Variance and Sample Size: How Many Bets Before a Record Means Anything?

Sports results are noisy. Even a bettor with a real edge will have terrible months, and a bettor with no edge will have great ones. Understanding variance is what stops you from trusting luck, or from quitting a good approach too early.

The margin of error on a win rate

When you observe a win rate over n bets, the uncertainty is roughly 1.96 x the square root of (p x (1 - p) / n), where p is the win rate. For a rate near 50%, the 95% margin of error is:

• 50 bets: about plus or minus 14 points
• 100 bets: about 10 points
• 200 bets: about 7 points
• 400 bets: about 5 points
• 1,000 bets: about 3 points

A 60% record over 100 bets could be anything from about 50% to 70% in reality. A record has to be large before the number can be trusted.

What that means for profit

The uncertainty on ROI is wider than on win rate, because the odds amplify each result. Take 100 bets at odds of 2.00 with a 52% win rate:

• Reported ROI: 0.52 x 2.00 - 1 = +4%
• At the low end of the range (42% win rate): ROI = 0.42 x 2.00 - 1 = -16%
• At the high end (62%): ROI = +24%

The same result fits both a losing and a winning bettor. This is why a short record cannot prove skill.

Losing streaks are normal

People assume streaks mean something has gone wrong. Maths says otherwise. Using a 50% chance of winning each bet:

• In 100 bets, the chance of at least one run of 6 or more losses in a row is about 55%.
• The chance of a run of 8 or more is about 17%.

For a bettor winning only 40% of the time, as happens at odds near 2.50, the effect is stronger: across 500 bets, the chance of a run of at least 10 losses is around 70%. Long droughts are a normal part of betting at any win rate.

How many bets do you need?

Rules of thumb:

• Under 100 bets: almost no information.
• 300 to 500: a rough picture.
• 1,000 or more: a reasonable view of a large edge. Small edges can need thousands.

The smaller the true edge, the more bets are needed to see it. Because genuine edges in modern betting markets are small, you should expect any honest verdict to take a long time.

How to use this

• Do not judge a tipster, or yourself, on a month. Judge on hundreds of bets.
• Expect streaks and plan for them, in your bankroll and in your head. See bankroll basics and chasing losses.
• Look for faster signals, such as whether the price you took beat the final price. See closing line value.
• Be wary of anyone who sells a sure thing. The maths says nobody has one.

Where this leaves our own record

The Track Record page shows every settled tip. As the number of settled tips grows, the figures become more meaningful, and we encourage you to read them with the margins above in mind. We have not yet shown that our picks beat the bookmaker, and our methodology explains why.

Takeaways

• Short records are mostly luck.
• A 95% margin of error is about 10 points at 100 bets and 3 points at 1,000.
• Long losing streaks are normal.
• Judge results over hundreds of bets, and use faster signals as well.

Vantip Team. Information only, not betting advice. 18+. Betting carries risk; see our Responsible Gambling page.