Thanks Robert! I was about answering that all the info was not in the same post.Robert Pope wrote: ↑Fri Jul 19, 2019 4:57 pmRebel wrote: ↑Fri Jul 19, 2019 7:52 amI am missing the dedinion of [z] in your post or I am in need for new glasses.Ajedrecista wrote: ↑Thu Jul 18, 2019 6:10 pmGiven the big difference of played games of the 'Big Four' (43.18%, 36.48%, 10.57% and 8.08%), I obtain plausible weights IMHO although the math is not so simple.

You can tweak the parameterszanda.z~ 1.96 orz= 2 are pretty standard, butais more subjective and susceptible of being tested.

Regards from Spain.

Ajedrecista.It's in one of the very early posts.z ~ 1.959963985 (95% confidence in a normal distribution; you can change z)

**z**is the z-score in a normal distribution, so you can pick

**z**from a wide variety, though

**z**= 2 looks both reasonable (confidence ~ 95.45%) and an easy value to remember.

------------

Glad to see that it might be useful! It would be interesting to know if the method can hold extreme cases like very few games with scores near 0% or 100%; or overwhelmingly played moves with very poor scores, since n^Rebel wrote:I like the formula especially because it's so easily to tune with a parameter [a], I think I am going to use it, so thanks.Ajedrecista wrote:As you can see,a= 1 gives your original weights.a=< 0 gives weird weights (like giveaway, worst is best) anda-> +infinity awards the most played move regardless its score.

**a**intends to provide a kind of 'smooth' (not the right word probably) in the frequency of moves (that is, to provide more variety on similar good-performing moves like e4 and c4 in your example, with very different number of games between them).

Using the lower bound of Wilson score interval in the performance instead of the performance itself tries to not bias in favour of moves with high performances but low number of games (like the following example: which is more significant? A comment with 1 'like' and 0 'dislikes' or other one with 99 'likes' and 1 'dislike'?).

It looks like continuity correction lowers the weights of moves with very low percentage of moves while raise a little the weights of top played moves, in comparison with not using continuity correction. The formulas are there:

https://en.wikipedia.org/wiki/Binomial_ ... e_interval

https://en.wikipedia.org/wiki/Binomial_ ... correction

It is up to you to choose either solution.

Regards from Spain.

Ajedrecista.