If you're kind enough to read this, thanks. And please let me know if this has been discussed before

Even though poker is a zero-sum game and golf isn't, the two games have pretty much the same mathematical structure. In both games, players enter the field of play with the goal of repeatedly going around a circuit, trying to capture as much EV as possible along the way (in golf you capture EV by scoring lower on a hole than the field's average score on that hole.) It should make sense that this is the case, because when you strip away the bells and whistles, poker and golf tourneys are both merely occasions in which individuals gather for the sole purpose of competing to see who can capture the most EV on their way to claiming a top heavy 1st place with many smaller, subsequent prizes up for grabs, and with a majority of the field receiving nothing.

It's easy to see that in such competitions, if the field size is N and all players are equally skilled, then each individual has probability 1/N of winning, probability .01 of finishing in the top 1%, probability .1 of finishing in the top 10%, etc.


But we know players aren't equally skilled, and some will win (or lose) more than others. All this means mathematically is we can perhaps find some multiplier for each entrant i, c_i, to (1/N) to better capture player skill. Good players have c_i>1; bad players have c_i<1; in the equally-skilled case, c_i=1 for all i. I recognize that ultimately the individual (c_i)*(1/N) for each entrant i would need to sum to 1 (which just implies the c_i's sum to 1). I'm not sure what kind of restrictions that would put on c_i

But on an individual basis it's pretty easy to empirically estimate someone's value of c_i. Set some thresholds--1%, 5%, 10%, whatever. Consider the equally-skilled case, and you see that the expected number of finishes at or above the chosen thresholds is simply Expected=Treshold*Total # of Events played. Then look at the results for the Actual number of , and compute the ratio Actual/Expected.

A higher ratio implies a higher degree of skill (at least it does more certainly in a game like golf who's outcomes are almost entirely dependent on skill). For example, Tiger Woods has 80 wins in 311 starts. With an average field size of 150, his Actual/Expected ratio is (80/(311*(1/150))=~40, which is totally absurd. For top 10 finishes, which is a top 7% finish, Woods has 193 which gives him an A/E ratio for Top 10s of (193/(.07*311))=~9.

I expect that an A/E ratio (which is the c I mentioned above) of 40 for golf is about the limit of human achievement in that sport (and no, poker's not a sport), and I suspect the ceiling for poker is much lower due to variance and due to poker frankly not being as tough as golf.

So a few things for you:

1. Does this seem like a valid approach? A/E ratios are used constantly in insurance, but not so much for other purposes I'm aware of.

2. Just how good do you think the Tiger Woods of Poker could be? In other words, in a 1000 player MTT, what do you think is the limit for how high one can get their win probability to be (what's poker's max value of c that's humanly possible to achieve?)

3. In poker, we sometimes don't know what the field size is because we bust before late reg ends.

I just look at roi, itm, and itmroi. It's pretty simple: negative roi is bad, neutral roi is neutral naturally, 5% roi is ok, 10% roi is good, 15% roi is great, 20% roi is expert.