Betting variance is the gap between what you expect to happen and what actually happens over a run of bets. It explains why a good bet can lose, and why a bad method can look great for weeks.
This guide uses simple maths to show how big those swings are, how long losing runs last, and how many bets you need before results mean much.
Read the transcript
Even a real edge loses, often. Here's why.
Imagine a bettor with a genuine five per cent edge, betting ten pounds at odds of two, a thousand times.
On average, they'd be five hundred pounds up. But averages hide a lot.
Here are forty bettors with exactly the same edge. Some end up well ahead. Some are still behind after a thousand bets.
After a hundred bets, roughly three in ten are still behind. Losing runs of eight in a row are normal.
So judge yourself on hundreds of bets, keep your stakes small, and check your prices against the closing line.
Please bet responsibly.
The short version
- A value bet is one where the odds are bigger than the true chance suggests. It can still lose, and often does.
- With a 5% edge at odds of 2.00, you would still be behind after 100 bets about 31% of the time.
- After 1,000 bets, that falls to about 6%, but it does not reach zero.
- Losing runs of 8 or more are normal, even with an edge.
- Most bettors have no edge at all, so for them betting variance only hides the long-run loss.
Why value bets still lose
A value bet is about price, not certainty. Say a coin is weighted to land heads 52.5% of the time and someone offers you 2.00 on heads. That is a good price, because fair odds would be about 1.90. Even so, you will lose 47.5% of those bets.
So each bet is close to a coin flip. The edge only shows up over many bets, and even then it is buried under a lot of noise. That noise is betting variance. For more on judging the price, see our guide to expected value betting.
A betting variance simulation: 1,000 bets at 2.00
Let’s put numbers on it. Take £1 bets at odds of 2.00, with a true chance of 52.5% (p = 0.525). That is a 5% edge, which is more than most bettors ever achieve.
Worked example
For one £1 bet, you win £1 or lose £1.
- Expected profit per bet: 0.525 × £1 − 0.475 × £1 = £0.05
- Standard deviation per bet: √(1 − 0.05²) = about £1.00
Over n bets, expected profit grows with n, but the standard deviation grows only with √n. Then, using a normal approximation, the chance of being behind is the chance of falling more than (expected profit ÷ standard deviation) below the average.
Here is what that gives. All figures are approximate.
| Bets | Expected profit | Standard deviation | Chance of being behind |
|---|---|---|---|
| 100 | £5 | about £10 | about 31% |
| 1,000 | £50 | about £31.60 | about 6% |
After 100 bets, the swing (£10) is twice the expected profit (£5). As a result, roughly 3 in 10 people with this real edge would be down. About 95% of outcomes fall between roughly £15 down and £25 up.
After 1,000 bets, the picture is clearer. Expected profit is now bigger than the swing, so the chance of being behind falls to about 6%. Even so, a range of about £12 down to £112 up is still normal. An exact binomial sum gives slightly lower figures (about 27% and 5%), but the message is the same.
Use the calculator below to run your own simulation with different odds, edges and numbers of bets.
Variance simulator
How long losing runs can be
Losing runs are part of betting variance, and they are longer than most people expect. In our simulation of the same 1,000 bets at 2.00, the longest losing run was usually about 8 bets. In roughly 1 in 8 runs, it reached 11 or more.
At longer odds, runs get longer still. For example, at odds of 3.00 with the same 5% edge, the longest losing run in 1,000 bets was typically about 14. Those figures are approximate, taken from 5,000 simulated sets of bets.
That is why stake size matters so much. With flat stakes of 1% of a bankroll, a run of 14 losers hurts but does not end things. With 10% stakes, it would. Our guide to bankroll management covers this in detail.
Sample size: how many bets before results mean much?
One simple test is to ask when expected profit becomes bigger than one standard deviation. With a 5% edge at 2.00, that takes about 400 bets. For two standard deviations, it takes about 1,600 bets.
With a smaller edge, it takes far longer. Halve the edge to 2.5%, and you need about four times as many bets. Therefore, a few weeks of profit or loss tells you very little about your method.
That is one reason careful bettors also track closing line value. It gives a faster, if imperfect, read on whether your prices are any good. If you want the statistics behind this, see the normal approximation section of the binomial distribution article.
What betting variance means for you
First, judge your bets on price, not on results. A loss at a good price was still a good bet, and a win at a bad price was still a bad one.
Next, keep stakes small and flat, and only bet what you can afford to lose. Also, be honest about edge. Most bettors have none, and for them betting variance simply hides a slow loss behind lucky spells.
Finally, never chase a losing run. It is a normal part of betting variance, and bigger stakes only add risk. Our guide to value betting myths covers more of these traps.
Related guides
18+ only. Betting should be fun, and every bet can lose. Set a budget you can afford to lose and stick to it. For free, confidential support, visit BeGambleAware.org or call the National Gambling Helpline on 0808 8020 133.