Il Limite
The gambler's fallacy: spotting it in your own data
After three wins a side wins 56% of the time, against a 37% average: it looks like proof that streaks are real. We redid the sum properly, and almost all of that gap disappears.
Pubblicato il 14 settembre 2026
The gambler's fallacy is the idea that an outcome is «due»: after five reds at the roulette table, black becomes more likely. It doesn't, because the ball has no memory. Its opposite twin is the hot hand: whoever just won will keep winning.
In football the question is more interesting than at roulette, because matches aren't genuinely independent: a strong side is still strong the following week. So the useful question isn't «do streaks exist?» but «does a streak add anything to what we already know about that team?».
We tried to answer with our archive, and the route is instructive because the first answer is convincingly wrong.
First sum: it looks like the hot hand is real
Take every match in five leagues and record, for each team and each round, whether it won. Then look at what happens after a win, after three wins in a row, and after three defeats in a row.
| Competition | Wins overall | After one win | After three wins | After three defeats |
|---|---|---|---|---|
| Serie A | 37.1% | 42.5% | 56.1% | 29.1% |
| Premier League | 37.2% | 41.1% | 51.2% | 29.4% |
| La Liga | 37.2% | 40.6% | 55.4% | 26.9% |
| Bundesliga | 37.9% | 41.0% | 53.5% | 28.3% |
| Ligue 1 | 37.3% | 40.3% | 49.0% | 30.8% |
openfootball archive (CC0), 260,125 distinct matches; between 7,892 and 26,392 team-match observations per league. The «after three wins» column rests on 543-1,893 cases. ⚠ Here the sequences run across seasons: May's last match and August's first count as consecutive. The two sums that follow work within a season instead, which is why their numbers don't add up to these.
Read that way it looks obvious: a side that has won three in a row wins the next one 56% of the time against a 37% average. Nineteen points of difference. If this were the right sum, the hot hand would be one of the strongest effects in football.
Why that sum is wrong
The «after three wins» group isn't a random sample of teams: it is made almost entirely of strong ones, because they are the sides that string three wins together. Comparing it with the average of all teams means comparing the best with the whole, and calling «streak effect» what is really the gap between a Real Madrid and a promoted side.
It is a comparison between different teams dressed up as a comparison between different situations, and it is the most common error you meet when reading sports statistics.
Second sum: each team against itself
The correct sum compares each team with its own average, within the same season. For each team-season we compute its overall win rate and its win rate in the matches that follow a win, and look at the difference.
The result changes sign: the average difference is −2.8 points in Serie A, −2.2 in the Premier League, −3.9 in LaLiga, −3.6 in the Bundesliga, −3.0 in Ligue 1. After a win, a side wins slightly less than its own average, not more.
Third sum: the method has a flaw too, and it can be measured
One doubt remained: is that −3 a fact about football or a flaw in the way of counting? There is a direct way to find out. Take the same sequences of results and shuffle them at random within each team-season: every side keeps exactly its own wins, but the order becomes random. If the method were neutral, on shuffled data it should give zero.
It doesn't give zero. It gives −1.52 points in Serie A, −1.52 in the Premier League, −1.60 in LaLiga, −1.47 in the Bundesliga, −1.55 in Ligue 1, across forty shuffles per league with a standard deviation between 0.31 and 0.64. It is a bias in the estimator, not a fact about football: in short sequences, looking at «what happens after a win» systematically underestimates.
Removing it, the real effect is what remains: between −0.7 and −2.3 points depending on the league. Small, and slightly negative. ⚠ The honest comparison is with the naive gap on the SAME quantity, meaning after ONE win: in Serie A that is +5.0 points (42.5 against 37.1), and what remains of it is −1.3. The nineteen points in the headline concern «after three wins», which is a different measurement: redone within team, that too shrinks to values between −1.6 and +1.4, all inside the shuffle's noise.
What to take away
- A streak isn't extra information: what it seems to say — «this team is in good shape» — is almost entirely contained in the team's strength, which the market prices by itself.
- The first sum that comes to mind is nearly always confounded by selection. Asking «who ends up in this group?» before reading the percentage is the quickest way to avoid being fooled.
- Even a correct method can carry a bias. A random shuffle is a cheap control: if on data with no order the method doesn't return zero, the number it returns on real data needs correcting.
- ⚠ None of this says what to play. It says a phrase like «they're on three straight wins» adds nothing to a price that has already seen those three wins.
How to spot it in your own data
In a bet log the fallacy shows up in two recognisable shapes. The first is chasing: after a run of losses, larger stakes to «win it back». It shows up immediately by checking whether average stake rises after the bad days.
The second is selecting after the fact: remembering the times the streak held and not the times it broke. It is why a written log beats memory: memory keeps the episodes, a log keeps the ones that contradict them too.
The OddSonar log tracks both without anyone having to do the sums by hand.