Don't Understand Grading Calculation

General discussions about grading.
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Brian Towers
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Don't Understand Grading Calculation

Post by Brian Towers » Mon Oct 07, 2019 12:54 pm

Last season we had a foreign student join our club with a FIDE rating that equated to about 115. Playing quick games against him we decided that he was probably a bit stronger than that and placed him in our teams based on our estimates. At the end of the season his results were 8 wins against opponents with the following grades - 132, 129, 121, 118, 125, 128, 144, 107. That looks to me to be an average grade of 125.5 which I would have thought would have resulted in a grade of 176. Instead his grade is 187. What aspect of the calculation have I failed to understand?

BTW, I did warn him that he would have an inflated grade with all wins but he went away over the summer rather than play congresses where he would have faced stronger opposition. Although we moved him up during the course of the season we were constrained by league grading difference limits and by the end of the season were perhaps exceeding them but not by enough for any other teams to lodge an official complaint.
Ah, but I was so much older then. I'm younger than that now.

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Christopher Kreuzer
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Re: Don't Understand Grading Calculation

Post by Christopher Kreuzer » Mon Oct 07, 2019 1:00 pm

One of your player's games was against a junior (the one graded 118), that is what the asterisk (*) indicates. If you click through to that junior's grading page, their actual grade (calculated using the junior grading thingy method) is 124. I think this will account for some of the difference. OK, that is not enough to account for the difference. Maybe your player (as a new player) also has their grade calculated in a particular way (like for juniors).

I think what might be happening is that at least four of the players are "50 points below" the grade that the system is trying to assign to your player, so the performance there is recalculated. Take the initial estimate of 176 and redo the calculation with those four grades redone as "126" grades instead. And see what the result is.

132, 129, 121 [126], 118 [124 then 126], 125 [126], 128, 144, 107 [126].

New average: 180.

Then do this again:

132, 129 [130], 121 [126 then 130], 118 [124 then 126 then 130], 125 [126 then 130], 128 [130], 144, 107 [126 then 130].

New average: 182.

Then do this again:

132 [132], 129 [130 then 132], 121 [126 then 130 then 132], 118 [124 then 126 then 130 then 132], 125 [126 then 130 then 132], 128 [130 then 132], 144, 107 [126 then 130 then 132].

New average: 183.5 (round this to 184)

Basically, only the highest grade of 144 (bolded below) will not get bumped up this way.

The final iteration is:

132 [132 then 134], 129 [130 then 132 then 134], 121 [126 then 130 then 132 then 134], 118 [124 then 126 then 130 then 132 then 134], 125 [126 then 130 then 132 then 134], 128 [130 then 132 then 134], 144, 107 [126 then 130 then 132 then 134].

New average is 185.

Do it one more time (it wasn't quite the final iteration):

132 [132 then 134 then 135], 129 [130 then 132 then 134 then 135], 121 [126 then 130 then 132 then 134 then 135], 118 [124 then 126 then 130 then 132 then 134 then 135], 125 [126 then 130 then 132 then 134 then 135], 128 [130 then 132 then 134 then 135], 144, 107 [126 then 130 then 132 then 134 then 135].

New average is 186.

Maybe do it one more time?

New average is [(136*7 plus 144)/8]+50= 187

There we are! :D

Roger de Coverly
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Re: Don't Understand Grading Calculation

Post by Roger de Coverly » Mon Oct 07, 2019 1:16 pm

Christopher Kreuzer wrote:
Mon Oct 07, 2019 1:00 pm

I think what might be happening is that at least four of the players are "50 points below" the grade that the system is trying to assign to your player, so the performance there is recalculated. Take the initial estimate of 176 and redo the calculation with those four grades redone as "126" grades instead. And see what the result is.
You always get something for winning, so the minimum grade is yours minus 40.

How strong is someone who chews up 120 players on a regular basis? The grading system struggles, but so do all rating systems?

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Christopher Kreuzer
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Re: Don't Understand Grading Calculation

Post by Christopher Kreuzer » Mon Oct 07, 2019 1:16 pm

From the help page:

"If an opponent (or the player himself) is ungraded, a "starting grade" is estimated, using all available information. See Estimating a starting grade for an ungraded player below."
Estimating a starting Grade for an ungraded player (or a junior)
A Rapid grade, where available, will be used in default of a Standard grade; and vice versa. If the player has no grade at all, a starting grade is calculated as follows, using all their games in the latest three years (for adults) or one year (for juniors), inclusive of the current year.

Stage 1 is to calculate a 'grade' for each ungraded player on all their games against graded opponents in the relevant period. The 40-point rule is not used. If all their opponents are graded, it stops there and Stage 2 is omitted. The result will be used as their starting grade.

