Some stat discussion

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This thread and other threads have made me believe that the AF is pretty much a useless stat unless you have mined hands on villains.


So does any of you stat guys (Leader) know wther some of the other aggression stats you can use in HUD converges faster? Namely the "aggression frequency"?

I am not quite sure what that stat measures, but I beleive its how often a player either bets or raises on any (postflop) street

[Leader]

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This thread and other threads have made me believe that the AF is pretty much a useless stat unless you have mined hands on villains.

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I would agree with that.

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So does any of you stat guys (Leader) know wther some of the other aggression stats you can use in HUD converges faster? Namely the "aggression frequency"?

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Aggression frequency is a much better stat in terms of reliability because it's a basic binomial random variable. Variables of this nature either happen or don't. So in this case, there's either a bet or raise or there's not. So it converges at the same rate as VPiP/PFR with the stipulation that it only occurs post flop. Convergence in all these spots is about number of observations. In contrast, AF you have three binomial interacting. Wikipedia has a good article on binomial random variables. People really should read it so that they can understand the basic dynamics. This is Stat 101 stuff BTW not like my new friend the Box-Jjong statistic, which estimates the joint probability that all preceding lags in a time series are non-significant.

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I am not quite sure what that stat measures, but I beleive its how often a player either bets or raises on any (postflop) street

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bets and raises as a % of total actions.

All this said, I rarely use any postflop stats aside from WtSD anymore. Pre-flop stats are an effective and IMO essential tool if available, but postflop is the realm of reads, experience, and theory a million times more then it's the realm of "% folded to river c/r" or some other crazy stat that happens once every 500 hands. Even something like AFreq is going to converge slowly, and in the end, it tells you very little because it's so broad. So you're faced with a paradox with post flop stats. Stats that converge over any reasonable time frame tell you almost nothing about how villain plays in any spot and specific stats take 50K hands to converge by which time villain probably doesn't even play the same.

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Leader, are you saying that WTSD converges much faster than AF?

I've always been under the impression, that WTSD was one of the stats, that took longest to converge.

[Absolution]

I've found aggression factors fairly useless for the most part. I like to have flop aggression up though because it can tell you if someone likes to overplay the flop. The other thing about aggression factor is that an overaggressive player can have the same aggression factor as a raise or fold player. The stat isn't going to tell you which one it is. You might see an aggression factor of 3 and think, well I can call down here now because he's likely full of it, but he might actually just be the type of player that raises when he hits and folds when he doesn't. Also, a small aggression factor doesn't mean a guy won't make weird bluffs and value bets with 2nd pair.

[Oink]

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The other thing about aggression factor is that an overaggressive player can have the same aggression factor as a raise or fold player. The stat isn't going to tell you which one it is.

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This is the other reason why I like the aggression frequency better.

[Absolution]

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The other thing about aggression factor is that an overaggressive player can have the same aggression factor as a raise or fold player. The stat isn't going to tell you which one it is.

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This is the other reason why I like the aggression frequency better.

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So an overaggressive player would have a somewhat high aggression frequency, whereas a raise or fold player is going have an aggression frequency around 90%. That sounds good to me. Street by street aggression frequency would also be more useful than aggression factor.

[Oink]

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The other thing about aggression factor is that an overaggressive player can have the same aggression factor as a raise or fold player. The stat isn't going to tell you which one it is.

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This is the other reason why I like the aggression frequency better.

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So an overaggressive player would have a somewhat high aggression frequency, whereas a raise or fold player is going have an aggression frequency around 90%. That sounds good to me. Street by street aggression frequency would also be more useful than aggression factor.

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No. A raise/fold guy who sint raising that much but have the same AF as an overaggor guy will have a lower aggr freq.

I have been experiementing a bit and it looks real promising using the frequency instead.

[rzk]

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the probability of a bet or raise is also 30%

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I don't think you can do that. Bets and raises are distinct random variables. For example, the SD of two binomial with mean .15 is about 9% greater then the SD of one with mean .01 and one with mean .29 after 10K hands.

