Expected value (EV) betting
Expected value, EV for short, is what a bet wins or loses on average if you could make it many times. A bet is positive EV when the price pays more than the chance of winning is worth. It is the only measure of a bet that matters, and it can't be read off one result.
The sum
EV is two numbers added together: what you win times how often you win, and what you lose times how often you lose.
Take a point spread at -110 on a game that is a true coin flip. You risk $100 to win $90.91.
- Half the time you win: 0.50 × $90.91 = $45.45.
- Half the time you lose: 0.50 × -$100 = -$50.00.
Add them and the bet is worth -$4.55 for every $100 you stake. That is the vig written as EV, and it is why a player who picks exactly half his games goes broke slowly. On any single bet you either win $90.91 or lose $100. You never lose $4.55. The EV is what those results average out to over hundreds of bets.
When the price beats the chance
Now take an underdog at +150, and say you rate it a 44 percent chance. The price only needs 40 percent to break even.
0.44 × $150 = $66, and 0.56 × -$100 = -$56. The bet is worth +$10 for every $100.
That is a positive EV bet, often written +EV, and it is the only kind I'd ever want to make. The sum is simple. The hard part is the 44 percent. Get that wrong by four points and the same bet is worth nothing, and get it wrong by six and it is a losing bet. Every EV figure is only as good as the probability you put into it, so the honest question about EV is never the arithmetic. It is where your percentage came from.
Where the probability comes from
There are two ways people answer that.
The first is their own handicapping: a model, a rating, a read on a team. That is the old way, and it works for the few people who are better at estimating a game than the market. Most aren't, and the book's price is built from more money and more information than any one player has. I'd be very slow to believe my own number against a line that has been bet all week.
The second way is what most people mean today by "EV betting" or a value betting system. Instead of trusting your own number, you take the price at a book that takes big bets and moves fast, strip the margin out of it, and treat what is left as the true chance. Then you look for a slower book offering a better price on the same side.
Say the sharp book has a game at -125 and +115. Those come to 55.56 and 46.51 percent, which add to 102.07. Divide each by the total and the underdog's fair chance is 45.57 percent. A second book still has that underdog at +130.
0.4557 × $130 = $59.24, and 0.5443 × -$100 = -$54.43. That is +$4.81 per $100, worked out from nobody's opinion but the market's. The no-vig calculator does the middle step, and the implied probability page shows the method.
I think this is the sounder of the two methods for most people, because it borrows the market's judgment instead of relying on your own. It is the same idea as closing-line value, measured before the game instead of at the close, and it rests on the same belief: that the sharpest price in the market is a better estimate than yours.
What +4.81 feels like
Small. Bet that underdog 100 times at $100 and the expected profit is $481. The swing around that figure is about $1,145 either way, one standard deviation, so a perfectly good run of +EV bets can easily finish 100 bets behind. It takes many hundreds of bets before the edge shows through the noise.
That is why I'd keep each stake at 1 or 2 percent of the bankroll, however good the EV looks. An edge of 4.81 percent is a fine edge. It is not protection against a bad month.
The book's side of it
Books know this game better than the players do. A player who keeps taking prices the rest of the market has already moved away from is easy to spot in the account records, and most books respond by cutting his limits, sometimes to a few dollars. The +EV bettor's real problem is rarely finding the bets. It is keeping somewhere to place them.
So if you go this way, spread the action, bet like a normal player and expect the good prices to last only as long as the book doesn't notice. Line shopping is the plain version of the same habit, and I'd recommend it to every bettor whether he thinks in EV or not.
A bet is not good because it won, or bad because it lost. It is good if the price paid more than the chance was worth.