Variance in betting is how widely real results spread around what your bets should return on average, and it is why a method with a real edge can lose for months. With illustrative numbers, 1,000 bets of $10 at $3.00 with a 2% edge should make $200 on average, yet a run of 1,000 such bets still finishes behind about 1 time in 3.
The spread grows with the price you bet at, and only a large number of bets lets an edge show through it. Variance explains swings around a real edge. It rarely explains a record that keeps losing at about the margin's rate over thousands of bets, which is usually the bookmaker's margin at work.
What variance measures
For a run of bets, variance is usually read through its square root, the standard deviation: the typical distance between a result and the average your edge implies. For one $1 bet at decimal odds with a chance p of winning:
- expected profit per $1 = p x odds - 1, which is the edge
- standard deviation per $1 = odds x square root of (p x (1 - p))
Over four times as many bets, the expected profit is four times as large, while one standard deviation only doubles, because it grows with the square root of the number of bets. So the edge gains on the swings slowly, and the longer your price, the more bets it takes before the edge shows.
Why long-priced bets swing more
A $1.50 bet wins most of the time and pays little; a $20.00 bet loses most of the time and pays a lot. Give both the same 2% edge and their averages match, but the second spreads far wider. With illustrative prices, each with a 2% edge, so each bet's chance is 1.02 / odds:
| Price | Win chance | Standard deviation per $1 | One standard deviation, 1,000 bets of $10 | Chance of being behind after 1,000 bets |
|---|---|---|---|---|
| $1.50 | 68.0% | 0.70 | $221 | 18% |
| $2.00 | 51.0% | 1.00 | $316 | 25% |
| $3.00 | 34.0% | 1.42 | $449 | 33% |
| $5.00 | 20.4% | 2.01 | $637 | 36% |
| $10.00 | 10.2% | 3.03 | $957 | 40% |
| $20.00 | 5.1% | 4.40 | $1,391 | 42% |
The working for $3.00: standard deviation per $1 = 3 x square root of (0.34 x 0.66) = 3 x 0.474 = 1.42. Over 1,000 bets of $10 it is 1.42 x $10 x square root of 1,000 = 1.42 x $316.2 = $449. Every row expects the same $200 profit, 2% of the $10,000 staked, and at $20.00 one standard deviation is almost seven times that. The last column counts exactly how often the winners fall short of break-even.
The table settles the sports and racing question too. Line and total bets priced near $1.90 swing about as little as the $2.00 row, while racing bets on $10.00 chances, or multis at similar odds, sit near the bottom. Any difference in variance between sports betting and racing comes from the prices, not the code.
Risk: Betting involves risk. The 2% edge in every row is assumed for the arithmetic; a bet at an ordinary bookmaker price carries a margin instead, and a longer price only widens the swings around it. See responsible gambling for limits and support.
The range of results over 1,000 bets at $3.00
Example: Illustrative assumptions: 1,000 bets of $10 each, all at $3.00, with a true 34% chance of winning, which is a 2% edge (0.34 x 3.00 - 1 = 0.02).
Expected winners = 1,000 x 0.34 = 340, and expected profit = 2% of $10,000 = $200. A run's profit is $10 x (3 x winners - 1,000), so 340 winners make $10 x (1,020 - 1,000) = $200. Counting every way the 1,000 bets can land (the binomial distribution) gives the range:
| Where a run finishes | Winners | Profit |
|---|---|---|
| Worst 1 in 20 | 315 or fewer | -$550 or worse |
| 1 in 10 from the bottom | 321 | -$370 |
| 1 in 4 from the bottom | 330 | -$100 |
| The middle | 340 | +$200 |
| 1 in 4 from the top | 350 | +$500 |
| 1 in 10 from the top | 359 | +$770 |
| Best 1 in 20 | 365 or more | +$950 or better |
Break-even needs 333.3 winners, so 333 or fewer is a loss, and that happens 33.3% of the time: about 1 run in 3 finishes behind with a real edge. The chance of still being behind falls slowly as the bets add up:
| Bets placed | Expected profit at $10 a bet | Chance of being behind |
|---|---|---|
| 100 | $20 | 46% |
| 500 | $100 | 37% |
| 1,000 | $200 | 33% |
| 2,000 | $400 | 26% |
| 5,000 | $1,000 | 16% |
| 10,000 | $2,000 | 8% |
At about 20 bets a week, 1,000 bets is roughly a year, so a punter with this edge still has about one chance in three of a losing year.
Risk: Betting involves risk. The 2% edge here is an assumption, not something 1,000 bets can prove, and a method that has a real edge can still finish a year behind. See responsible gambling for limits and support.
