
04 May '08 18:10
Originally posted by Phillidor
I propose that the "OpponentRating" variable and the "YourRating" variables be determined by the respective ratings AT THE START OF THE GAME. (See formula calculation at the bottom of this post)
Do the calculations from your first post assuming I'm an 2000 rated player, who has just resigned all of my games to get me down to 600. I then start 100 games against 1400s.

I'm looking forward to seeing my final rating.

D
5. 04 May '08 18:24
See the second and third post.
6. 04 May '08 19:10
We must do better than:
1) To miss the point completely - the site idea being suggested
2) To proceed to level a criticism already identified by the author

It is neither constructive or original.
7. Ragnorak
04 May '08 20:23
Originally posted by Phillidor
We must do better than:
1) To miss the point completely - the site idea being suggested
2) To proceed to level a criticism already identified by the author

It is neither constructive or original.
It may be just me, but I tend to read threads sequentially, and respond to posts before reading further.

Posting site ideas when you have already identified THE major flaw in the proposal is not constructive, but definitely original.

You could have saved me and other readers a lot of time by skipping your original post, and starting your site idea with posts 2 and 3. BTW: how did I miss the "point completely"? I reread your first post, and you repeatedly wrote that calculations should be done using the rating at the start of the game. Even capitalising for punctuation.

Anyway, the idea contained in the third post has merit.

D
8. 04 May '08 21:27
Originally posted by Ragnorak

Anyway, the idea contained in the third post has merit.

D
Thank you.
9. 05 Jun '08 17:38
Originally posted by Phillidor
I propose that the "OpponentRating" variable and the "YourRating" variables be determined by the respective ratings AT THE START OF THE GAME. (See formula calculation at the bottom of this post)
Hiya

This is certainly an interesting idea.

I am not so keen. For detail, read on.

Gezza

I am not sure of the benefit of using the out-of-date rating as the basis for allocating rating points.

Assume you start playing in a tournament, with other guys of the same sort of rating, and play no other games.

If I start a tournament, I get say 20 games starting at once. These games finish in whatever order, but the rating points allocation after the last game in the round treats both players as having the rating they had at the start.

Assume that the round winner and the round loser play their last game of the tournament against each other. This means that the guy who is improving gets lots of rating points, and the guy who was at his peak at the start of the tournament loses lots of points. But in the meantime, all their other tournament games have finished.

In comparison to the current system, where the ratings difference between them (due to the other tournament games) is now large, neither gets/loses many points.

I think that making the change is likely to give an "overshoot" of rating - the guy who is doing well gets more points added. The guy who is losing loses more.

This is pretty much based on my "gut feel". I haven't analysed too much. It somehow feels wrong that stating each game when the last has finished should give a lower final rating than starting them all at once, which is what I expect your change to do.

I agree with you that some improvement to the rating system might be possible, but I think that effectively deciding how rating will change (for a given result), and then delaying the change for the duration of the game does more harm than good. I see rating as a "best guess at ability/future result, based on past results". Each win or loss tweaks it a bit, up or down. If you store the change which will be made, for a lot of games starting at the same time, when those games finish you overcompensate for a "current" rating which was too high or low, when they started.

On the later posts with average and weighted average.
These feel like a tweak to the first system, to work around the disadvantages.

Simple average: Easy to calculate. But less of an advantage. For your 1500 - 1700 example, it is still worth B waiting because it is better to lose against (1800+1500)/2= 1650 than against (1650+1500)/2= 1575, as less points are lost by B in the first case.

Weighted average: Lots of calculation, but data should be available, and computers are fast. However, is there enough gain for all of this calculation? If someone's rating rises, the weighting still biases it towards the rating at the start for calculation purposes. Would it solve the 500 games against players rated 900? If I calculate correctly, no, as rating levels off at 2032, rather than 1630 with the current system.

I'll agree that the weighted average looks interesting.

How do you deal with a new player, rated low, but quite strong, playing in an open tournament? The guy at the top of the ratings list starts playing him, and as the game progresses, the new guy gets closer to his "final/ability" rating. The top guy eventually loses to the new player, who is now rated the same. Under the current system, the top guy loses a few points. Under the system you suggest, he loses a lot more.

I think you introduce a disincentive to start to play people whose rating change a lot.