Expected value in sports betting: how to calculate EV

Most bettors judge a play by one question: will it win? Expected value asks a better one: is the price worth it?

Expected value, or EV, is the average amount a bet would win or lose per play if you could make it over and over. A bet can win and still be a bad price. A bet can lose and still be a good one. EV is how you tell the difference before the game starts, instead of after.

The formula

EV = (chance of winning x profit if it wins) - (chance of losing x amount risked)

Say you bet $100 at +150. A win pays $150 profit. A loss costs $100. You think the real chance this side wins is 45%.

• Win side: 0.45 x $150 = $67.50
• Loss side: 0.55 x $100 = $55.00
• EV: $67.50 - $55.00 = +$12.50 per $100 bet

That's +12.5% of your stake. Now change one thing. If the real chance is 40%, EV is 0.40 x $150 - 0.60 x $100 = $0. Nothing gained, nothing lost on average, because +150 already has an implied probability of exactly 40%.

That's the core idea. EV is positive only when your estimate of the true chance is higher than the chance the price implies.

A faster way with decimal odds

If you convert to decimal odds, the math gets shorter:

EV per $1 = (true chance x decimal odds) - 1

+150 is 2.50 in decimal. 0.45 x 2.50 - 1 = 0.125, or +12.5%. Same answer, one line.

Favorites work the same way

People treat big favorites as safe. EV doesn't care how often a bet wins. It cares whether the price is right.

A -200 favorite pays $50 profit on a $100 bet. Its breakeven is 66.7%.

• If the true chance is 70%: 0.70 x $50 - 0.30 x $100 = +$5.00
• If the true chance is 64%: 0.64 x $50 - 0.36 x $100 = -$4.00

The 64% side still wins almost two out of three times. It still loses money over the long run. Winning often and winning money are not the same thing.

The hard part: estimating the true chance

The formula is easy. The input is not. Nobody hands you the real probability. You have to estimate it, and every EV number is only as good as that estimate.

One common method is to use a sharp market as a reference and strip out the vig. Here's how it works.

A book lists Team A at -150 and Team B at +130.

• -150 implies 60.00%
• +130 implies 43.48%
• Together that's 103.48%. The extra 3.48% is the book's margin.

Divide each side by 1.0348 to remove it. Team A comes out to 57.98% and Team B to 42.02%. Those are the no-vig odds, about -138 and +138.

Now say a second book has Team B at +145. That's 2.45 in decimal. Using the fair 42.02%:

0.4202 x 2.45 - 1 = +2.94%

The breakeven at +145 is 40.82%, and the fair estimate is 42.02%. That gap is the edge.

Two cautions. First, this method assumes the first market is close to accurate. If it isn't, your EV number is wrong too. Second, this simple version splits the margin evenly by proportion. There are other ways to remove vig, and they can give slightly different answers, especially on long shots.

Positive EV still loses, a lot

This is where most people quit on a good process. Go back to the +150 bet at a true 45%. You lose that bet 55% of the time. More than half your results are red.

Over 100 bets of $100 each, the expected profit is $1,250. But the swing is big. One standard deviation over those 100 bets is about $1,244. Run the exact numbers and you finish 100 bets in the red about 13.4% of the time, and not ahead at all (down or exactly even) about 18.3% of the time.

That's with a real 12.5% edge, which is large. Smaller edges take far longer to show up. This is why a short losing run tells you very little, and why closing line value is a useful check. Beating the closing price shows up faster than results do.

How much to bet on a +EV play

EV tells you whether to bet. It doesn't tell you how much. One well-known sizing rule is the Kelly criterion, from a 1956 paper by J. L. Kelly Jr., a researcher at Bell Labs.

The common sports betting form is:

Kelly fraction = (b x p - q) / b

Here b is the net decimal odds (decimal odds minus 1), p is your win chance, and q is 1 - p.

For +150 at 45%: b = 1.5, so (1.5 x 0.45 - 0.55) / 1.5 = 0.0833. Full Kelly says bet 8.33% of your bankroll. On a $1,000 bankroll that's $83.33.

That's aggressive. Full Kelly has deep drawdowns, and it assumes your 45% is correct. If you overestimate your edge, Kelly makes you overbet. That's why many bettors use a fraction, like half or quarter Kelly. Quarter Kelly here is 2.08%, or $20.83.

A simple EV checklist

Before you place a bet, run through this:

• Convert the price to implied probability. What does it need to win?
• Write down your own estimate. Where does it come from?
• If your estimate isn't higher than the breakeven, pass.
• Check other books. A better price raises EV without changing your read.
• Size it small. Your estimate has error in it.
• Track results and closing prices. Judge yourself over hundreds of bets, not a weekend.

EV won't tell you who wins tonight. It tells you which prices are worth paying, and that's the part you control.

The DARIMARKET board ranks every play by confidence and shows the price it needs to beat.