[AaronBrown]

Okay, we have to do a little math, and 2+2 doesn't have a LaTex editor to show equations. It's going to be a bit messy.

The idea is that when you enter a tournament you can model your finish with a power distribution. There's no reason for that, it's just handy mathematically and not unreasonable. The chance of finishing with X fraction of the entrants or less ahead of you is X^a. If a = 1, this is just the uniform distribution. The chance that you're in the top 25% is 0.25^1 = 0.25. The chance that you're in the top 50% is 0.5^1 = 0.5.

If a > 1, you're worse than average. If a < 1, you're better than average. The closer a is to zero, the better you are. If a = 0.5, then the chance of being in the top 10% is 0.1^0.5 = 0.32, so you accomplish that in one third of your tournaments. The chance of being in the top half is 0.5^0.5 = 0.71.

One way to estimate a from observed data is to take the average of the natural logarithms of the finishes (-1.7449) and solve:

ln(a)/(1-a) = -1.7449

You can use the Excel "Goal Seek" function to do this, or do an iterative solution. There's no closed form solution for a.

Once you get a = 0.2894, you can plug it back in to find out your chance of finishing in the top 10% (.1^0.2894 = 0.51). This may seem high given that you only did it one out of four times, but you get a lot of credit for never being below average.

With more data, you could make sure the power distribution assumption seems right, and you could get a more reliable estimate of a.