Three professional players and win rates

[bigpooch]

Suppose there are three professional players and each of
them meticulously records their yearly poker results.

In the year 2002, Al had a bigger hourly rate than Bob who
in turn had a bigger hourly rate than Carl. The same will
be true of 2003. Would you conclude Al had a bigger hourly
rate than Carl for the two years?

By hourly rate, I simply mean the total dollars won divided
by the total hours played for the year and not what the
"theoretical" or actual rate would be in the long run.

Answer to be posted after Xmas.

Happy holidays, everyone!

[MrBlini]

(Answer in white below)

<font color="white">No. You have only half the data you need to determine this.</font>

[Nottom]

No, Lets say for example that in year 1
Al averages $10/hour over 1000 hours
Bob avgs $9/hour over 500 hours
and Carl avgs $8/hour over 1 hour

in year 2 they all improve

Al wins $30/hour over 1 hour
Bob wins $29/hour over 500 hours
and Carl wins $28 over 1000 hours

Over the 2 years Al averages [1000(10)+30(1)]/1001= $10.02/hour
Bob = [500(9)+500(29)]/1000=$18.5/hour
Carl = [1(8)+1000(28)]/1001=$27.98/hour

[bigpooch]

Right. One can't conclusively say just because player A's
win rate has been higher than player B's win rate every year
that A has a higher win rate. And obviously you could not
even conclude that A even played any better! Good enough
counterexample.

[tubbster]

This is an example of Simpson's Paradox, which is pretty neat. It's pretty powerful because it allows you to manipulate data. For example, one drug can claim that their drug works better in men and in women, while another can claim that theirs works better in the population as a whole, and both can be correct.