EV Calculations and Error Ranges
The expected value formula has some hidden traps in it that may be hurting your win rate.
The expected value calculation is one of the most straightforward and utilized formulas in sports betting. The calculation is simple: (probability of winning a bet * payout) - (probability of losing bet) = expected value. If the result of that formula is positive, it’s expected to be a winning bet, and if it’s not, it’s supposed to be a losing bet. It powers everything in sports betting, including the tools we use at Betscope, and is absolutely an indispensable formula for finding winning bets. There are some pitfalls, however: it sits in the exact sweet spot of simple enough to use on your own and sufficiently complicated that it can make you feel sophisticated and smart enough that it papers over some assumptions that go into the formula. We’ll go over exactly how those flaws might arise, and what you can do to account for these flaws to enhance your utilization of this formula.
Let’s break down where the quantities in this formula come from, specifically the win probability of the bet and the payout. The latter is straightforward: it’s the odds you get from a sportsbook, and there is precisely zero ambiguity or assumptions that go into what this quantity is. Put another way: when you make a bet at +165, there’s zero chance that you’re somehow actually getting +155 or +175 or any other number; once the bet is accepted, your odds are your odds and they don’t change. The bet win probability, however, comes downstream of your handicapping process, whether it’s originating your own numbers, deriving them from projections or top-down sources, or any other process used to estimate true win probabilities. And I’m emphasizing the most important word again in that sentence: estimate. All win probabilities used in the EV formula are exactly that: an estimate. If there were an undisputed source of ground truth that was perfectly accurate for predicting sports, then sports betting would not exist, as the skill in sports betting is coming up with the best estimates. And if a quantity is an estimate, by definition, it also has error baked into the process. Error is something that the EV formula doesn’t account for: it assumes the win probability is the win probability, and has no concept of how strong or weak the estimated win probability is.
Typically, errors are more or less evenly distributed around the estimated probability with fixed effects. If your estimated probability is 62%, it might have some built-in error of +/- 3% all else being equal, so the true probability is really in the 59-65% range instead of being 62% on the nose. Accounting for these error bands is a crucial and almost never-utilized step in finding value in the sports betting market: bettors don’t like to admit they could be wrong in general, and this effect gets compounded once you start applying math formulas to sports betting. Let’s go through an example to see how accounting for these potential errors can influence your bet/no-bet decision.
Let’s take two bets we might want to make: for one bet, we estimate the win probability to be 62%, and we’re getting -141 odds on the bet, and for the other bet, we estimate the win probability to be 40%, and we’re getting +165 on the bet. Using the expected value formula above, we can see that both bets have an expected value of 6%. But what happens when we introduce the error bands into the equation? Using our fixed-effects rule, let’s decrease the win probability by 3% for both bets. With new bet win probabilities of 59% and 37% respectively, the EV of bet 1 drops to 1%, and the EV of bet 2 drops to -2%, so bet 2 is actually a bad bet now under this scenario.
This illustrates a practical condition about the expected value formula that can be summarized in two short bullet points:
All bet win probability estimates have errors baked into the process.
The higher the payout, the more those errors are magnified.
Put another way: I am much more likely to fire on a 3% EV bet with -150 odds than a 4% EV bet with +230 odds, because once I account for errors, it’s more likely that the -150 bet is in fact a positive EV bet than the +230 bet, even though the +230 has a higher expected value. Some of you might be thinking that if errors truly cancel out on both sides, then shouldn’t this not matter, because you’re equally likely to get even more value and it all averages out? If we treat our errors as truly 50/50 on both sides of the bet win probability, then yes. But every seasoned sports bettor learns the hard way that for bets that show +EV, errors are not randomly distributed: they almost always have a bias towards the -EV side of the spectrum. This deserves its own post for further elaboration, but the short version is for most cases, if your number disagrees with the market, there’s a greater chance than not that your number is wrong, not the market. That’s not to say there’s no value to be found in sports betting market, only to say that in the case of evaluating +EV bets, you should assume the errors are biased towards your number being wrong rather than being right.
So what are some practical strategies to account for this error? One rule of thumb people have been using on our new Best Bets page is to not fire on EV values below a certain threshold, aka only bet numbers 2% EV or above. I think this is generally a good rule of thumb, and I would amend it for a slightly more comprehensive strategy: the higher the payout of the bet, the higher your safety threshold should be. Bets with -150 should have a minimum EV of 1%, bets with +130 should have 3%, bets with +175 should have 5%, etc. There’s no hard and fast rule, since every win probability estimate will have different levels and ranges of errors, so a lot of these rules should be experimenting and seeing what does and doesn’t work. But if you’re 1) accounting for errors in the EV calculation and 2) accounting for it with a scale that slides with payout, you are ahead of 99% of the bettors out there, and it will do a good job of reducing false positives in your bets and help keeping your win rate positive.