February 16, 2010

When's The Best Time to Play? An Empirical Answer...

First, a blog note: Just like last season, I will recap High Stakes Poker action, but probably not every episode, but more like a post every other episode or so discussing the biggest hands. The Season 6 premier aired on Sunday, so some time next week I'll try to put up a post on the first couple of eps. Gabe Kaplan did promise that durrrr and Phil Ivey will be playing in every episode, so that's certainly something to look forward to.

On to the main purpose of this post...It seems to be a general assumption that weekends are the best times to play, and during the week, evenings are best. Well, I did some data analysis to test this idea. All data are hands from 15 mid-stakes full ring FTP regulars. I took these hands and ran the following linear regression:

pi_i,t = a_i + b_1*1{weekend} + g_1*h1_t + g_2*h2_t + g_3*h3_t + g4*h4_t + g5*h5_t + error_i,t

To clarify: pi_i,t represents the winnings in a given hand for player i at time t. The right hand side of the equation is made up of data (1{weekend}, h1_t}, etc.) and parameters to be estimated (a_i, b_1, g_1, etc.). a_i represents a fixed effect for player i in predicting pi_i,t. That is, some players win more on average than other players and I don't want to think that, for instance, weekdays are more profitable only because the players within this sample who have higher win rates at all times play more of their hands on the weekdays. I want to hold fixed a player's skills and ask at what times they make the most money.

1{weekend} is an indicator variable that equals one when the hand is played on Saturday or Sunday, and zero when it is played on the other five days of the week. The b_1 parameter estimates what effect a hand being played during the weekend has on that hand's expected winnings.

The hk_t variables are also dummy variables. I put each hand into one of six four-hour blocks: 12:00-3:59am, 4:00-7:59am, etc.. The FTP hand stamp records EST, so those are the times given here. In order to make the regression work, one category must be omitted (if you have no clue why this is the case, it's too much to explain here, but if you remember a little bit of undergraduate econometrics, it's because the sum of the time dummies and the player fixed-effect dummy are then co-linear). For this regression, I omitted the first four hours of the day, so the interpretation of each coefficient is the change in predicted profitability of one hand RELATIVE to the first four hours of the day.

If you don't understand or aren't familiar with regressions, here's another way of thinking about it. Since all the RHS variables are dummies, you can think of it just as taking how much better each player is on weekends than weekdays, and then taking a weighted average of that statistic, where the weights are given by the total number of hands that each player has in the data set. Doing similar calculations for the hour dummies will yield coefficients identical to those obtained from regression estimates.

Here are the results on the coefficients of interest, in bb/100 hands:

b_1(weekend effect): 0.77
g_1 (4-8am): -1.26
g_2 (8am-noon): -0.38
g_3(noon-4pm): -1.26
g_4(4pm-8pm): -2.52
g_5(8pm-midnight): -0.84

A note of caution is that none of these coefficients are statistically significantly different from zero. In other words, it could be due to just random variation that the weekend turned out to be more profitable in this data. Since there's such wide variance in profits across hands, this isn't too surprising. So proceed with caution, but the data seems to indicate that: i) weekends are in fact more profitable ii) 8pm - 4am EST are the best times to play. These results pretty much corroborate what you might think. The main surprise is that the 4-8 pm EST time block seems to be so bad. In fact this is the coefficient that gets closest to statistical significance, with a 95% confidence interval of (-5.55, 0.51).

Note that I did not include interaction terms in the explanatory variables, so I can't pick up things like: i) better players are more better on weekends/during certain hours ii) certain hours are more better than other hours on weekends than weekdays. And, of course, since I put the hours into groups, I can't say anything about how things change within the time blocks I have.