Quote:
Originally Posted by Nozsr
Browni, being a simple engineer and not being a stat guy, I had to look up what exactly a z-score is. Seems like it represents the decimal number of standard deviations one player might be better than the mean of a large sample of players, i.e. half a SD, .75 SD, whatever value represents the "how much better than average" a player is.
Presumably a better than break-even player will have a positive z-score, and a great player a larger z-score.
What value would you estimate the z-score of:
* an exceptional player, maybe with an estimated equivalent win-rate of 12 BB/hr, in your example, what z-score did you use? 1+12/80? Or something else?
* a good player, maybe with a win-rate of ?
* a barely winning player, maybe with a win rate of ?
I'm pretty far from an expert, too. Everything I've learned is from self study or helping my wife with her math homework.
z-score is just a term to denote the number of standard deviations from the mean that a data point is in a normal distribution. It represents and can be converted to a probability by using a chart (google z-tables, in this case we are considering the probability of running breakeven or worse, so we want the left tail probability given our z-score). When I say a player with a 12 BB/h win-rate and an 80BB/h standard deviation has a 17% probability of breaking even or worse over 40 hours, I had inputted the known variables, u = 12, σ = 80 and N
0 = 40 and solved for z to get -.95, looked the value up in a table to see that it corresponds with a 17% probability.
If we were looking at a distribution of player win-rates then the z-score could represent player ability, but that's not what we're looking at. We're looking at the expected distribution of the length of a breakeven stretch for a player whose bankroll expects to grow 12 BB/h with a standard deviation of 80 BB/h.