Variance is the spread of observed results around a theoretical expected value. It explains why short-term results can land far from what you expected, without any mistake being made. The higher the odds played and the smaller the number of decisions, the longer and wider the runs get, winning and losing alike.
Variance in two sentences
Variance is the spread of your results around a theoretical expected value. Repeat the same decision under comparable conditions and you'll never get a tidy run of wins and losses, even when the estimate behind it was spot on.
A good decision can lose. A bad one can win.
Expected value and variance answer different questions
Expected value tells you what should happen on average. Variance tells you how far single results can wander from it. Mixing the two up is the most common mistake on this topic.
A positive expected value says nothing about how big the swings around it can be. Two bets with the same expected value can behave very differently: one plods along, the other lurches.
Good process, bad result, and the other way round
On an uncertain event, how good a decision is and how it turns out are separate things. An outcome estimated at 70% fails three times in ten. Those misses aren't analysis errors: the estimate already allowed for them.
| Favourable result | Unfavourable result | |
|---|---|---|
| Sound decision | Consistent, the expected case | Normal, uncertainty played its part |
| Weak decision | Misleading: it reinforces a worthless method | Readable, but often blamed on bad luck |
I find this idea harder to accept than variance itself: a stroke of luck looks like skill until you start counting.
Winning runs, losing runs: expect both
Several losses in a row aren't a statistical oddity. They're normal behaviour for any sequence of uncertain decisions. Even a perfectly balanced 50% event throws up stretches of several misses in a row over enough repeats.
The reverse holds too. A run of good results validates a method about as little as a bad run invalidates it. Either can show up without the quality of your decisions shifting at all.
What the odds do to variance
At equal expected value, higher odds mean more variance than lower odds. An unlikely outcome pays a lot when it lands and costs the whole stake the rest of the time. The gap between the two scenarios is wide, so runs in both directions get longer and bigger.
Lower odds give more frequent, smaller swings. Variance is still there, but it smooths out faster over the same number of decisions.
Variance is the normal spread of results around an expected value. Bad luck is the everyday word for the same thing, with nothing measurable behind it. A bad strategy rests on a structurally wrong estimate or line of reasoning, and you judge it on the process, not on a run of results. Drawdown is what variance does to your capital: a dip measured from a peak.
Four terms that often get swapped by mistake.
What the number of decisions does
The more decisions you add, the closer the average result gets to the theoretical expected value. It gets there slowly, though, far more slowly than intuition suggests. Over ten decisions, variance dominates almost everything. Over several thousand, it weighs a lot less, but it never fully disappears.
That's why a record of ten bets proves next to nothing, whatever the result.
What variance can't tell you about a method
On its own, variance can't tell a solid method from a worthless one. It describes the spread you should expect around an expected value, whether that value is positive or negative.
A run of losses doesn't mean a method is bad, and a run of wins doesn't mean it's good. It takes a large number of decisions before the two start to separate.
How many decisions it takes to decide
Telling a solid method from variance takes a sample whose size depends on the odds played and the edge you assume. There's no universal threshold beyond which a result becomes reliable.
What determines how much data you need to decide →
Variance explains why a result strays from the expected value. How many decisions do you need to watch before concluding anything? That's the subject of the next page.
Responsible gambling: variance isn't something you can control. Sports betting carries a risk of financial loss. Set yourself a budget, don't chase your losses, and use the deposit limits and self-exclusion tools available. Learn more about responsible gambling.
Put it into practice
Apply this guide to real odds.
See a market reading
A real match with its odds, movements and 0-100 signal.
Open the demoMargin calculator
Measure a bookmaker's margin on any market.
Calculate the marginDig into the market
Odds movements are only part of the story. Here are the next topics to read.
Profitability and risk: the complete guide
The full picture: profit, ROI, expected value, variance, sample size, drawdown, risk.
Read the guideExpected value: the theoretical edge of a bet
The theoretical figure results scatter around.
Understand EVHow many bets to judge a performance?
What it takes for a method to stand out from variance.
See the methodDrawdown: measuring the dips in a bankroll
What variance does, in practice, to the capital you've committed.
Understand drawdownBankroll in sports betting
How to size your stakes against normal runs.
Understand bankrollThe risks of sports betting
The psychological risk of confusing result and decision.
See the risksFrequently asked questions
What is variance in sports betting?
It's the spread of observed results around a theoretical expected value. It explains why the same type of decision can give very different results from one run to the next, even with no error in the analysis.
Why does variance exist even with a good estimate?
Because a sporting event stays uncertain however good the analysis is. An outcome estimated at 70% fails three times in ten. Those misses aren't mistakes: the estimate already allowed for them.
Why do higher odds produce more variance?
An unlikely outcome pays a lot when it lands and costs the whole stake the rest of the time. The gap between possible results is bigger, so runs in either direction get longer and wider.
Does a losing run prove a method is bad?
Not on its own. Over enough decisions a losing run is normal, especially at high odds. It only becomes a signal when you cross-check it against other measures, over a large sample.
How do you tell variance from a bad strategy?
Variance is read on the process (the quality of the reasoning, how well calibrated the estimates are) and not on the result of a handful of decisions. You need a large number of decisions before a method starts to stand out from the noise.
Sources & methodology
This page draws on the mathematics behind stake sizing: Kelly's formalisation and Thorp's work on favorable gambling systems, which deal with the spread of results around a theoretical expected value. The Gambling Commission and BeGambleAware cover the regulatory side and player support. The odds-analysis method is the one developed by OddScore.
- Define variance as the spread of observed results around a theoretical expected value, never as a sign of a flawed method.
- Link the size of the variance to the odds played: the higher they are, the longer and wider the runs, winning and losing alike.
- Separate the quality of a decision from its isolated result, which stays subject to the uncertainty built into any sporting event.
- Send the question of how much volume it takes to tell a method from noise to the dedicated sample-size page.
- Kelly, J. L. (1956). A new interpretation of information rate. Bell System Technical Journal, 35(4), 917-926.
- Thorp, E. O. (1969). Optimal gambling systems for favorable games. Review of the International Statistical Institute, 37(3), 273-293.
- Gambling Commission, public and players
- BeGambleAware, support for players