How reliable is my sample scores?

Question

How confident can I be that my sample score is representative? For example, in a 306 bets, 201 (65.7%) were correct...but how confident can I be that this betting strategy will hold? Or put another way, with a 95% confidence level, how much could that win % deviate by?

By being more selective with my bets, I can increase the win % but then the sample size becomes smaller, for example taking only 100 bets and getting 70 wins (70%).

Answer 1

In the first case, n, your sample size is 306, and p, your chance of success, is .657

In the second case, n = 100 and p = .700.

Your standard error for this sort of situation is sqrt(p*f/n), where p = chance of success, f = chance of failure, and n = sample size.

1st case: s.e. = .0271

2nd case: s.e. = .0458

In both cases, your 95% confidence interval is going to be +/- 1.96 standard errors from your mean.

1st case: (0.647,0.753)

2nd case: (0.567,0.747)