19-06-2013, 01:03 PM
Phil Thomas Wrote:Let us do a mind experiment. Suppose Murad played another 4 congresses and scored identical results to the first 4. His strength would then be evaluated from these 8 numbers.
1663, 2065, 1654, 2180, 1663, 2065, 1654, 2180.
The correct way to do this would be to average all 8 – result is still 1891.
The incorrect way to do this is to average the highest 4 and get 2123.
Where did the extra 232 points come from ?
Its not magic its a serious mathematical flaw.
Cherry picking data this way gives, in effect, a set of corrupt raw data.
If you are going to only use 4 results out of the 8 it would be better to use the middle 4 results rather than the highest 4 results. This gives 1864.
There are pros and cons to using all of the results or only some of them. On the plus side using all of the results may be more "accurate". On the minus side taking an average(arithmetic mean) is vulnerable to being excessively influenced just by one very low or very high result.
Perhaps you should do the same as is proposed for the selectors' estimates and exclude the lowest and the highest and take the average of the rest - just using 4 out of the 8 results is probably ignoring too much data.
On the subject of very low or high results there are problems using TPRs. Most congresses are probably only 5 rounds whereas taking a lead from the CS grading system at least 8 would be better. This is less of a problem though if the average of several TPRs is taken. There are also problems with TPRs not existing or not being meaningful if someone scores either 0% or 100% cf. the CS grading system requiring a new player to score at least 1/2 point (and presumably not winning all their games although it does not appear to say this anywhere.) While 0% is probably not a problem for the players under consideration 100% could well be.