Expected Value in Betting with Betfair Commission: Is This Bet Worth Placing?

The question

"My model says 55% and Betfair says 1.90. Is this bet actually worth placing?"

Expected value in betting with commission answers that in one line. It tells you what a bet is worth on average, after Betfair's cut, before the result is known. Every good betting decision rests on it.

The idea in one sentence

Expected value (EV) is your average profit per bet if you could place the same bet thousands of times: the chance of winning times what you'd win, minus the chance of losing times what you'd lose.

The picture

Picture one bet split into two branches. On one branch you win, and it happens with your estimated probability. On the other you lose. Multiply each branch's money by its chance and add them up. That total is the expected value.

A positive EV doesn't mean you'll win this bet. It means that if your probability is right, a long run of bets like it will make money. A negative EV means the opposite, however lucky you feel.

Commission matters because it only bites on the winning branch. It shrinks your wins, not your losses, so it lifts the win rate you need to break even. On Betfair it's 2% of net winnings in each market, and every EV on this page already includes it.

Try it · Expected value

Your probability it wins55.0%

Commission2.0%

Decimal odds

Stake

Expected value

+£0.70

+3.51% of stake

├─Selection wins 55.0%+£17.64

├─Selection loses 45.0%−£20.00

Before commission the EV would be +£0.90.

Break-even

53.13%

Your edge

+1.87 pts

Your fair odds

1.82

EV per £1 staked against your probability. The dot is you.

Worth placing: +3.5p per £1 staked if your probability is right.

EV is what the bet makes on average if your probability is right. Commission is taken from winnings only, so it is already in every figure here.

Worked Betfair example

Your model rates Over 2.5 goals at 55%. Betfair offers a back price of 1.90, and you stake £20. Commission is 2%. (Illustrative figures.)

What a win pays. £20 at 1.90 wins £18. Commission is 2% of £18, which is £0.36. You keep £17.64.
What a loss costs. £20.
Expected value. 0.55 × £17.64 − 0.45 × £20 = £9.702 − £9.00 = +£0.70 per bet. That's +3.51% of your stake.
Without commission. 0.55 × £18 − 0.45 × £20 = +£0.90, or +4.5%. Commission has taken about a fifth of your edge.
Break-even probability. 1 ÷ (1 + 0.90 × 0.98) = 1 ÷ 1.882 = 53.13%. The raw price implies 52.63%; commission adds half a point.
Your edge in points. 55% − 53.13% = 1.87 points. A small edge, but a real one if your 55% is right.
Over a season. 1,000 bets like this at £20 each have an expected profit of £702.

How sensitive the answer is to your probability

The same bet at 1.90, after 2% commission:

Your probability	EV per £1
50%	−5.90p
52%	−2.14p
53%	−0.25p
54%	+1.63p
55%	+3.51p
57%	+7.27p

Each point of probability is worth about 1.9p per £1. Get your estimate a couple of points wrong and a value bet becomes a losing one. That's why your probability needs to be calibrated.

The lay side

You think the draw in a match is 27%, and you can lay it at 3.40 for a £20 backer's stake.

Liability. £20 × (3.40 − 1) = £48. You pay this if the draw lands.
What you win. If it isn't a draw, you keep £20 less 2%: £19.60.
Expected value. 0.73 × £19.60 − 0.27 × £48 = £14.308 − £12.96 = +£1.35 per lay.
As a share of liability. £1.35 ÷ £48 = +2.81%. Judge lays on liability, because that's the money at risk.
Break-even draw chance. 0.98 ÷ (2.40 + 0.98) = 28.99%. You make money laying at 3.40 as long as the true draw chance is below that.

The formula

EV of a back bet

\text{EV}_{\text{back}} = p\,(O-1)(1-c) - (1-p)

p is your probability that the selection wins.
O is the decimal price you back at.
c is the commission rate: 0.02 on Betfair.

In plain English: the chance of winning times your winnings after commission, minus the chance of losing times your stake. The answer is per £1 staked.

EV of a lay bet

\text{EV}_{\text{lay}} = (1-p)(1-c) - p\,(O-1)

p is still the chance the selection wins (so the lay loses).
The answer is per £1 of backer's stake. Divide by (O − 1) for EV per £1 of liability.

In plain English: you win the backer's stake (less commission) when the selection loses, and pay the liability when it wins.

Break-even probability

p^{*}_{\text{back}} = \frac{1}{1+(O-1)(1-c)}, \qquad p^{*}_{\text{lay}} = \frac{1-c}{(O-1)+(1-c)}

$p^{*}$ is the probability at which EV is exactly zero.

In plain English: back only when your probability is above $p^{*}$ ; lay only when it's below. The gap between your probability and $p^{*}$ is your edge.

Commission is on the market, not the bet

Betfair charges commission on your net winnings in each market. If you have two bets in the same market and one wins while the other loses, commission is worked out on the combined profit. For a single bet held to the result, the formulas above are exact.

Try it

Set back, probability 55%, odds 1.90, stake £20 and commission 2%, and check the EV reads +£0.70 with a break-even of 53.13%. Then drop your probability a point at a time and find where the bet stops being worth placing.

Common mistakes

Calculating EV before commission. At 1.90 it turns a 53% view from a small winner into a small loser. Always use the net figure.
Treating a positive EV as a prediction. A +3.5% bet still loses 45% of the time. EV is about the long run, not this match.
Trusting a probability you haven't tested. EV is only as good as your p. A model that says 55% but is really 52% has negative EV on every bet at 1.90 (Lesson 7.1).
Judging lays on the backer's stake. A lay at 3.40 for £20 risks £48. Measure the return against £48.
Chasing big EV on long shots. Big EV numbers at long odds usually mean the probability is wrong, not the market. Check it against the closing price.

Why EV on paper doesn't always survive contact with the market: why good models still lose money.

Expected value and commission