Predicting Tournament Performance

[Thundrdan]

Does anyone know of a better way of predicting tournament performance than the method that I use below? I would like to know what everyone thinks. The method I use I think is good when playing tournaments with similar field sizes. If most sized tournaments are small and there is one huge tournament you play in, the results may be thrown off a bit.

#Players Ranking
12 3
18 7
20 5
10 1
15 11

Ave # of Players = 15
Average Finish "Rank" = 5.4

Now, from these two numbers, I calculate what I refer to as the "P-Value". I use this P-Value to evaluate how well I am doing. If the "P-Value" is equal to one, I have am an average player compared to the opponents I typically play against. Anything lower means that I typically have an advantage. Below is how I calculate this "P-Value", and how I use it to determine my chance of winning any given sized tournament (assuming the players are of typical skill that I usually play against).

P-Value = Ln(1/2) / Ln (Ave Rank / Ave Players)
P-Value = Ln(0.5) / Ln (5.4/15)
P-Value ~ 0.678
(The 0.5 is used because based on my performance, I am just as likely to rank higher than 5.4th place as lower than 5.4th place.)

Once I have my "P-Value", I use it to calculate my chances of winning, or lasting until a certain point. Below are a few examples.

What are my chances of winning a 22 man tournament?
Chance of 1st = (Rank/#Players)^P-Value
Chance of 1st = (1/22)^0.678
Chance of 1st ~ 12.3%

In a 25 man tournament, the last 4 places are payed out. What are my chances of getting ITM?
ITM% = (ITM/#Players)^P-Value
ITM% = (4/25)^0.678
ITM% ~ 28.8%

EV for a $50 buy-In tournament with 20 people,
1st = $600
2nd = $250
3rd = $150

EV = $600*[(1/20)^0.678] + $250*[{(2/20)^0.678}-{(1/20)^0.678}] + $150*[{(3/20)^0.678}-{(2/20)^0.678}] - $50

EV ~ $58.35

[Dunkman]

One problem I see is that I don't think the average finish rank stat is particularly meaningful. You could have someone who gambles it up early to either get a big stack or bust, then another guy who's halfway decent but way too weak and tight. Lets say a 100 person tournament, the aggressive guy busts out 80-100 a lot, but also makes a bunch of final tables and is a big winner. The weak tight guy never busts early, but the blinds slowly eat his stack and he rarely makes the money or FT. These guys would likely have very similar average finish ranks, but one would be a big winner and the other a big loser. If I'm missing something here let me know.

[Thundrdan]

This is a problem I've thought of quite a bit, however, there is not accurate way to rate how weak/tight or passive/aggressive each player in the field is. If the human factor is completely ignored, and I look only at statistics, would this be an accurate method? I have a little background in statistics, but does any statistical experts out there know of a better way? I would think this would be similar to a reliability problem. If I were to cycle 20 parts to failure, and only 3 reach the desired number of cycles, while the other 17 fail at different numbers of cycles, can I determine the chance of failing at any given number of cycles?

[Sherman]

I'm not sure about your math Thundrdan. I've done some similar analyses and posted about them before. I have yet to convince myself that they are better than simple ROI analyses however. Mine was like this:

Prob. of getting 1st = 1 / # of entrants
Sum these for every tournament played.
This sum = your expected wins based on chance alone.
Divide actual number of wins by the number based on chance alone.

This is your skill edge. Anything above 1.00 is above chance levels.

I also developed Confidence internval for it, but again, I have yet to convince myself that it is any better than simply using ROI.

Sherman

[Jetto2]

I have try to find a way to calculate RoR in S&G <= 27 players and there is similitude between your formula and yours. But I based my formula on observation.

I adapt a video poker article : http://www.blackjackforumonline.com/content/VPRoR.htm

As probability of wining I use the number of time I was in each place on my previous game. This give me an observed EV. This also make possible to calculate a RoR.

But this very hard to know the confidence to the result.