Theory again: Let's take a couple of steps back

[AtticusFinch]

Your points are reasonable, and I certainly considered them. However, I concluded that the model would still be useful for the following reasons.

First, you are correct that I would have to estimate cEV and then run the model for individual players. In fact, that is exactly what I plan to do. However, your notion that I would actually have data for a player's cEV at the level I'm trying to predict is actually a good thing, as it allows me to fully test the validity of the model. If the model fits the data, or can be adjusted to do so, then it could be used to predict results for other players.

Second, while I agree that relative skill level is a vague concept, I think that cEV per hand is a reasonable proxy for it. Limit players use BB/hour as a proxy for skill regularly. The variance is much higher in a NL setting, of course, but with enough data I think that we could produce cEV/hand estimates that would serve as reasonable proxies for broad skill categories such as fish, average, decent, good, excellent, world-class.

All that remains then is to place a player in one of these broad categories, and consult the model for that cEV value.

[PrayingMantis]

OK fair enough. Analyzing data from big number of MTTs should be a good thing, and any conclusions, even very vague ones, could be interesting.

[gergery]

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Largely that it doesn't take into account the size of the blinds.

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The current level of blinds shouldn't have any impact on someones % to win the tournament. (Assuming everyone is equal, skill differences are being neglected for now)

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If there are 10 people in a tourney with the following chip counts:

1 100k
2 90k
3 55k
4 50k
5 47k
6 38k
7 29k
8 27k
9 24k
10 19k

Then would you rather have blinds at 500-1,000 or blinds at 5,000-10,000? Does it matter if you are 1st in chips or 10th in chips?

--greg

[justT]

I’m not fully sure where you are going with this, but I generated some numbers from an actual tourney to see what was possible.

The “stack building” rates in (% stack gained/hand) are from the first hand up to the start of the FT, I stopped there because the rate at the FT depends a lot more on the individuals involved, especially when its head-to-head.

$20 Party Tourney, 600+ Entrants, standard Party 15 minute blinds

Hero played 232 hands to get to FT and had an average stack at the start of the FT. Hero sported an average “stack building” rate of 1.75%/hand.

The chip leader had about 2X the average stack the short stack had about ¼ the average stack. I don’t know how many hands they played, but it was probably similar to the number Hero played. Assuming this is the case, their rates were about 2.05%/hand and 1.20%/hand, respectively. These rates are consistent with what I’ve seen from other low buy-in Party tourneys. To get to the FT in decent shape, you need a rate somewhere in the 1-3% range. Lower and you’ll be short stacked. Higher would be better, but 3% is my best guess for a ceiling of what’s achievable in this type of tourney.

On individual hands, Hero’s rate ranged from -65% to +220%. The number of chips your opponents have is a significant constraint on the possible rate for an individual hand, but it may not be a very significant constraint on the average rate (think players that pick up lots of small pots)

Hero clearly has the “skill” to win this tourney and build his stack at a rate of 1.75%/hand, but what does that mean? How much skill does he have compared to the 2+2er that won the same tourney the very next day? Their rates were similar, but you know nothing about their skill level. A skilled player who makes the FT with a cold deck and an unskilled player who makes the FT with a hot deck will both sport similar chip building rates.

It looks like the problem is going to be defining/determining how skilled a person is, then somehow relating that to rates. Looking at a long term rate (i.e. over many tournaments) is also problematic, notice if you don’t win you’ll have a negative rate for a tourney. The faster you bust out, the more negative your rate. An early bust out may be a very skilled player busting out by pushing any edge, and a late bust out could be an unskilled player holding on for dear life.

I suspect this may be like investing, the rate is one measure, but you have to somehow incorporate the risk they took to make that rate.

[gergery]

Seems to me you are over-complicating things.

