November 02, 2011
I am still looking into seeing if I can easily calculate the expected rate of downswings, it is not in order to soak and dwell in the misery but rather that I am interested in maths and this tickled my fancy.
Anyway, I did start looking into some of the risk of ruin maths and it all still seems like a reasonable approach when calculating downswing probabilites. I decided that I would need some data to test its accuracy and so decided to do my own sets of game simulations. This has been quite interesting and I have been generating blocks of millions of results. Using this and a bit of maths I can now generate nice downswing probability graphs, I am still trying to comfirm their accuracy but so far they seem to be pretty good. Due to the way I am simulating I still have to approximate the number of possible points at which a downswing could possibly start, basically counting each game start when not in one so the current high water mark is the highest point - at all other points it is already part of a downswing. Using this info. I can then use a binomial distrib model to arrive at the possibilities. Here are a couple of the graphs - I'll try to confirm some on the results (at the moment there is a still a little bias but it is still only out by a quite a small factor, I hope to get it eve more accurate)
and then I can easily turn them out for larger fields (I am interested in how 180's behave with reasonable roi's).
If I get a bit of time I'll stuff a lot more graphs up so people can have an estimate of what to expect in the larger field tourneys.