Stage 2 brings in games between the ungraded players. Once again the 40-point rule is not used. The players are 'graded' on all their games, using as starting grades the figures obtained from Stage 1. The resulting 'grades' will not be very accurate. So they are fed in again as new starting grades, and Stage 2 is repeated. This continues, with increasing accuracy each time, until the figures (more or less) stop changing. The starting grades can then be considered accurate, and they are used in the grading proper.

The effect of Stage 2 is that the points scored for a game against an ungraded opponent are repeatedly adjusted till the starting grades are right. But it is important to note that the adjustment applies only to games from the most recent (so not previously calculated) grading period. Games from earlier periods are included every time round, but always with the original points value. A previous-period game, once calculated, is never recalculated except for corrections.

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Christopher Kreuzer
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Re: Don't Understand Grading Calculation

Post by Christopher Kreuzer » Mon Oct 07, 2019 1:20 pm

Roger de Coverly wrote:
Mon Oct 07, 2019 1:16 pm
Christopher Kreuzer wrote:
Mon Oct 07, 2019 1:00 pm

I think what might be happening is that at least four of the players are "50 points below" the grade that the system is trying to assign to your player, so the performance there is recalculated. Take the initial estimate of 176 and redo the calculation with those four grades redone as "126" grades instead. And see what the result is.
You always get something for winning, so the minimum grade is yours minus 40.

How strong is someone who chews up 120 players on a regular basis? The grading system struggles, but so do all rating systems?
Oops. I did my iterations doing the grades minus 50 not minus 40. Any iteration would have eventually converged on 187 I think. Is that what has happened here? The grading calculations guidance seems to indicate that this should NOT have happened here, as only one of his opponents was 'ungraded' or a 'junior'. Strange.

[I think my iteration would have eventually got to 194, i.e. 144+50.]
Last edited by Christopher Kreuzer on Mon Oct 07, 2019 1:25 pm, edited 1 time in total.

Roger de Coverly
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Re: Don't Understand Grading Calculation

Post by Roger de Coverly » Mon Oct 07, 2019 1:23 pm

Christopher Kreuzer (Grading Help) wrote:
Mon Oct 07, 2019 1:16 pm

Estimating a starting Grade for an ungraded player (or a junior)

Stage 1 is to calculate a 'grade' for each ungraded player on all their games against graded opponents in the relevant period. The 40-point rule is not used. If all their opponents are graded, it stops there and Stage 2 is omitted. The result will be used as their starting grade.
Now there's an anomaly. If the player in question hadn't played a junior, the iteration would have stopped at the lower value. That may help to explain why new players and juniors doing extremely well or extremely badly seem to get grades that a player with an established grade and the same performance wouldn't.

Roger de Coverly
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Re: Don't Understand Grading Calculation

Post by Roger de Coverly » Mon Oct 07, 2019 2:26 pm

Christopher Kreuzer wrote:
Mon Oct 07, 2019 1:20 pm

Oops. I did my iterations doing the grades minus 50 not minus 40. Any iteration would have eventually converged on 187 I think. Is that what has happened here? The grading calculations guidance seems to indicate that this should NOT have happened here, as only one of his opponents was 'ungraded' or a 'junior'.
I have this idea that at least part of the iteration uses minus 50 rather than minus 40. It may have to, otherwise you get a convergence to highest player plus 50.

From the grading Help.
Stage 2 brings in games between the ungraded players. Once again the 40-point rule is not used.

Kevin Thurlow
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Re: Don't Understand Grading Calculation

Post by Kevin Thurlow » Mon Oct 07, 2019 5:49 pm

I think Chris was on the right track. I also think that all grading/rating systems struggle with 100 (or 0!) % scores. It's a "new" player and only 8 games as well. Many players on this forum would probably get 8/8 against that opposition but as we tend to have established grades the system can handle it without iterations of the results.

Brian Valentine
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Re: Don't Understand Grading Calculation

Post by Brian Valentine » Mon Oct 07, 2019 7:26 pm

The calculation here is fairly straightforward, but difficult to justify.

The iteration method will get to the average of opponent's grades plus 50; which as already pointed out gives 176. In the final iteration the 40 point limit is introduced so 7 of those results become 186 with the other being 194. The new average is 187 and published as the grade.

Angus French
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Re: Don't Understand Grading Calculation

Post by Angus French » Mon Oct 07, 2019 7:47 pm

It's perhaps worth pointing out that between five and eight results with at least one of those in the most recent 12-month grading period gets a player an 'F' category grade. 'F' category grades are not used for future grading calculations (instead a new estimate is calculated) and are treated by some with caution (since the sample size used in the calculation is small and some of it may be dated).

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