Quantifying Variance – Heads-Up Tilt Calculator
Quantifying Variance is a biweekly column in which we’ll take a look at some of the math underlying poker, with the goal of understanding just how probable or improbable various occurrences actually are, and how to tell the difference between what is random and what is not.
Do you know how much you tilt, or how much it costs you? It can be hard to tell. Losing streaks will happen by chance as well as through tilt, and they feel bad no matter the reason. Our minds have a way of playing tricks on us, and it can be easy to convince yourself that you’re just getting unlucky when you are in fact on tilt, and vice versa. The first goal that I set for myself in this series of articles was to find objective evidence for tilt, a goal which I finally made good on in the most recent instalment.
The nutshell version of my findings is that individual players’ responses to winning and losing streaks can be quite idiosyncratic, and hard to discern through the random noise, but that overall it’s clear that most players experience more losing streaks of around 4 to 8 games than they would if their win rates were consistent. It would be nice, however, if we could get some handle on how much an individual player is prone to tilt.
So, to finish off this study of variance and tilt in heads-up sit-and-gos, I’ve built a simple tilt calculator using Google Spreadsheets to help you analyze your statistics – or someone else’s – and determine if you’re tilting and how badly, as well as when it happens, and an estimate of how it’s impacting your bottom line.
How to use the calculator
The source copy of the spreadsheet is locked to be read-only, so the first thing you’ll need to do is make your own copy of it so that you can edit the data. You can either Select All, then Copy and Paste manually, or you can create a new spreadsheet, then click the tab at the bottom of the Tilt Calculator sheet and choose “Copy to…” and send it over that way.
Once you have an editable copy of the sheet, you need to enter your own data into the green cells only. All the other cells (including “Single Losses”) need to be left untouched, as their values are computed automatically based on the data you input.
Sharkscope only provides streak data to paying users, so you will need at least a bronze subscription, unless you use tracking software which can provide you the same data. Be sure to use the advanced search filters so that you are getting data only on heads-up matches – including losing streaks from other formats will of course throw the calculations off entirely.
Note that the streaks entered into the green boxes are exact streaks, as given by Sharkscope. For example, “2-Streaks” means streaks of exactly two consecutive losses, not including streaks which are extended to three or more games. The cumulative streaks (i.e. streaks of at least the given length, including longer ones) are calculated automatically by the spreadsheet.
Once you’ve entered all your data, look at the Win Rate and ROI Loss columns. The win rates represent your historical odds of winning the next game after having lost the specified number of games in a row. If, like most people, you are inclined to tilt, you will notice that many of these figures will be below your overall win rate.
The ROI loss is an estimate of how much of your overall profitability is lost due to playing worse than your average while on a losing streak of the given length. It is calculated by taking the difference between your win rate at that point and your overall win rate, and multiplying by the proportion of your total games accounted for by these streaks. (There is an additional factor of 2 included, because a 1% change in win rate translates into a 2% change in ROI.)
Typically, these values will be only a few tenths of a percent, because shorter streaks probably don’t make you tilt much, while longer ones account for a much smaller fraction of your overall volume. Negative numbers represent an increase in overall ROI, because your win rate for that streak length is actually higher than your overall average.
At the bottom of the spreadsheet is the Total ROI Loss, which is the sum of all the individual values. Based on the users I’ve looked at, a figure of about half a percent is typical. If yours is close to or above 1%, then you probably have a serious tilt problem which is eating into your profits – for heads-up grinding, a difference of 1% in ROI is huge! Conversely, if you’re closer to 0% (or negative), then you should congratulate yourself on being more level-headed than the average heads-up player.
A couple of grains of salt
There are two things you should keep in mind before putting too much weight on the calculator’s results. The first is sample size. Most of the users I’m looking at have samples of at least 10,000 games. If you’re using a sample of fewer than 5000 or so, the results are likely to show a lot of random noise, particularly for the longer (and therefore less frequent) streaks.
Secondly, the tilt calculator can only figure out whether or not losing several games makes you more likely to lose the next; it can’t tell you why that is. I’ve been assuming the reason is tilt, but there are other, non-psychological effects that could cause similar results, which would be hard to distinguish.
If your play is improving over time as you learn the game, then your early games will have been played at a lower win rate than your later ones, which could result in more streaks in general than if you were playing at a steady win rate. Also, if you tend to use the rematch feature a lot, some streaks might be the result of playing a long series of games against a slightly stronger or weaker opponent than your average competition. There are other possibilities as well – for instance, multi-tabling combined with a poor internet connection could cause a player to lose many games at once upon being disconnected.
All that said, if the calculator is showing a significant ROI loss on a reasonable sample size, then you’ve got a problem of one form or another and recognizing that is the first step to fixing the leak. It might be that you need to take a break after a few losses, or stop rematching an opponent who annoys you, or play fewer tables when the cards are running bad. On the other hand, if your stats show that you don’t have a problem with tilt, that’s good to know as well.
Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.