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Examples of Point Changes

This page gives examples of point changes for a single match. See How the Rating System Works for an explanation of how the rating system works and the terminology used below.

The number of points gained or lost in a single match depends on both the ratings (means) of the two players and on their standard deviations. Ignoring the standard deviations when looking at point changes is a frequent cause of confusion. The larger the standard deviation of a player’s rating, the less sure we are of the player’s playing strength, and so a single match result should have more effect, i.e., the match should be given more weight. Conversely, the smaller a player’s standard deviation, the surer we are of the player’s playing strength, and so a single match should have less effect.

The standard deviation takes into account how many results we have for a player, how informative each was (win or loss, opponent’s rating and standard deviation), how long ago each was, and any prior information (about the player or the subpopulation the player is from).

While the website displays ratings with a plus/minus (±) sign before the standard deviation, this does not mean that the player’s playing strength must be within one standard deviation of the mean. While it is likely that the player’s playing strength is within one standard deviation, it might be as much as two standard deviations from the mean.

Keeping the preceding comments in mind should make the values in the tables below agree with your intuition.

The tables give the points gained or lost by player P when player P plays player Q. The values in blue with the plus signs (+) are the number of points P gains if P wins the match, and the values in red with the minus signs (−) are the number of points P loses if P loses the match.

Q’s mean = 500
Q’s rating
500±30500±50500±100500±200
P’s rating1500±30+0 −13+0 −13+0 −13+0 −13
1500±50+0 −37+0 −37+0 −37+0 −36
1500±100+0 −149+0 −149+0 −149+0 −138
1500±200+0 −577+0 −573+0 −550+0 −435

Q’s mean = 1000
Q’s rating
1000±301000±501000±1001000±200
P’s rating1500±30+0 −13+0 −13+0 −13+0 −9
1500±50+0 −37+0 −37+0 −36+0 −25
1500±100+0 −146+0 −145+1 −135+2 −90
1500±200+7 −405+8 −396+9 −360+15 −264

Q’s mean = 1300
Q’s rating
1300±301300±501300±1001300±200
P’s rating1500±30+1 −12+1 −12+1 −10+1 −5
1500±50+2 −33+3 −32+3 −26+4 −15
1500±100+12 −107+13 −102+14 −85+15 −54
1500±200+59 −239+59 −234+59 −214+57 −163

Q’s mean = 1500
Q’s rating
1500±301500±501500±1001500±200
P’s rating1500±30+6 −6+6 −6+5 −5+3 −3
1500±50+16 −16+15 −15+13 −13+8 −8
1500±100+52 −52+50 −50+44 −44+32 −32
1500±200+136 −136+134 −134+126 −126+104 −104

Q’s mean = 1700
Q’s rating
1700±301700±501700±1001700±200
P’s rating1500±30+12 −1+12 −1+10 −1+5 −1
1500±50+33 −2+32 −3+26 −3+15 −4
1500±100+107 −12+102 −13+85 −14+54 −15
1500±200+239 −59+234 −59+214 −59+163 −57

Q’s mean = 2000
Q’s rating
2000±302000±502000±1002000±200
P’s rating1500±30+13 −0+13 −0+13 −0+9 −0
1500±50+37 −0+37 −0+36 −0+25 −0
1500±100+146 −0+145 −0+135 −1+90 −2
1500±200+405 −7+396 −8+360 −9+264 −15

Q’s mean = 2500
Q’s rating
2500±302500±502500±1002500±200
P’s rating1500±30+13 −0+13 −0+13 −0+13 −0
1500±50+37 −0+37 −0+37 −0+36 −0
1500±100+149 −0+149 −0+149 −0+138 −0
1500±200+577 −0+573 −0+550 −0+435 −0

You may find it curious that a 1500±50 player gains the same number of points beating a 2000±30 player as they do beating a 2500±30 player. But, with a standard deviation of 50, P’s previous results have convinced us that P can’t be more than about 1600, so we are just as surprised when they beat a 2500 player as when they beat a 2000 player. While we adjust our estimate, we are not going to throw out all of P’s previous results because of one win.

Note that the values in the tables above were calculated assuming that the player laws are normal. While player laws start out as normal, they do not remain normal, although they are usually approximately normal. This and the fact that ratings and standard deviations are rounded to the nearest integer when displayed on the website means that actual point changes may be slightly different (a point or two) from the examples, even if the players’ ratings and standard deviations appear to be identical to those in the tables.

Philip Gammon has a spreadsheet that lets you calculate examples like the ones above.