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#1
12-07-2005, 02:16 PM
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Are Winrates Normally Distributed?
BIG thanks to Justin A for coming to me about this. He was the one who first noticed it and most of this was his idea. I had some free time last month on my flight to Vegas so I did most of the tedious Excel stuff.
Also, Barron, I know this doesn't have anything to do with high stakes poker, but I feel that it is an interesting topic that many posters will be interested in. If you don't agree, please move it to MHHUSH. I am not a statistician but based on my not-quite-intermediate understanding of statistics, this is what I've come up with. Methodology: I took a database of about 150k hands at one limit. I took these hands and put them into Excel. I chopped them up into blocks of hands (in chronological order) and plotted them in a histogram. Theory: BB/100 is the average BB you will win every 100 hands. If you've played a large enough sample of hands (technically 50 samples should be enough, so 5,000 hands), the sample should behave normally and form the shape of a bell curve. Results: The following graphs are of BB/25, BB/50, BB/100, etc. Notice that they are skewed toward the low end. This would suggest that winrates are not normally distributed, which would mean you are more likely to run good but the bad runs will be worse. I don't remember the exactly mean but figure it's somewhere between 2 and 2.5 BB/100. for BB/10 it would be between 20 and 25, etc. Can someone with a better understanding of statistics explain this?       
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#2
12-07-2005, 02:23 PM
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Re: Are Winrates Normally Distributed?
i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up
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#3
12-07-2005, 02:57 PM
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Re: Are Winrates Normally Distributed?
[ QUOTE ]
i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up [/ QUOTE ] Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts.
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#4
12-07-2005, 03:15 PM
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Re: Are Winrates Normally Distributed?
[ QUOTE ]
[ QUOTE ] i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up [/ QUOTE ] Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts. [/ QUOTE ] It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be.
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#5
12-07-2005, 03:32 PM
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Re: Are Winrates Normally Distributed?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] i can't speak on math, but i know that people tend to play a lot when they're down and tend to leave when they're up [/ QUOTE ] Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts. [/ QUOTE ] It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be. [/ QUOTE ] If Josh wins his first hand and quits immediately, then plays again later, then will the hands from his second session be put in the same block as his first hand? If so, then it doesn't matter if Josh locks up his wins. If Josh's one hand forms its own block, then that's different -- but I don't think that's what is happening.
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#6
12-07-2005, 04:30 PM
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Re: Are Winrates Normally Distributed?
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Astro, that shouldn't matter since even if Josh leaves, his next session gets grouped in the stats (if I understand correctly). This would only matter if Josh tilts. [/ QUOTE ] It should matter. If you quit early to lock up a win, and "play through your downswings," then you're going to have a smaller winrate, and the center of your distribution will be more to the left than it could be. [/ QUOTE ] If Josh wins his first hand and quits immediately, then plays again later, then will the hands from his second session be put in the same block as his first hand? If so, then it doesn't matter if Josh locks up his wins. If Josh's one hand forms its own block, then that's different -- but I don't think that's what is happening. [/ QUOTE ] Ok you're right about that. However, what I think Astro was getting at and I know I was, is that people play longer when they are losing. Over a large sample, this is going to mean that you play more hands when you: have a worse image, a tougher table, less confidence, etc. If you put more hours in with a lesser expectation, you move your curve to the left. If you practice excellent game selection without regard to your immediate results (aka don't tilt - just like you said) then your point stands. Many people do not do this.
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#7
12-07-2005, 03:34 PM
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Re: Are Winrates Normally Distributed?
This is a cool idea.
I don't know about the conclusions, though, as the distributions look pretty normal to me. The variance is pretty high, so even with a lot of observations its not that surprising to see things look kind of choppy. Another suggestion to redo the graphs using the same number of "bins" (divisions for bars) in each histogram. You have a lot more bins in the first couple, which makes things look slower to converge on a normal than they probably are. I think something might be wrong with your BB/100 histogram. It doesn't look like there are 1500 observations there.
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#8
12-07-2005, 02:35 PM
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Re: Are Winrates Normally Distributed?
It looks pretty close to normal here, but I think the way you did the sampling is not quite right.
You need to draw random samples from the total group of hands. Chopping them up into blocks is easier, but not appropriate. The way you have done it, we might find a different results using a different database.
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#9
12-07-2005, 02:45 PM
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Re: Are Winrates Normally Distributed?
[ QUOTE ]
It looks pretty close to normal here, but I think the way you did the sampling is not quite right. You need to draw random samples from the total group of hands. Chopping them up into blocks is easier, but not appropriate. The way you have done it, we might find a different results using a different database. [/ QUOTE ] i could easily randomize it
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#10
12-07-2005, 02:54 PM
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Re: Are Winrates Normally Distributed?
[ QUOTE ]
[ QUOTE ] It looks pretty close to normal here, but I think the way you did the sampling is not quite right. You need to draw random samples from the total group of hands. Chopping them up into blocks is easier, but not appropriate. The way you have done it, we might find a different results using a different database. [/ QUOTE ] i could easily randomize it [/ QUOTE ] You can easily randomize the order of the hands in your database, but that is not what I was suggesting. You need to randomly select X number of hands and compute the win rate for that sample. Then you need to do it over and over and over again, each time selecting X number of hands from the total set of hands. Then you plot the win rates for each of those samples. I don't know of any easy way to do that in Excel. It could be done in some statistical packages, but a data set of that size is too big for a desktop computer, it would need to be run off of a server or a mainframe computer. There is type of statistics called Bootstrapping which does not rely on the assumption of normality. I assume there is some bootstrapping software that does this kind of thing, but I don't know enough about it.
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