Poker Efficiency Rating (very long, nerdy)

[Nate tha\\\' Great]

For a long while I've thought about how we can place better context around the stats that we gather from Pokertracker in order to get an idea of just how effectively we're playing. I'm going to call this attempt Poker Efficieny Rating (PER).

How could something like PER be useful? Well, Pokertracker stats tend to converge much more quickly than win rates themselves. So, if you had a decent PER but a comparatively low winrate, this would be a good indicator that you were running poorly. Conversely, if your PER was also low, this might indicate that your overall approach to the game was lacking. The analogy, for those of you who are into baseball, is that stats like strikeout and walk rate tend to converge much more quickly for a pitcher than ERA. If a pitcher has good K/BB numbers but a poor ERA, this is almost always an indication that he's "running poorly".

Of course, Pokertracker stats (like pitcher peripherals) are subject to luck too. But I believe that a lot of variance in poker, particuarly in the short term, is the result of winning or losing large 10+ BB pots. If you're fortunate enough to spike your nut flush draw on the river in a family pot, or have AA on a blank board when your opponent has KK, you're going to win a lot of money. On the other hand, having your opponents hit a couple of 2-outers against you -- or being on the losing side of a KK/AA war -- can kill your session, even if your overall numbers are pretty good. I believe that there is relatively little a player can do to avoid losing (or winning) a lot of money in these scenarios. But because these situations might come up only a handful of times per large number of hands, it can take a long time for the luck to even out. PER, which focuses more on the "nitty gritty" type of hand, might be a helpful workaround for this.

The PER is based on three components, each of which concern whether you're winning more than your fair share of pots at different stages of the hand. Make no mistake: the primary goal of limit hold 'em is to win pots, provided that you're not paying too much in order to do so -- it would be much more difficult to come up with an appropriate statistic for NLHE, which is primarily about controlling pot size.

In particular, the PER components are as follows:

EF1 - Efficiency Factor 1 - Win Efficiency

This is simply an indicator of whether you win more than your fair share of pots those times that you are dealt in at the table. For example, at a 5-handed table, the average player will win 20% of the pots. Most good players, of course, will not win their fair share of pots under this metric, since they'll correctly throw away hands that have insufficient odds of winning once a flop or showdown is seen. Nevertheless, it's clear that if two players had the same W$WSF and W$SD -- meaning they were getting about as much bang for their buck per hand played -- the one who played a higher percentage of his hands would be inclined to have the higher winrate. PER should account for this.

EF1 is calculated as:

Win% x A#P

...where Win% is literally the percentage of times that you win the pot those times that you are dealt into the hand, and A#P is the average number of players dealt in.

For example, in my 2006 database, filtered for <=6 handed, my Win% is 19.5% and my A#P is 4.95. This gives me an EF1 of .964.

EF2 - Efficiency Factor 2 - Flop Efficiency

The second factor is a measure of how effective you are at winning pots when you see a flop. In particular, it is calculated as:

W$WSF x ASF

Where ASF is the average number of players seeing a flop those times that you see the flop. (I'm assuming that W$WSF is well known).

ASF is a bit of a pain in the butt to calculate. It requires using filters in Pokertracker and taking a weighted average. For example, in my 2006 db, the number of players seeing the flop when I see the flop are as follows:

8000 Seen Flop w/ 2 Players
3646 Seen Flop w/ 3 Players
841 Seen Flop w/ 4 Players
165 Seen Flop w/ 5 Players
11 Seen Flop w/ 6 Players

12663 Total Flops Seen

My ASF is calculated as (8000x2 + 3646x3 + 841x4 + 165x5 + 11x6) / 12663 = 2.46.

This gives me a EF2 of 47.1% x 2.46 = 1.159. This is a good number; it means that I'm winning about 16% of the time more often when seeing a flop than an average player would.

