A good bet and a winning bet are not the same thing, and the gap between them is where most bettors lose their money. A sportsbook that prices a coin flip at -110 asks you to risk $110 to win $100 on something that happens half the time, and that bet loses money forever no matter how many times you happen to cash it. Expected value, or EV, tells you which side of that line you are on before the game kicks off.
Expected Value Is the Price Measured Against the Truth
Every bet carries two probabilities. One is the price, which converts to a percentage as shown in our guide to reading betting odds: -110 is 110 divided by 210, or 52.4%, and +150 is 100 divided by 250, or 40%. The other is how often the thing actually happens, which nobody knows for certain and you have to estimate.
EV puts those two numbers side by side. The formula is your win probability times the amount you win, minus your loss probability times the amount you risk. If your estimate of the true probability beats the probability baked into the price, the bet is positive EV; if it falls short, the book expects to make money on you.
The book builds its edge into the price, which is why -110 on both sides of a spread adds up to 104.8% instead of 100%. That extra 4.8 points is the vig, and a bettor who picks sides as well as a coin does loses about 4.5 cents of every dollar risked to it. Stripping the margin out to see what the book really thinks is covered in our guide to implied probability and removing the vig.
The Arithmetic at -110
Say you have a spread bet at -110 and you believe the side covers 55% of the time. You risk $110 to win $100. The win side of the formula is 0.55 times $100, which is $55. The loss side is 0.45 times $110, which is $49.50. Subtract and the bet is worth $5.50 for every $110 you put up, a return of 5% on the money risked.
Now say your honest estimate is 50%. The win side is $50 and the loss side is 0.50 times $110, or $55. The bet is worth negative $5 per $110 risked, which is the vig doing exactly what it was designed to do. The break-even point sits at 52.4%, and every percentage point of true probability above that is worth about $2.10 per $110 bet, because each point adds $1 to the win side and takes $1.10 off the loss side.
That number is the whole case for reduced juice. At -105 the same 55% bet risks $105 to win $100, so the loss side drops to $47.25 and the bet is worth $7.75 per $105 risked, a 7.4% return instead of 5%. SportsBetting.ag posts -105 on NFL and NBA sides, and a bettor with a real edge picks up almost half again as much profit there from the same opinions.
The Arithmetic at +150
Underdog prices work the same way but the numbers feel backwards. A +150 moneyline pays $150 on a $100 stake and implies 40%. If you believe the dog wins 44% of the time, the win side is 0.44 times $150, or $66, and the loss side is 0.56 times $100, or $56. The bet is worth $10 per $100 risked, a 10% return, even though you expect to lose it more often than you win it.
Drop your estimate to 36% and the same bet is worth negative $10. Eight points of true probability separate a good +150 bet from a bad one, and nothing on the ticket tells you which you are holding.
The same dog at +160 implies 38.5% instead of 40%, and at a 44% true probability it is worth $14.40 per $100 instead of $10. A half-step in price added 44% to the EV with no change in your opinion, which is why line shopping is the one edge every bettor can take without being smarter than the market.
A Lost Bet Can Still Be a Good Bet
The 44% underdog above loses 56 times in 100. The 55% favorite loses 45 times in 100. Both are bets you should make every time you find them, and both leave you holding a losing ticket about half the time. One game’s result says almost nothing about whether the price was right.
Judging a decision by how it turned out is what poker players call resulting, and it teaches the wrong lessons. A -110 bet that lost on a late turnover was not a bad bet if the line closed at -125 on your side, because the market moved toward your number after you took it. That is why we treat closing line value as the honest scorecard: it measures whether you beat the price, which you control, rather than whether you beat the game, which you do not.
How Many Bets Before EV Shows Up
EV is an average, and averages take a long time to show in a game with this much variance. Take the 55% bettor at -110 again, betting to win 1 unit each time. The expected profit per bet is 0.055 units, but the standard deviation of a single bet is about 1.04 units, roughly 19 times the edge.
Over 100 bets the expected profit is 5.5 units and the standard deviation of the total is about 10.4 units, so a true 55% bettor finishes 100 bets in the red about 30% of the time. The hit rate over those 100 bets lands anywhere from 45% to 65% as a matter of routine, because the standard deviation of a 100-bet win percentage is 5 points.
Stretch it to 500 bets and that bettor is ahead about 88% of the time. At 1,000 bets the bettor is ahead about 95% of the time, and at 2,000 bets about 99%. So a bettor with a real and fairly large edge needs on the order of 1,000 bets, several full seasons for most people, before the bankroll confirms what the process already said. The reverse cuts as deep: a 50% bettor losing to the vig is still ahead after 100 bets about 32% of the time, and usually concludes the method works.
Where a Real Edge Comes From
Positive EV does not come from liking a team. It comes from having a number for the fair probability that is better than the book’s number, and being able to say why. A bettor who models a total at 44.5 when the book has 42 has an opinion that can be tested; a bettor who thinks the over feels right has a guess that drifts toward 52.4% over time.
Edges in the major markets are small. Beating the closing NFL spread by 2 to 3 points of implied probability over a season puts a bettor among the winners, and the books know it, which is why a book that limits winners, as Bovada does, reacts to the prices a bettor takes rather than to the money won. Because the edge is thin, the stake has to match it, and our guide to bankroll management covers why a 5% EV bet still gets 1% to 2% of the roll and not 10%.
Before the next bet, write down the probability you think the side covers and set it against the price, and bet only when your number beats the book’s by more than you could be fooling yourself. A bettor who cannot name a fair probability has no way of knowing whether the ticket is a good bet or a winning one, and the book is counting on nobody checking.