Some interesting statistics on ROI variance

This is an example intended to help anyone who does not fully understand how significant variance can be over large numbers of games. I know it is talked about ad nauseum here, but it still seems to be underestimated by many and since it is probably the single most important concept for any player who wants to take their game seriously to understand, I though I would share some interesting statistics.


In an attempt to understand what a difference a weekend can make, I played at nearly identical times over the past two weekends:

Last weeked
------------
SNGs: 700
ROI: 25.7%
Variance within any given 100-game sample: 61%

This weekend
------------
SNGs: 750
ROI: 3.4%
Variance within any given 100-game sample: 76%


After studying the differences between the two sets it appears that the main reason for the difference was that I was getting lucky in the early game with a significant # of double-ups and large pots so that I was coming into the middle-game with far mor chips than this weekend, where I was also underperforming on the bubble (even in relation to my low chipstack).


Obviously this is an extreme example, but the point being that to many players 750 SNGs represents many weeks (or even months) of playing and that even 1,000 sngs is truly insignificant in terms of ROI. Over my last 10,000 SNGs I have found that any given sample of 1,000 tournaments has a variance of roughly 17%. I potentially play a style that aggravates the variance a bit, but in other ways I am less prone than most.


So what I find the most difficult about poker is when making adjustments to our game, how do we determine whether or not these new "plays" or "styles" actually gave us any improvement? I think it is actually impossible in the short-term (at least with the resources most of us have). For me this is the reason why poker is both so compelling and so hideously aggravating!


-asimo

dedicated to freeing the Variance Slaves!

[citanul]

what does:

[ QUOTE ]
Variance within any given 100-game sample

[/ QUOTE ]

mean?

c

[tigerite]

You played 700-750 SNGs in one weekend?! Even 10-tabling continuously that's impossible.

[downtown]

So you play 700-750 SNGs a weekend?

Do you dream of electric sheep?

[Shilly]

What level is this at?

[downtown]

[ QUOTE ]
You played 700-750 SNGs in one weekend?! Even 10-tabling continuously that's impossible.

[/ QUOTE ]

At least I'm not going crazy, I was thinking the same thing.

[citanul]

[ QUOTE ]
You played 700-750 SNGs in one weekend?! Even 10-tabling continuously that's impossible.

[/ QUOTE ]

10 tabling -> ~14 an hour?
700 sngs at 14 an hour = 50 hours.

very doable. /images/graemlins/smile.gif and playing 20 tables at once makes it a laugher!

c

[tigerite]

Barely, unless he didn't sleep, or is including Friday night.

20-tabling, sure, but I don't think there's many people that do that, other than raptor.

[eniven]

Wow, that's an interesting post. Thanks.

[ QUOTE ]
what does:

[ QUOTE ]
Variance within any given 100-game sample

[/ QUOTE ]

mean?

c

[/ QUOTE ]

This just means that if you take any sample of 100 consecutive tournaments from within the 700 (or 750) the number is the differrence between the group with the highest ROI and lowest ROI.

For example, in the 750-sng weekend there was a run of 100 tournies with an ROI of +41%, and a 100-sng run with an ROI of -35%, thus the variance within any sample of 100 sngs was 76%

[raptor517]

[ QUOTE ]
Barely, unless he didn't sleep, or is including Friday night.

20-tabling, sure, but I don't think there's many people that do that, other than raptor.

[/ QUOTE ]

i know of like 4 people now that do it, and im sure there are others.. though i doubt it is approaching the double digits. i dont really do it any more as it requires an insane amount of concentration that cant be held for long periods of time. i dont recommend it to anyone.

also.. i havent been playing much poker at all, as my hours are consumed by being a college student in pledgeship. soon though.. it will all be over.. and i should be able to play 40ish hours a week. im looking forward to making money again.. holla

what I dedicate as a "weekend" is not limited to Sat/Sun.

the results I can assure are valid, whether you find them useful or not.

[multifast1]

When I first read it I assumed "from one weekend to the next" meant he was comparing one weeks worth of playing to the next weeks.

He makes some great points to keep in mind but the variance of 100 games within the 700 or 750 blocks is totally meaningless... unless you consider 100 game sample size to be significant. Now maybe you should look at the variance of any 750 game block within a set of say 5000.

I think you main point I took is that it's near impossible to tell if any adjustments you make are actually working, or if it's due to dumb luck. Even 750 games later you still can't be sure if your increased ROI is due to you getting better or stumbling over a luckbox.. Humbling thought indeed.

great question, because variance does appear to discriminate by buy-in. Actually, the lower buyins just dictate a style of play that is more prone to variance, I think. I think there are more +EV opportunities that have greater inherent variance in the 11's than in the 50's. For example, calling QQ to two pushes in level 1 is more +EV in the 11's (and the situation occurs more frequently as well). I'd be curious whether other people find this to be true.

This sample is from the 11's.

variance is wins and losses am I right?

[citanul]

[ QUOTE ]
variance is wins and losses am I right?

[/ QUOTE ]

variance is neither wins and losses nor "the difference between two things," (as it is being used by the original poster) in statistics.

c

[sofere]

[ QUOTE ]
[ QUOTE ]
what does:

[ QUOTE ]
Variance within any given 100-game sample

[/ QUOTE ]

mean?

c

[/ QUOTE ]

This just means that if you take any sample of 100 consecutive tournaments from within the 700 (or 750) the number is the differrence between the group with the highest ROI and lowest ROI.

For example, in the 750-sng weekend there was a run of 100 tournies with an ROI of +41%, and a 100-sng run with an ROI of -35%, thus the variance within any sample of 100 sngs was 76%

[/ QUOTE ]

Thats the Range of ROI, not the variance.

[Nicholasp27]

sample variance is the sum of the square of the differences from the mean of each data point in the sample divided by n-1

range is the highest data point minus the lowest data point

std deviation is the square root of variance


to find roi variance in your stats:

1) determine roi for each set of 100 sngs
2) add up all of these rois and divide by number of sets of 100...this is your mean
3) subtract each roi from the mean separately
4) square each of these differences
5) sum these squares from #4
6) divide answer in #5 by n-1, where n is # of sets of 100

[citanul]

[ QUOTE ]
sample variance is the sum of the square of the differences from the mean of each data point in the sample divided by n-1

[/ QUOTE ]

and then, of course, when you're done doing that calculation, you can be left with a number that is totally meaningless to you, but at least it will actually be variance!

c