Rates of convergence for various stats

[Cerril]

I'm trying to get together a list of the various important stats and trying to figure which converge most quickly to useful numbers (say +/- 10% of their 'true' values).

So let's run down the list, add any I miss.

VP$IP: 1k hands, though you can make generalizations as early as 50 hands (or earlier, as with opponents); here's our 'standard' number

PFR: About twice VP$IP

WR: Never. Well not really, but this is terribly unreliable. You can make generalizations starting in the 50k hand range, but 100k or 200k+ are better.

WSD: Probably about ten times VP$IP, and you can't make generalizations with less than several hundred hands.

W$SD: About twice WSD

Positional stats: The same number of hands played in that position (so anywhere between about five and about forty times as many hands).

Hand stats (AK, etc): Way too many. At least 100 times more.

Folded to Steal: Tricky. I'm thinking maybe twenty times VP$IP, maybe ten.

Attempt to Steal: About the same.

AF: This seems to converge pretty quickly, maybe two to five times VP$IP

Anything else that's important? I'm trying to have an idea in mind when I talk about my stats, what sort of things I can say 'I have this number' and what sort I can say 'I can't say exactly, but it's around here,' and for which I can say 'I have no idea, only this number at an insufficient number of hands.'

[Siegmund]

A great many of the things on your list are statistics of the form (#times a player took a particular action)/(#times a player was in a given situation).

These all will follow the classic "expected number of actions = n*p, variance = n*p*(1-p)" form. For rare events, np(1-p) is very nearly np. If you want these 'good to within 10%", you need mean/stdev > 10 for 1-sigma confidence, mean/stdev > 20 for 95% confidence.

So, a useful rule of thumb is your level of certainty is proportional to the square root of the number of times you see a player take the action you are interested in.

After you see me take an action 100 times, your estimate of how often I do it should have a standard error 10% of the frequency: that is, if I put money in 100 pots out of 1000 my VPIP is 10±1; 100 pots out of 500, 20±2; 100 pots out of 333, 30±3, etc.

To see me raise 100 times you probably need to watch something like 1200 hands vs. 600 to see me VPIP, as you estimated. To see me go to showdown 100 times? Maybe 2000. To see me raise in blindstealing position 100 times? Might be 2000 hands at a very tight table, but could be 10,000 or more at a loose passive table. To see me checkraise on the flop 100 times? Something like 20,000 hands maybe.