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that's true if we are taking the sum/average of two binomials. but if we select the result of one binomial distribution with probability 1/2 and the result of the other binomial distribution otherwise, then it's exactly the same as a single binomial with mean .15. this is obvious because the resulting distribution will simply correspond to selecting 1 with probability 1/2*.1+1/2*.29=.15 and selecting 0 otherwise. our case corresponds to this latter scenario since the definition of AF doesn't distinguish between bets or raises so all we care about is the probability that either a bet or a raise happens. the only thing is we don't know this probability exactly but whatever it is the standard deviation is clearly less than 5% in 100hands since 5% is the maximum possible sd for a binomial. but it's pretty close to 5% if that probability is around 30%.

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sqrt((5/30)^2+(5/30)^2)*(30/30)

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I see where the numbers come from but I'm not sure why your doing it. I guess you're saying that the SD of one binomial RV divided by another is the sqrt of (variance of the first plus the second) times the ratio of one to the other. Conceptually I have some concerns about this. Could you link me to something that talks about that?


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i studied this formula in one of my undergrad physics classes. it's not an exact expression for the sd of a ratio but it's a good approximation. it can be derived from taking F(A,B)=A/B where A and B are your two binomials and expanding dF=(dF/dA)*dA+(dF/dB)*dB = F*(dA/A - dB/B). the estimate gets more and more precise as the sample size increases because then dA and dB get smaller and smaller compared to A and B.

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of course a better, but slightly longer way of doing is is to examine data from pt for small samples of hands and see how AF fluctuates. or better yet, write an sql query.

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Well different AF are going to converge at different rates so this would be kind of hard. It's not impossible or statistically unsound though.


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i agree that this is statistically sound but disagree that this is hard. it doesn't matter that different AF converge at different rates. you just take any AF you care about (flop, turn, total, whatever), and examine how it fluctuates. it's not normally distributed of course but who cares if all we want to know is how good the estimate becomes after so and so hands. if i'm feeling not too lazy i might write an sql query to do that for me at some point.

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as for my 100th post calculation, what assumptions are you wondering about? if you mean the relationship between wtsd and fold to bet, i got it simply by looking at pahud stats various players. these variables are strongly correlated.

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While I believe you looked at it and saw a good correlation, these things have some complex dynamics. It's not as if fold to bet=1-WtSD.

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yes, of course, i never claimed otherwise. but this correlation is sufficient to derive an order of magnitude correction to the AF, which was my concern. with the limited number of hands we have on villains that's all we really care about.

[rzk]

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Leader, are you saying that WTSD converges much faster than AF?

I've always been under the impression, that WTSD was one of the stats, that took longest to converge.

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as for which converges faster, wtsd or AF, it's misleading to think that wtsd converges faster. for our purposes AF converges faster in the following sense:

over all villains, AF is usually somewhere between 0.5 and 2.5, an interval of 2.

over all villains, WTSD is usually somewhere between 30% and 45%, an interval of 15.

over 100 hands, the error in AF is roughly 0.4 or 1/5 of the interval in question.

over 100 hands, the error in WTSD is roughly 8% or 1/2 of the interval in question.

so after a 100 hands we will have a much better idea of how the villain compares with other villains in terms of AF than in terms of WTSD.

but i definitely agree that aggr. freq. is a better measure, as i talked about in my 100th post calculation. in fact this is precisely what my "adjusted AF" attempts to approximate from regular AF and WTSD as initial data. i did this calculation because nobody seemed to be using aggr. freq. and all people looked at was regular AF and WTSD.

[Absolution]

I just pulled up some tables and examined agg. freq. vs AF + WTSD and after 100 hands they actually seem to agree most of the time. If someone has a low aggression factor (say 0.5), they tend to have agg. freq. around 20. If someone is 60/2/1.4/40 or 25/18/1.8/32, they tend to have agg. freq. around 45, which makes sense. If someone is 23/21/2.75/50, they have an agg. freq. around 65. So, aggression factor seems to do a good job of predicting the aggressiveness of a player, but you need to have it in the context of the other numbers, whereas agg. freq. seems to sum it all up nicely in one number.