Expected value
"Will this team win?" is the question everyone asks. Expected value, or EV, is the question that decides whether you make money. It combines two things: how often a bet wins, and what it pays when it does.
The formula
EV is what a bet earns on average per $100, if you could make it many times:
EV = chance it wins × profit if it wins − chance it loses × stake
Say the Lions win 45% of the time and you bet $100 at +130. 45% of the time you win $130; 55% of the time you lose $100. That is 0.45 × $130 = $58.50, minus 0.55 × $100 = $55.00, for an EV of +$3.50: about $3.50 profit per $100 bet over the long run.
No single bet earns $3.50. This one either wins $130 or loses $100. EV is the average across many bets like it: make 100 of them, win 45, and you collect 45 × $130 = $5,850 and lose 55 × $100 = $5,500, a profit of $350, or $3.50 a bet. Over a short run anything can happen (see variance).
Edge and EV
EV is positive only when your chance beats the price's break-even rate. At +130 the break-even is 43.48%, so a 45% chance is an edge of 1.52 points. Edge is measured in percentage points; EV turns it into dollars. The same edge is worth more EV at a longer price, because each win pays more, but those bets also swing harder.
The price changes everything
Keep the 45% and change only the price, and EV moves from clearly positive to negative. The pick stays the same; the price decides whether it is a good bet. The example below shows three prices for the same Lions.
EV is only as good as the chance you plug in
The arithmetic is easy. The hard part is the chance. In the last lesson the market's fair chance for these Lions was 41.74%. A 45% estimate says the market is wrong by more than 3 points. Sometimes it is, but most of the time the market is closer to right. Plug in 41.74% and the same +130 bet is worth −$4.00 per $100. Positive EV built on an overconfident chance is a loss in disguise.
How Consensus Edge shows EV
We work out EV from our consensus chance at the best price we track. If you've picked your book, we also show your EV at your book's price, which can be lower. Positive EV is not a promise: a +$5 bet still loses often. It means that, made at this price many times, the bet comes out ahead on average. Stake it from your bankroll in small units, whatever the EV says.
Try it: put a chance and a price into the calculator below to see the EV per $100.
Example. You estimate the Lions win 45% of the time, and three books offer different prices (illustrative prices, not live data):
| Price | Break-even | EV per $100 at 45% |
|---|---|---|
| +140 | 100 ÷ 240 = 41.67% | 0.45 × $140 − 0.55 × $100 = $63.00 − $55.00 = +$8.00 |
| +130 | 100 ÷ 230 = 43.48% | 0.45 × $130 − 0.55 × $100 = $58.50 − $55.00 = +$3.50 |
| +120 | 100 ÷ 220 = 45.45% | 0.45 × $120 − 0.55 × $100 = $54.00 − $55.00 = −$1.00 |
Same team, same 45%. At +140 and +130 the bet is worth making; at +120 it is a small loser, because 45% falls short of that price's 45.45% break-even.
And if the real chance is the market's 41.74%, even +130 is worth 0.4174 × $130 − 0.5826 × $100 = $54.26 − $58.26 = −$4.00 per $100.
Try it
Terms in this lesson
Expected ValueEdgeBreak-evenVarianceBest OddsYour EVFair Probability