What is +EV betting?

Expected value is what a bet returns on average if you could place it over and over. For a bet at decimal odds d that wins with probability p, the expected profit per dollar is p × d − 1.

A fair coin flip at +110 (2.10 in decimal) is worth 0.5 × 2.10 − 1 = +0.05, or $5 per $100. The same coin flip at -110 is worth -$4.55 per $100: that is the margin a standard price charges you. Most bets at most books are negative for exactly this reason. +EV betting is finding the exceptions.

The hard part is p. ArbWins estimates it from Pinnacle, a sportsbook that takes large bets from winning bettors and moves its line in response instead of limiting them, so its prices carry the sharpest opinions in the market. Pinnacle still charges a margin, so the first step is to take it out. Say Pinnacle has a moneyline at -150 on the favorite and +130 on the underdog:

The implied probabilities add up to 103.48%. The 3.48 points over 100 is Pinnacle's margin. ArbWins removes it with the power method: it raises each side's implied probability to the same power, the one that brings the total to exactly 100% (1.053 here). 60.00% becomes 58.40%, and 43.48% becomes 41.60%. Those are the fair chances, and -140 and +140 are the matching prices with no margin at all.

Books load more of their margin onto the underdog than the favourite, and the power method takes it back off where it sits. The simpler multiplicative method divides each side by the total (57.98% and 42.02% here), shrinking both by the same proportion, and so leaves the longshot too much: on a three-touchdown college favourite priced 1.08 / 8.53 it calls the underdog an 11.2% chance against 8.5% with the power method, enough to make a book's +1100 on that underdog look like a +35% bet when it is about +1.5%. ArbWins uses the power method on every row of the +EV board; the no-vig calculator uses it too. ArbWins only de-vigs a complete market at one line: both teams on a moneyline, both sides of a spread at the same number, or the over and under at the same total.

Now another sportsbook offers the same underdog at +145, or 2.45 in decimal. That is longer than the fair +140, so the bet is +EV: 0.41602 × 2.45 − 1 = +1.92%. Per $100:

At +140 the same bet would be worth about nothing (-$0.16 per $100), and at +135 it would be worth -$2.24. The +EV board lists bets worth +0.5% or more against Pinnacle, with Pinnacle's fair price and win probability beside each one.

A +1.92% bet still loses 58% of the time. One $100 bet at +145 has a standard deviation of about $121, around 63 times its expected value. The swings shrink relative to the edge only as the bets pile up:

Even after a thousand good bets, roughly one bettor in three is still behind. And that assumes the fair price is right. It is an estimate: if Pinnacle's line is off, or moves after you bet, your real edge is smaller or larger than the number on the board. +EV betting needs a bankroll you can leave alone through a bad month, and a lot of bets.

The Kelly criterion gives the stake that grows a bankroll fastest when the edge is known exactly: f = (b × p − q) ÷ b, where b is the decimal price minus 1, p the win probability and q = 1 − p. For the +145 bet: (1.45 × 0.41602 − 0.58398) ÷ 1.45 = 1.33% of the bankroll.

ArbWins shows a quarter of the Kelly stake, rounded to the dollar: $17 here. Full Kelly assumes p is exact, and with an overstated edge it overbets. It also swings hard. Under the standard long-run approximation, a full-Kelly bettor has about a 1 in 2 chance of seeing the bankroll fall to half its size at some point. At a quarter of Kelly that chance is under 1 in 100, and you keep a bit under half of full Kelly's growth rate.

Sportsbooks limit +EV bettors just as they limit arbitrage bettors. A book that sees you take only the prices it has left behind the market will cut your stakes, and nothing prevents that. Settlement rules matter less than in an arb, because there is only one bet, but the comparison still has to be like for like, so each row on the +EV board says whether ArbWins has checked that book's settlement rule for the market. The settlement rules table has the detail by book.

If you want a result that does not depend on who wins, read what arbitrage betting is. For two bets that can both win, read what a middle is. ArbWins's track record shows how long price gaps between books actually stay open.