Towards a Skill Ratio : is it a joke ?

[Jetto2]

Hello Mr Ryne A. Sherman

This title of this is a little too much a provocation, but I hope to get the answer "No it is really serious" (maybe not the better thing for a first post).

You imagine the dream it is for all player to know the partition form skill and luck in there poker result. So even if I am band new poker player I'm very interested to know.

I carefully read your two article, I also try to speak on this on French poker forum but I only get bad feed back. I wish it is +EV to post here.

My skill in mathematics is poor even I have university grad, but try to redo the computation in the fist part of the May article.

I think a little and I haven't be convince that doing that kind of random autocorrelation would give interesting result.

I quickly try to check the correlation as you say (randomly split the series in two and compute the Pearson r correlation) of a normal then a with uniform distribution. The result look like to be quite the same in the both case (I use a little Rprogram for this).

Can you tell me where is my mistake and how to redo you calculation ?

Thank you

PS: This post is addressed to the author of the article but as it is in a public forum constructive answer from every body are welcome.

[Jetto2]

Here is the little R function I write
[ QUOTE ]

> tptcor
function(x){
res<-c()
l<-length(x)
hl<-as.integer(l/2)
for (n in 1:length(x)) {
rindex<-sample(1:l,replace=FALSE)
res<-c(res,cor(x[rindex[1:hl]],x[rindex[(hl+1)2*hl)]],method="pearson"))
}
return(mean(res))
}


[/ QUOTE ]

[Sherman]

Jetto,

I'm not 100% sure what your question is, but I will do my best to answer.

First, without gathering the data that I have gathered, I am not sure how you could compute the same correlations I computed. When you say you "randomly split the series in two" I have no idea what you are splitting and I am not sure that is the best approach. Of course I would be more than happy to send you the data if you would like to try it yourself. Anyone who wants it can simply PM me.

In any case, let us take a simple example, say number of hits in a single baseball season. For this metric, I correlated the total number of hits each player had from Season 1 with his total for Season 2. This single correlation represents the degree of association between hits in season 1 and season 2. I did the same thing for all possible pairs of seasons ( [1,3]; [1,4];...[5,6]). This yielded a total of 15 correlations. I then simply average these 15 numbers to represent the average assocation from one season to the next. These average r's are the ones presented in Tables 1 and 2 of this month's article. As I mentioned in the article however, these correlations do not control for the number of at bats (or attempts) that a player makes.

To control for the number of attempts, things get a bit more complicated. First, I predicted each player's hits based on his number of at bats for each season using linear regression. I then saved the residuals. These residuals can be thought of as the number of hits a player gets when his at bats are controlled for. I did this for each of the six seasons. Then, repeating the earlier procedure I computed the correlations for all possible pairs of the 6 residuals for each season. Again this yielded 15 correlations. I once again took the average of these correlations.

These average r's are the ones you see in Tables 3 and 4 of this month's article.



If your question is about the calculation of the individual r's, I simply used standard statistical packages to do so. The general forumula is sum(Zx*Zy)/N. Where Zx are Z-Scored values for variable 1 and Zy are Z-Scored values for variable 2. N is the total sample size. Most statistical packages use N - 1 in the denominator however to provide population estimates.

I hope this makes it more clear how the procedure worked.

Ryne Sherman

[Jetto2]

Thank you for your answer.

I think I have been confused because you say "... randomly select ½ of a player’s at bats and compute the average. Then take the remaining ½ of that player’s at bats and compute the average"

But I didn't do the same as you because I didn't calculate the correlation of the mean but the mean of the correlation. This at least where I'm wrong.

[Sherman]

[ QUOTE ]
Thank you for your answer.

I think I have been confused because you say "... randomly select ½ of a player’s at bats and compute the average. Then take the remaining ½ of that player’s at bats and compute the average"

But I didn't do the same as you because I didn't calculate the correlation of the mean but the mean of the correlation. This at least where I'm wrong.

[/ QUOTE ]

Ah yes. This would be one way of estimating the skill for hitting in baseball for a single season. However, because the database I have has multiple seasons, a better estimate is to take the average r from the pairs of seasons.

[Steven Mason]

no joke, I think they drink too much