In favor of Smaller Sample Sizes and Beyesian Statistics

Matt Walker · #1 06-28-2005, 02:32 PM

I realize that this may come across as heresy on these boards but I think we are all getting way to preoccupied with huge sample sizes. Someone posts "here are my results through 200 SNGs" and everyone says "Come back after 1000 more."

Large sample sizes have just as many problems as small ones. After playing 1000 tournaments it's unreasonalbe to use the entire data set to try to model someones ROI because any donkey is a better player after that much practice. Also in the several months that it took to play these extra tourneys, the competition is better. How can you reasonably construct a confidence interval around this, and why is it better than after 200 tourneys?

Also I think it would be better to do all these problems using Bayesian statistics. For example if ZeeJustin says I think I'm a 25% ROI player and playes 500 and has an ROI of 25%, it would be nonsense to simple construct a simple confidence interval around his data and say "No way, statistics says this data is only accurate to x percent with 95 percent confidence." or "In the last 2 years, your total ROI was 10 percent at this level so you're just on a heater." Bullshit. We should all try to use some sort of previous assumptions when working these problems, and then the smaller sample sizes will be accurate enough.

Matt

gildwulf · #2 06-28-2005, 02:33 PM

Why is the competition better after a few months? I've been playing the 20s for a while and the competition is just as sh%%%y as always.

Slim Pickens · #3 06-28-2005, 02:40 PM

[ QUOTE ]
I thought about it a little and I'm going to take a guess as to the value of the extrinsic uncertainty in SNG tournaments. It's about 3% in a typical player's long-term ROI, and most of that is from skill drift relative to the field.

[/ QUOTE ]

a similar thought

Matt Walker · #4 06-28-2005, 02:41 PM

The main point is that you are better, but I also think the competition is constantly adjusting too. Its obvious that in a year the competition will be a lot better than it is today, and I think it is more of a gradual adjustment that you don't notice at any one day than a sudden one. Sometimes though it can be a sudden adjustment like the PVS no longer working at the 50s.

Matt

valenzuela · #5 06-28-2005, 02:45 PM

I disagree with you, I dont think the games are getting any tougher, because online poker is still getting more and more players to play, I expect thing to get more porfitable after the 2005 WSOP.

spentrent · #6 06-28-2005, 02:45 PM

Its obvious that in a year the competition will be a lot better than it is today

Why is this obvious? It's not obvious to me, I should say.

Matt Walker · #7 06-28-2005, 02:54 PM

I shouldn't say it's obvious but I do think the games are changing. More and more people are coming to this site. More and more people are multitabling. The worst players are constantly going broke. Its true that more bad players are starting to play but I don't think this can make up for the first three points. Also I was playing these games last year and can tell you that they were a hell of a lot easier when ICM didn't exist and no one nkew to push any two and rape the bubble with a big stack. Few even followed the 10x BB rule. 50 percent was attainable by many at the 10+1 level. I can only imagine we will see similar improvements in the future.

Matt

AKQJ10 · #8 06-28-2005, 03:08 PM

Very good points. Perhaps a good approach would be to model the development of a typical player in his first N games? Then "detrend" the results and identify the remaining unexplained deviation as either random noise or actual slower- or faster-than-normal development?

I'm just thinking aloud. Sounds like a lot of work, frankly, and I'm not sure if that would make sense or not.