What Is Variance?

What Is Variance?

Wednesday, 16 April 2014

Latest wisdom from Alex Rousso.

Players often tout ‘variance’ as their reason for losing, but it’s not that simple, says Alex Rousso.

Believe it or not, the term ‘variance’ is a mathematical concept, related to a statistical calculation. In poker, you might be forgiven for thinking it was just another term for luck.

Some players may have started off using the word correctly, but before long, the use of it degenerated into just another excuse for why things were going badly. “Busted last level of the night due to variance,” they would tweet.

Yes, variance is a measure of luck, but it relates more to how much luck will affect a set of results, rather than to luck itself. Randomness is just randomness. How much of it you might encounter when doing a certain thing can vary, and the term variance is one of many measures of this.

I want to take this article to make plain what variance is. I’m going to concentrate on tournaments for this article, but the same could be applied to cash games (you would simply count each hand, rather than each tournament, as a data point for a sample set).

To measure variance, the first thing you need is a set of results. The results don’t have to be all of the same type, but the more homogenous (alike in type) the data is, the more useful calculating variance will be.

Simply put, the bigger the variance, the more variation you can expect to find in your results. As a general rule, variance in poker will increase with the following:

1. An increase in the size of the player pool

2. A decrease in the edge you have in a tournament

3. An increase in your general level of aggression, and tendency to put chips in the pot.

So, for example, you might expect there to be more variance in your results for higher buy in tournaments, because the average skill level of the field will be higher, and thus your edge will decrease.

In sum, when collating a sample set, try to do so for like tournaments. That doesn’t just mean the same buy in, but also (roughly) the same number of runners, and – if you can – the same average skill level of opponents.

You should also make sure you’ve recorded every tournament you’ve played in this category, in case there have been any non-random omissions. You may think that the $30 graveyard tournament you played the other night when you were pissed might not “count”, but, believe me, you would have counted it in your results if you had won it, so be consistent!

The other major caveat is that the larger the sample set you have, the more accurately it will reflect the wider reality of your results. This is an important point. The sample set you have is only a sample: it’s a reflection of the full picture, but it will never actually be the full picture. Hence, even if you recorded your results for many years, the variance of one yearly set of results will not be the same as another year. The bigger the sample size, the closer it’ll get to the “truth”, but you’ll never get to a definitive answer – just one that is close enough.

And what counts as close enough? That’s a question for another article, but I refer the reader to articles I’ve written on the subject, for example: I’d Rather Be Lucky Than Good (Bluff Europe, August 2008) and The Vegas Trip Simulator (Bluff Europe, June 2010).

For now, I want to concentrate on what the term variance is useful for, other than, of course, sounding intellectual on Twitter when cursing your luck. There are plenty of websites which explain how to calculate variance. You’ll need a sample set, collated as of the above, and a spreadsheet. By the way, it’s often best to express your results in the terms of a parameter. In the case of tournaments, ROI is good. So, instead of plugging the individual dollar results of tournaments into a spreadsheet (busted: lost $33; cashed for $165; etc.), divide each result by the buy in to get an ROI figure. So a bustout will be -1; a cash of $165 in a $33 buy in tournament will be +4 (remember to subtract the buy in from cashes), and so on.

Using the above example, you will not only have your ROI figure (which many tournament players know these days), but also its variance. The variance is an expression of how reliable this ROI figure is. Often, you’ll find that even if your sample set is huge (say, 3,000 tournaments), there’s a decent chance that it could be very inaccurate.

You could go even further. Imagine your sample set spits out an overall ROI figure of +30%. Using the variance of the sample set, you could even query the chances that your ROI is in fact negative, yet you’ve just been lucky over this sample of results. I’m guessing most poker players would like to query the opposite: given a negative ROI, what are the chances they are actually a money making player, and they’ve just been unlucky . . .

I hope that the reader takes away the idea that variance isn’t a synonym for luck, it’s a measure of how much randomness will affect your results or, literally, a measure of deviation from the average in a given sample set. This in turn will hopefully direct the player to understand that if there’s more variance in a certain type of poker, it might take longer to realise one’s edge – whether it’s positive, or indeed negative!

Tags: Alex Rousso, variance