Predicting BB/100 based on other stats

[Nate tha' Great]

Hi all,

This is another follow-up in the discussion of various statistical metrics and their relationship to win rates. I asked people for their data in a separate thread here , but being an impatient guy and all, I decided to pull up my own databases and see what I could gather.

The database I'm working with, taken from www.pokerhandhistories.com, contains approximately 500 players who played at least 1,000 hands of $15/$30 Party Poker hold 'em. My goal was to use regression analysis to determine which stats have the strongest relationship with BB/100 (win rate). The vast majority of these hands involve full table play, so the specific results obtained will not be applicable to players who primarily play shorthanded, though the same principles should apply.

It turns out - and I'm skipping some of the methodological detail here - that you can explain about 60% of BB/100 with reference to just three statistics:

-VPIP
-W$WSD (Won $ when seeing showdown)
-W$WSF (Won $ when seeing flop)

The other statistics don't have a statistically significant impact on win rates, after these three numbers are accounted for. This will sound counterintuitive at first, until you consider that the other stats will feed into these metrics in some way, shape or form. For example, there is a strong correlation between PFR%, and W$WSF, since frequent preflop raises limit the number of players in the hand, and allow you to take initiative after the flop and pick up more pots. Similarly, there is a strong inverse correlation between WtSD (went to showdown) and W$SD (won at showdown); avoiding showing down at bad times should increase your W$SD, but it's showing down winners that's really what impacts your bottom line in terms of win rate.

Specifically, the equation specified by the regression equation is as follows:

(Note: stats are specified in whole numbers rather than in decimals or percentages. For example, a VPIP of 20% should be represented as 20, and not .20).

BB/100 = (.753 * VPIP) - (.0102 * (VPIP^2)) + (.435 * W$SD) + (.658 * W$WSF) - 56.12

For example, using this equation, a player with a VPIP of 18, a W$SD of 55, and a W$WSF of 35 would be expected to have a win rate of 1.08 BB/100.

Or, a player with a VPIP of 18, a W$SD of 52, and a W$WSF of 38 would be expected to have a win rate of 1.75 BB/100.

A LAG with a VPIP of 30, a W$SD of 49, and a W$WSF of 31 would be expected to have a win rate of -1.00 BB/100.

An expert with a VPIP of 19, a W$SD of 54, and a W$WSF of 39 would be expected to have a win rate of 3.66 BB/100.

And so forth.

One thing a few of you may notice is that higher VPIPs appear to be associated with higher win rates. This will seem counterintuitive at first, until we consider that there are strong inverse correlations between VPIP and W$SD, and VPIP and W$WSF. In other words, a player with a 30% VPIP would likely have some very profitable results if was in fact able to maintain good W$SD and W$WSF rates. However, it is unlikely that he would do very well in these categories, since he'd be coming in with a lot of weak hands that wouldn't win as many pots, and since his opponents would be making some correct adaptations to his play.

That said, a player with a VPIP of 20, a W$WSF of 38, and a W$SD of 53 would be expected to earn quite a lot more (in fact, about 2.00 BB/100 more) than a player with a VPIP of 15, a W$WSF of 38, and a W$SD of 53. In other words, the fewer hands that you play, the more pots and showdowns you need to win in order to make up for this.

The relationship between W$WSF and W$SD themselves is a little bit more ambiguous. It does appear that, if we hold VPIP constant, there is some *slight* trade-off between W$WSF and W$SD, with higher aggression postflop levels leading to more pots won, but fewer showdowns won. However, for the most part they operate independnetly, and the very best players will be able to have their cake (winning a lot of pots) and eat it too (having a lot of winners at showdown).

Another, more verbally-oriented way to look at this. Perhaps the two most important skills in limit hold 'em are the following:

- Picking up more pots by protecting your hand before and after the flop, exercising good hand selection, and continuing to push when you can expect your opponents to fold. This is represented by W$WSF.

- Avoiding making and paying off with second-best hands by reading hands well, making good folds in the face of strength, and avoiding trouble hands with skilled preflop play. This is represented by W$SD.

If you can accomplish both of these things while playing more hands, you'll do better than if you play fewer hands. However, for most people it is very hard to play too many hands while maintaining strength in these elements of their game.

A third essential characteristic of playing winning hold 'em is the ability to extract the most money out of your winning hands. I don't believe that any of the Pokertracker stats do a very good job of accounting for this ability, and it is probably represented in the 40% of win rate the regression equation could *not* explain. Somebody who is really expert in this department should do a little bit better than the number obtained from the equation.

As a final note, none of this analysis distinguishes running well from playing well. If you're running well, your VPIP, W$WSD, and W$WSF should all increase, which in turn will increase your win rate. Over the long-run, playing well will be a proximate cause of higher W$SD and W$WSF numbers, but W$SD and W$WSF exert the largest *immediate* influence on win rate.