EF3 - Efficiency Factor 3 - Showdown Efficiency

The final factor is the easiest to calculate and measures whether I'm winning my fair share of showdowns. It is calcuated as:

W$SD x 2

This assumes two players to a showdown. Technically, the average number of players at showdown is more than two, since you'll occasionally have a hand in which three or more players have a hand at the end. On the other hand, Pokertracker counts chops toward W$SD (provided that you make enough from your chop to cover the rake). In any event, the simple number 2 should suffice for accuracy.

My EF3 is 52.0% x 2 = 1.040.

PER - Poker Efficiency Rating

This is determined by mutliplying the three component factors together; we also multiply the result by 100 to make the number a bit easier to digest. e.g.,

PER = EF1 x EF2 x EF3 x 100
(now plugging in my stats)
PER = .964 x 1.159 x 1.039 x 100
PER = 116.1

My PER is 116.1. Note that an average player will have a PER of 100.

You can download an EXCEL sheet to calculate your PER at this location; just fill in everything in yellow. This will probably take about 10 minutes of your time.

I think PER should do a reasonably good job of giving credit for those things that make you a winning limit hold 'em player. Nevertheless, I'm sure that the concept can be improved upon. Any thoughts are appreciated. I'd also be curious to see other people's PER's; if you also feel comfortable posting your win rate that might be especially helpful.

[PartyGirlUK]

Nate this is really interesting stuff, thanks for taking the time to do it.

[El Ishmael]

ty

[PartyGirlUK]

How do you filter for the number of people seeing a flop when you saw the flop? I can filter for x number of people seeing a flop, but cant see how to do it when I also saw the flop.....

[gaming_mouse]

Nate,

Good post. I've been wondering about stats like this ever since I saw the "Luck Factor" a couple years ago in the original version of the Poki software. I think that was a more complex formula but I have no idea how "accurate" it was.

Anyway, two things.....

My PER for my last 24K hands of 10 data is 98. I'm running at -.24 and don't know how much is due to bad play vs running bad. I did think this was interesing....

EF1: .8
EF2: 1.12
EF3: 1.08

How should I interpret this?

Thanks,
gm

EDITED TO REFLECT CORRECT FILTERING

[Nate tha\\\' Great]

[ QUOTE ]
How do you filter for the number of people seeing a flop when you saw the flop? I can filter for x number of people seeing a flop, but cant see how to do it when I also saw the flop.....

[/ QUOTE ]

This is probably easiest to do with a pic.

[Gildwulf]

Nate,

V. interesting post. I'm somewhat concerned with your methodology though; did you basically just work backwards from your stats to determine this method? I would like to know how you came about determining this scale.

I would be interested in seeing a crosstabulation of this data with a large sample size of respondents (i.e. 100 fish, 100 tags, 100 lags).

I think this methodology has a lot of promise in comparing vastly different (50/30 vs 30/20 vs 23/16) yet sometimes winning styles of poker.

[mantasm]

I used my 10/20 hands:

BB/100 1.9

ASF: 2.7
EF1: .786
EF2: 1.113
EF3: 1.125
PER: 98.5

[felson]

Nate,

Very interesting. All these metrics are focused on frequency of winning pots. Have you given any thought to metrics which reflect skill at extracting value?

[Nate tha\\\' Great]

[ QUOTE ]
Nate,

Good post. I've been wondering about stats like this ever since I saw the "Luck Factor" a couple years ago in the original version of the Poki software. I think that was a more complex formula but I have no idea how "accurate" it was.

Anyway, two things.....

My PER for my last 24K hands of 10 data is 96.4. I'm running at -.24 and don't know how much is due to bad play vs running bad. I did think this was interesing....

EF1: .8
EF2: 1.1
EF3: 1.1

How should I interpret this?

Thanks,
gm

[/ QUOTE ]

gm,

Well, I think it's too early to say how to interpret specific numbers (except that >=100 is probably desirable), or even whether this metric is useful at all.

However, one thing that I thought was interesting was that I calculated my PER for my last 4000 hands, over which I've run (played?) fairly poorly and lost -1.34 BB/100. My PER for these hands is 107.2, which is lower than my usual number, but still comfortably above 100.