How Accurate Is Aggression Factor For Small Sample Sizes?

[gaming_mouse]

This question comes up when you use PlayerView. You have 20, 50, 100 or more hands on somebody. You look at their postflop aggression factors when making decisions against them. But can you trust these numbers? I suspect that they are not that accurate, but I really don't know.

I thought of a good way to answer this question using MonteCarlo simulation, but I'm busy at the moment and was hoping someone else would be kind enough to do it. All you need is your PT database and some knowledge of a basic web scripting language like PHP or Coldfusion (or anything else that can do queries).

Let's take the 50 hands example. You'd write a script that would query 50 random hands from your own database. It would then compute the PF aggression factor for each street based on that sample, and add them to a list. Then it would take a another random sample of 50, and do the same thing. You'd do this maybe 1000 times and in that way bootstrap the distribution of each agg. factor for 50 hands. The main stat of this distribution we'd be interested in is its SD -- we want to know how accurate that stat is after 50 hands. Same thing for 100 hands, etc.
This is just a rough sketch of the algorithm. There are a number of implementations I can think of.

You could argue that this is player dependent (ie, your distribution may different from mine) but my instincts tell me it really won't be unless you happen to be extremely loose, which I don't think many players here are. So it would be a valuable experiment and should be relevant to everyone.

Anyway, if no one does it, I'll get around to it eventually, but I'm really curious and would appreciate any help.

TIA,
gm

[elitegimp]

bump because I'm interested but have no knowledge of anything that can query a DB.

Sidenote: I first read this as "pre-flop" aggression, and that would be real easy to simulate without the database queries. Good thing I re-read the post before replying [img]/images/graemlins/smile.gif[/img]

Anyway, I'll ask some CSCI friends for some help if nobody steps up to the plate in the next couple days.

[Reef]

I would guess it is comparable to how accurate VPIP and pfr are over a small sample size

[gaming_mouse]

[ QUOTE ]
I would guess it is comparable to how accurate VPIP and pfr are over a small sample size

[/ QUOTE ]

No, not at all. Or at least: there is no simple reason I see to think so. First of all, note that every hand played counts towared VPIP and PFR, wheras only hands where you see a flop count toward flop aggr, only hands where you see a turn count toward turn aggr, etc. So we should expect river aggr. to converge to its true value most slowly.

Also, note that aggr is a different kind of stat than a simple percentage stat. It's the proportion of bet/raise to call. So it may have a different kind of distriubtion than the binomial -- I can't think now what it would be.

In any case, I'm expecting the accuracty of these stats for small samples to be much lower than people give them credit for, but hoping they won't be.

gm

[elitegimp]

[ QUOTE ]
I would guess it is comparable to how accurate VPIP and pfr are over a small sample size

[/ QUOTE ]

I disagree because with a small sample, VPIP and PFR are still primarily related to the 169 possible hands you can be dealt (for the most part), while post-flop aggression involves the added chance that you hit on the flop/turn/river, plus the need for your opponents to have hands hit also. I think there are many more variables affecting total aggression than VP$IP and PFR.

In other words, PFR and VP$IP are percents used in binomial distributions so we can calculate what we expect the distribution to look like even for small n. Post-flop aggression depends on your holdings (like PFR and VP$IP), but also depends on the flop (of which there are 19,600 possible outcomes), as well as your opponents style of play / their holdings.

edit: D'oh, beaten by gm (both in time and in content)