What Is Expected Value (EV) in Betting? Formula + Football Example

Expected value is the average result of a bet if you could place it thousands of times under the same conditions. It's not what will happen tonight. Tonight you either win or lose. EV describes the long run.

Every bet has three ingredients:

• The odds you're offered (decimal odds in this article, e.g. 2.50).
• The probability that the outcome happens. Nobody knows this exactly, so in practice it's an estimate.
• The stake. EV scales with it, so it's easiest to think per 1 unit staked.

If the odds are generous compared with the probability, EV is positive. If they're stingy, EV is negative. Because bookmakers build a margin into their prices, most bets on most markets are negative EV. Value betting is the habit of only taking the exceptions.

There are two ways to write it. They give the same answer.

Version 1, per unit staked:

EV = (probability x decimal odds) - 1

Version 2, the long form with a stake:

EV = (probability x profit if it wins) - (probability of losing x stake)

If you'd rather work with fair odds than probabilities, there's a third form. The fair odd is just 1 divided by the probability, so:

EV% = (bookmaker odd / fair odd - 1) x 100

That last one is the formula JOPP shows on every row. Same maths, just easier to read when you've got two prices side by side.

Want to try it with your own numbers? The free EV calculator does all three versions at once.

A quick sanity check with a coin#

A fair coin lands heads 50% of the time, so the fair odd is 2.00. If someone offers you 2.10 on heads:

• EV = 0.50 x 2.10 - 1 = +0.05, or +5%.

Offered 1.90 instead, it's 0.50 x 1.90 - 1 = -0.05, or -5%. Same coin, same probability. Only the price changed, and that's the whole point: value lives in the price, not in the outcome.

Here's a worked example with made-up numbers. It's a hypothetical, not a real match or a real price.

Example. A striker is playing at home. You estimate he has a 48% chance of registering at least one shot on target (the "1+ shots on target" or "over 0.5" market).

• Fair odd = 1 / 0.48 = 2.08
• A bookmaker offers 2.30

Version 1: EV = 0.48 x 2.30 - 1 = +0.104, so about +10.4% per unit.

Version 3: EV% = (2.30 / 2.08 - 1) x 100 = +10.4% (using the unrounded fair odd of 2.083).

Long form, with a 10 unit stake:

• Win: 0.48 x 13 units profit = 6.24
• Lose: 0.52 x 10 units = 5.20
• EV = 6.24 - 5.20 = +1.04 units

So each time you place a bet like this, you "earn" about 1 unit on average, even though you'll lose it slightly more often than you win it. That's normal. Lots of positive EV bets lose more often than they win.

If you want to understand how a probability like that 48% gets built for this market, I go through it in shots on target betting.

How the price changes the answer#

Same player, same 40% chance, different odds. This is the table worth staring at for a minute.

Nothing about the player changed. The bet went from bad to good purely because of the number next to his name.

This is the hard part and the reason EV is easy to write down and hard to do well. Three common sources:

1. The market itself. Take a sharp or very liquid price, remove the bookmaker's margin, and treat what's left as the fair probability. Then look for softer bookmakers paying more than that. The fair odds calculator does the margin removal for you.
2. Your own model. Build the probability from player data: shots or expected goals per 90 minutes, how many minutes he's likely to play, the opponent, home or away, penalties. That's what JOPP does for each player market.
3. Your own judgement. Possible, but be honest about how precise it really is. If your "48%" could just as easily be 40%, the EV you calculate is mostly noise.

Whichever you use, the estimate is never exact. A model can be wrong, team news can change things, and prices move. EV% is only as good as the probability behind it.

People ask this a lot, and there's no clean answer, but here's how I think about it.

• Small positive EV (say +2% to +5%) is where most genuine edges live. It's also where a small mistake in your probability can wipe the edge out completely.
• Bigger EV (+10% and up) looks great, but ask why the price is so big. Sometimes the bookmaker is slow. Sometimes they know something you don't, like a player who's not starting. The bigger the gap, the more you should double-check team news.
• Very high EV on a long shot is often just model error on a rare event. A 5% vs 4% disagreement turns into a huge EV% at long odds.

So "good" is a mix of size and confidence. A modest edge you trust beats a huge one you don't.

This is the part nobody likes. Positive EV doesn't mean you'll be in profit next week, or next month.

Example. Say you place 100 bets at odds of 3.00, each with a true 35% chance of winning. EV per bet is 0.35 x 3.00 - 1 = +5%, so you expect roughly +5 units over 100 one-unit bets. But the spread is wide. The standard deviation of that result works out to about 14 units, and the chance of being down after those 100 bets is around 38%.

At 1,000 bets the expected profit grows to about +50 units and the chance of being down drops to around 14%. Still not zero. That's just binomial maths, assuming your 35% is actually right. If it isn't, the edge you think you have may not exist.

That's why EV betting goes hand in hand with:

• Flat or small stakes. No chasing. A fixed small unit per bet keeps a bad run survivable.
• Tracking. Write down the price you took and the fair odd at the time. JOPP's My Bets view does this for you, including ROI and a profit curve.
• Patience with the sample. Judge yourself on hundreds of bets, not a weekend.

• Using the wrong price. EV is calculated on the odds you actually got, not the price an hour later.
• Ignoring rules. If a player bet is void when he doesn't start at one bookmaker but stands at another, those prices aren't directly comparable. More on that in anytime goalscorer rules.
• Multiplying edges in a bet builder. Combining legs multiplies the bookmaker margin too, and correlation changes the maths. See bet builder tips.
• Confusing "likely" with "value". A 1.30 favourite can be a terrible bet and a 6.00 outsider can be a good one. EV doesn't care about likely.