
Originally Posted by
Dave Matuck
I have read on various boards/websites that only 3-5% of total sports bettors win in the long term. Is this correct.
It really depends on how you define the "long-term". If you define it in the mathematical sense of "that number of bets such that the impact of pure luck is negligible", then that's really a question best answered by the books, and one to which I wouldn't even attempt to hazard a guess.
If, however, you're referring to the long-term in the more pedestrian sense of the number of bets typically placed over some given stretch of time, then we can at least come up with a minimum figure using the binomial distribution and assuming coin-flip bettors.
Given coin-flip N bets, for a bettor to be profitable at -110, he'd need to hit at a rate > 11*N/21.
Hence, we'd expect purely by luck alone, for =BINOMDIST(N-11/21*N, N, 50%, 1) to be profitable over N bets. where =BINOMDIST() refers to the Excel binomial distribution function.
So purely by chance, given the stated number of coin-flip bets:
Over 500 bets we'd expect 15.1834% of bettors to be profitable.
Over 1,000 bets we'd expect 6.8584% of bettors to be profitable.
Over 1,500 bets we'd expect 3.3368% of bettors to be profitable.
Over 2,500 bets we'd expect 0.8648% of bettors to be profitable.
Over 5,000 bets we'd expect 0.0362% of bettors to be profitable.
etc.