10/26/2012 09:51 AM
You're absolutely right, finance: the trick is quantifying the edge - after making sure that you have any edge at all, of course :). There are too many random factors in any given game so it's not an exact science but if you have enough history data from previous bets, you can calculate it closely enough for practical purposes.
Here's how Kelly works for me (simplified explanation):
Let's say that I have a history of betting "over 3.5" in soccer (3+ years at various odds from about +100 to +170, 20+ games per week) which shows that I have 10% ROI in the long run. I want to bet a game that offers me odds of +120. I calculate my chance of winning the bet (based on the odds and my long term ROI) at exactly 50% or 0.5 (betting 1 unit, 50% of the time I win 1.2 units and 50% of the time I lose 1 unit which is exactly 0.1 units profit or 10% ROI). The formula for the bet amount is:
f = (p * (b+1) - 1)/b
f - percentage of bankroll to bet
p - probability of winning
b - winnings if 1 unit is bet
so in the example case p = 0.5, b = 1.2 and f calculates to 0.083 which means that I should bet 8.3% of my bankroll on the game for optimal results.
If the game offers me odds of +160 instead of +120, then my probability of winning (to keep the same long term ROI) is 42.3% so using Kelly I should only bet 6.24% of my bankroll. Which makes perfect sense as +160 compared to +120 leads to higher variation even if the long term ROI is the same.
But if this week I decide to bet on the Tigers in Game 3 of the World Series for example, I won't use Kelly because I have no history at all betting on baseball. So I can't calculate any edge, and I most likely don't even have an edge at all (and should expect to lose about 5% in the long term just like any other random bettor). I would only use Kelly for my "over 3.5" bets in the leagues that I've played the past 3 years.