The winks ratings were originally devised by Nick Inglis, mathematician and winker extraordinaire. Following Nick's self-imposed exile to Idaho in 1996, I volunteered to take over the ratings process - and in October 1997 the new ratings were published for all to see.

The original ratings were based on a series of programs Nick wrote for the BBC Computer in a combination of BBC Basic and 6502 machine code. Nick developed the program over the year and there were more than a dozen improvements made to the process I inherited.

The system works by estimating, for each game in a tournament, the average score for each player. This is done by taking the difference in ratings (in a singles game) or the difference in average ratings (in a pairs game) and using a function some of whose values are shown in the first table (the Percentage Expectancy Table) below. Thus a difference of 100 points suggests roughly a 4-3 win to the stronger player. The new rating of a player is R + K*(S-ES) where S is the actual score, ES is the expected score, R is the old rating, and K is a number depending on the number N of games in this tournament and the number M of games in the past year. A table of values for K is shown in the table below. Thus a game point is worth about 6 to 7 rating points if you've played 65 games in the past year, but only just over 4 if you've played 95. The M and N referred to are numbers of rateable games: a game is rateable for a player if:

- the player is unrated, or
- the player's partner is rated.

Games in which a rated player partners an unrated player are only used to rate the unrated player. The performance rating is the rating you would have had to have to give an estimated score equal to your actual score.

The table below shows the approximate results from the function used to derive expected scores based on ratings differences. So if you find two players with a ratings difference of, say, 450 - from the table the stronger player ought to be able to get a 5.5 - 1.5 score.

R1-R2 Expected Result R1-R2 Expected Result R1-R2 Expected Result

0 3.500 - 3.500 350 5.124 - 1.876 700 6.244 - 0.756 25 3.623 - 3.377 375 5.224 - 1.776 725 6.300 - 0.700 50 3.747 - 3.253 400 5.322 - 1.678 750 6.353 - 0.647 75 3.869 - 3.131 425 5.416 - 1.584 775 6.403 - 0.597 100 3.991 - 3.009 450 5.508 - 1.492 800 6.449 - 0.551 125 4.112 - 2.888 475 5.596 - 1.404 825 6.493 - 0.507 150 4.232 - 2.768 500 5.681 - 1.319 850 6.535 - 0.465 175 4.350 - 2.650 525 5.763 - 1.237 875 6.573 - 0.427 200 4.467 - 2.533 550 5.842 - 1.158 900 6.609 - 0.391 225 4.582 - 2.418 575 5.917 - 1.083 925 6.643 - 0.357 250 4.695 - 2.305 600 5.989 - 1.011 950 6.674 - 0.326 275 4.806 - 2.194 625 6.058 - 0.942 975 6.703 - 0.297 300 4.914 - 2.086 650 6.123 - 0.877 1000 6.730 - 0.270 325 5.020 - 1.980 675 6.185 - 0.815 1025 6.755 - 0.245

I have rewritten Nick's programs for WINtel (using Visual Basic with an Access Database).

After much faffing about, I have at last produced ratings which are vaguely reasonable. There are still some problems with them, but they are at least indicative.

The problem I still have with the ratings, is that the rating figure falls off too quickly (i.e. the gaps in ratings between players are not right - they're too high). In order to produce even these ratings, I had to introduce a fudge which involves adding 5 ratings points to a players rating whenever they're rating is recalculated (which only happens when they play games). This prevented the top of the ratings falling too fast (without this adjustment, the leading player ends up with a rating below 2,000). I'm still investigating this and will try to fix it soon.

Nick introduced a number of techniques for tackling the problem of falling ratings over the years. These were 95% successful. I leave it to Nick to describe this problem in his own words:

*"The problem of deflation is a well-known one with ratings systems. Basically
there is a tendency for players to start very weak, improve over time, and then fuck off
taking valuable ratings points with them."*

I initially thought this was the problem I saw in my ratings numbers, but I introduced a "fix" to deal with this and found it did not solve the problem. Because the ratings are set up such that winkers who do not play rated games for a 12 month period drop out of the system, there is a regular loss of rating points which can drag the overall average down. I calculated the number of ratings points lost in this way each time a new set of ratings was calculated, I re-credited them to the rated players proportionally based on the number of rated games played. This however only had a small effect and it was not consistently an upward revision - in some years it dragged the ratings down - so I abandoned the adjustment.

Last updated on April 02, 1998