I’d venture what you really want to do generate a regression equation with following variables:

Y=$ results
X1 = chip count
X2 = size of blinds
X3 = chip count relative to other key stacks at your table (would need to fiddle with this to get the right measure)
X4 = stage of the tourney (might not need this as chip count could serve as proxy)
X5 = maybe try to control for skill/luck/variance of our player by summarizing EV of hands that get showndown. (i.e if your control player gets all in with AK vs. JT then you give him credit for his equity at the time chips went in, as opposed to the result. Or maybe you use pokerstove to give him equity credit vs. a reasonable range. Obviously you’ll never get anywhere near true skill level or be able to control for luck, but this might get you closer than otherwise).
X6 = whether you outstack someone when playing hand vs. them
X7 = tightness of BB when in CO, etc.
X7 (thru X20) = control for skill of other players at table using same methodology. This might be too difficult to do given limited observations. My hypothesis is that big stacks gain a greater advantage when against bad players, since bad players will value survival and fold too much to them.
There are probably other variables I haven’t thought of.

You would then want to get fancy with X^2 variables to control for non-linear relationships, or interacting relationships. Like having a 2x stack is significantly more favorable, but 3x earns you no incremental fold equity.

What you would do is take many tournament from one player, and map out his results from given points in time, say, take 3 points during the tourney. Then do the same with another player. By using just one player you control for skill differences between different players. Then you can try to compare one player vs. another.

Fwiw, I understand the Freakonomics guy is doing something like this only for ring games looking at position and other variables.

Just some thoughts,
--greg

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One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be.

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What about expressing stack size in terms of BB's? This would allow you to estimate "BB-EV", rather than cEV, which is probably the more meaningful number anyway, right? Or maybe expressing it in terms of M would be better? It doesn't seem to me that the number of chips in your stack is meaningful in isolation, ie without knowledge of blinds/antes.

Keep up the good work, this is interesting.

[KneeCo]

I'm new to this, didn't really follow the last thread, so I've only read the first post in this one.

Question about the assumptions:
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1) The maximum amount of chips you can make at any time is proportional to your present stack size.
3) Your maximum cEV is limited by the sizes of your opponents' stacks


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Aren't these two contradictory?
Premise 1 suggests an indefinite positive correlation while premise 3 puts a cap on it.

In practice, we know that the correlation is not indefinite. #1 taken alone is misleading. The maximum amount of chips you can make at any time is proportional to your present stack size up to a certain point, this is no longer true once you are chip leader. #3 does seem to come in and rectify this, but the premises should stand alone, so shouldn't the two be married into one assumption?

Maybe I'm wrong.

[AtticusFinch]

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One possible way to factor the blinds in indirectly would be to look at the standard deviation of stack sizes. I'm guessing that the smaller the blinds are, the larger the standard deviation should be.

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What about expressing stack size in terms of BB's? This would allow you to estimate "BB-EV", rather than cEV, which is probably the more meaningful number anyway, right? Or maybe expressing it in terms of M would be better? It doesn't seem to me that the number of chips in your stack is meaningful in isolation, ie without knowledge of blinds/antes.


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I thought about that, but if you express your stack in terms of M, the ratio ends up having the same value, because the size of the opening pot ends up in both the numerator and denominator. So it just drops out.

I've thought of adding the average M as a factor, which would model both blinds and antes, but I haven't figured out how to factor it in, yet.

[AtticusFinch]

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I'm new to this, didn't really follow the last thread, so I've only read the first post in this one.

Question about the assumptions:
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1) The maximum amount of chips you can make at any time is proportional to your present stack size.
3) Your maximum cEV is limited by the sizes of your opponents' stacks


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Aren't these two contradictory?


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They're not contradictory -- they are conflicting forces.

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In practice, we know that the correlation is not indefinite. #1 taken alone is misleading. The maximum amount of chips you can make at any time is proportional to your present stack size up to a certain point, this is no longer true once you are chip leader. #3 does seem to come in and rectify this, but the premises should stand alone, so shouldn't the two be married into one assumption?

Maybe I'm wrong.

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No, your sense is correct. The assumptions only make sense when taken together, not individually, because they interact. If I were to add "all else being equal" to each, perhaps that would make it more clear.

[AtticusFinch]

Thanks for taking a look. One tourney isn't enough data to say much of anything, but it's good to experiment.

I agree that the model probably won't be too helpful on the final table, by the way. I'd go back to using ICM there.