## Introduction

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.

## Explanation of Nick's System

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).

## Remaining Problems

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