How deep a betting downswing gets
A downswing is a fall below an earlier high point, and its depth is the drawdown. Finishing ahead does not mean the run was smooth. For the same 1,000 bets at $3.00, measured in units of one $10 stake:
| Drawdown at some point in the 1,000 bets | Chance |
|---|---|
| 30 units ($300) or more | 84% |
| 40 units ($400) or more | 58% |
| 60 units ($600) or more | 22% |
| 80 units ($800) or more | 7% |
The typical worst fall is about 43 units, and 1 run in 20 falls about 85 units or more. These figures are exact: they track the gap below the running high bet by bet, where a loss adds 1 unit and a win takes 2 off, down to zero, across every way the 1,000 bets can land. Straight runs of losers, the steepest part of most downswings, have their own arithmetic in losing streaks in betting.
Set a review point before you start. For these bets a fall of 85 units or more comes in about 1 run in 20. Reaching it is the time to stop and check whether the run is bad luck or a bad method, not a reason to bet more.
Separating bad luck from a bad method
A bad run on its own cannot tell you which it is, but three checks narrow it down.
First, compare your winners with what your own prices said. Expected winners = the sum of your estimated chances, and the standard deviation of the number of winners = square root of the sum of p x (1 - p). With illustrative numbers, 300 bets each rated about 32% expect 300 x 0.32 = 96 winners, with a standard deviation of square root of (300 x 0.32 x 0.68) = 8.08.
| Winners | Shortfall | Standard deviations short | If your ratings are right, this or worse happens |
|---|---|---|---|
| 84 | 12 | 1.49 | About 1 time in 13 |
| 76 | 20 | 2.48 | About 1 time in 140 |
A tally of 84 is an ordinary bad run, while 76 is rare enough to go back over the ratings, the data and the prices you took.
Second, check closing line value: whether your prices still beat the final prices before the start. Positive closing line value through a losing run points at luck, and negative points at the method. It says something after far fewer bets than profit does, as sample size in betting explains.
Third, check what changed. If you stopped getting the prices you used to, a bookmaker limited your stakes, or you moved into new markets mid-run, the run is no longer the same method.
When a long losing record is not variance
Over a few hundred bets, luck can hide almost anything. Over thousands, the size of the loss starts to tell. With a real 2% edge, 3,000 bets of $10 at $3.00 still finish behind about 1 time in 5, but finishing 5% of turnover down or worse is far rarer. That takes 950 winners or fewer against 3,000 x 0.34 = 1,020 expected, since $10 x (3 x 950 - 3,000) = -$1,500, and it happens only about 1 time in 280. A record that keeps losing at about the margin's rate over that many bets is very unlikely to be bad luck.
For most people who keep losing, the cause is the margin built into bookmaker prices. With illustrative numbers: a punter with no edge betting at $3.00, where the margin costs about 5% of every bet, has a true chance of 0.95 / 3 = 31.7% per bet. Over 3,000 bets of $10:
- expected result = -5% of $30,000 = -$1,500
- one standard deviation = 3 x square root of (0.3167 x 0.6833) x $10 x square root of 3,000 = about $764
- the exact chance of being ahead at the end is about 2.4%, roughly 1 in 40
A record like that is the margin doing what it does, and can you make money betting explains why most punters end up on the wrong side of it.
Never raise stakes, bet more often or bet for longer to win a losing run back: the expected result per dollar staked stays the same, and bigger stakes only make the next swing bigger. Chasing losses explains why it backfires. If losing has you betting more than you planned or worrying about money, read the signs of a gambling problem. For free and confidential support call 1800 858 858 or visit gamblinghelponline.org.au.
A bankroll that survives variance
Size the stake to the swings, not to the expected profit. In the 1,000 bets at $3.00 above, the typical worst fall was about 43 units and the 1-in-20 worst about 85, so as a share of the starting bankroll:
| Stake per bet | Typical worst fall | Worst fall in 1 run in 20 |
|---|---|---|
| 0.5% of the bankroll | 21.5% | 42.5% |
| 1% | 43% | 85% |
| 2% | 86% | 170%, more than the bankroll holds |
The working is the fall in units x the stake share: 85 x 0.5% = 42.5%. Shorter prices shrink every figure and longer prices stretch them, so size the stake from the prices you actually bet at. Risk of ruin turns the same arithmetic into the chance of losing the whole bankroll. Stake size only sets how hard the swings land; whether any edge sits under them is a question for your betting strategy, not your staking.
A deposit limit caps the new money one bookmaker account will take in each period you choose, such as a day, a week, a fortnight or a month. A limit at one bookmaker does not apply at another. Under measure 6 of the National Consumer Protection Framework every Australian online bookmaker must offer a deposit limit: lowering it takes effect immediately, and raising it only after a 7-day wait.
Risk: Betting involves risk. Every figure here assumes the 2% edge is real, and an edge you have overestimated makes each fall deeper and each recovery less likely. There is no guarantee of profit over any number of bets. See responsible gambling for limits and support.