Kelly Stake

Expected value, variance and why results lie to you

16 September 2026 · 4 min read

A winning bet can be a bad bet, and a losing bet can be a good one. The way to tell them apart is expected value — and the reason it takes so long to see is variance.

Here is the hardest idea in betting, and the most important. Whether a bet won tells you almost nothing about whether it was a good bet. Good bets lose all the time. Bad bets win all the time. To judge a bet, you need a number that ignores the result.

Expected value

Expected value (EV) is what a bet is worth on average if you could place it a million times. For a simple win-or-lose bet:

EV = (probability of winning × profit if you win) − (probability of losing × stake)

Take a £10 bet at 3.00 where you believe the true chance is 40%. If it wins you make £20; if it loses you lose £10.

EV = (0.40 × £20) − (0.60 × £10) = £8 − £6 = +£2

Every time you place that bet, you are on average £2 better off — a 20% return on the stake. That is a good bet even on the days it loses. Now suppose the true chance is only 30%: EV = (0.30 × £20) − (0.70 × £10) = −£1. Bad bet, even on the days it wins.

A shortcut: a bet has positive EV whenever your probability × decimal odds is greater than 1. 0.40 × 3.00 = 1.20, so yes. 0.30 × 3.00 = 0.90, so no. That number minus one is your edge, and it is what the Kelly formula feeds on.

Variance

If your bets have positive EV, why is your balance not going up in a straight line? Because of variance — the natural scatter of results around the average. A 40% shot loses 60% of the time. Over ten bets it will often lose seven or eight. Over a hundred it might lose seventy. None of that means your estimate was wrong; it is what 40% looks like up close.

Variance is bigger at longer odds. A bettor who backs 1.50 shots sees a smooth line. One who backs 10.00 shots with the same edge sees long droughts and sudden spikes — and needs far more bets to know whether they are any good.

How many bets before you know?

More than you think. With a healthy 5% edge at around even money, you need well over a thousand bets before you can be reasonably sure your profit is skill rather than luck. A hundred bets tells you almost nothing. This is why most tipsters’ “proven” records are noise, and why a strategy needs to be tested across seasons of history, not weeks.

Closing line value: the shortcut

There is one faster way to check whether you have an edge. Compare the price you took with the price just before the start — the closing line. The closing price contains everything the whole market learned, so it is the best estimate of the true probability. If you consistently take 2.20 on things that close at 2.00, you are beating the market, and profit will follow. If you take 2.00 on things that close at 2.20, you are losing even if you happen to be ahead this month.

What this means in practice

  • Judge bets by EV, not by whether they won.
  • Judge yourself by many hundreds of bets, or by closing line value — not by a good month.
  • Expect long losing runs, and size stakes so you can survive them.
  • Write your probabilities down before the match. It is the only way to find out later whether they were any good.

Kelly Stake is built around this loop. Your model states a probability, the platform records it, compares it with the market, and after enough bets shows you whether your edge is real. The result of any single match is the least interesting number on the screen.

Next in the Academy

Put it to the test

Backtest a strategy on years of history before it costs you a penny.