I’ve been hearing so many sports betting experts and casual gamblers talking about the power of hedging bets that I felt a huge need to write this: no, there is no power; locking profits is a bad idea. Decisions in life are situational. For some people, in certain situations, hedging might be a good idea. In the long run though… it’s a bad play.
From these axioms, one can reason further that the hedge bet will rarely be a value bet. If it were to offer value indeed, then most probably the first bet was a mistake or certain events occurred that changed its status. In conclusion, the expected value of locking profits cannot be higher than the ROI achievable by simply placing value bets. We’ll leave the variance talk aside for another article, but for now keep in mind that the lower variance is not worth taking into consideration unless you’re able to consistently lock profits.
For the math lovers out there, let’s strengthen these assertions with an example!
Since odds are actually a method in which probabilities are expressed, I will do the whole example in probabilities. We’ll consider a bookmaker which simply adds 2% to the probability of each outcome in order to offer the odds. The event is A vs B and the odds are 52% on either side. You find out before the bookmakers and the public that A is actually the favorite to win and you estimate that the probability is reflected in these honest odds: 57%. If you bet on A, the ROI (or better said EV) should be:
ROI = 57*(100/52-1)-43 = (57*100-57*52-43*52)/52 = (5700-2964-2236)/52 ≅ 9.6154% Explanation: 57 times out of one hundred, you will take this profit, expressed as a percentage of your stake: 100/52 - 1; the rest of 43 times you will lose your full stake. The difference between them is the expected value.
Time passes and the odds on A go down until the honest odds reach 57%, therefore the bookmaker now offers 59% and 45% respectively. If you were to lock profits, you’d have to bet on B. How much? Well, to find out the answer in percentage of the initial stake, let’s write the profit locking equation as if the bet on A was 1:
1*(100/52-1)-x = (100/45-1)*x-1 Explanation: This is the profit locking equation (it helps you determine the size of the hedge bet in order to make an equal profit, regardless of the event outcome): profit made if the initial bet wins - stake of the hedge bet = profit made if the hedge bet wins - stake of the initial bet
x is 45/52 meaning we would have to place a bet on B with the stake equal to 45/52 of the initial bet in order to lock an equal profit, regardless of the outcome. It’s easy to check if the calculations are correct. If A wins, the ROI would be:
ROI = (100/52-1)-45/52 = (100-52-45)/52 = 3/52 ≅ 5.7692%
If B wins, the profit is
ROI = (100/45-1)*45/52-1 = (100-45-52)/52 = 3/52 ≅ 5.7692%
There you go… we would achieve a higher expected value by simply not placing the second bet. Keep it simple: find value bets, don’t worry about hedging them. I’m waiting for your opinions below.