Knockout upsets

Why does the strongest entrant in a knockout tournament win it far less often than their record suggests?

A team wins its league by ten points, having lost twice in thirty-eight matches. Everyone agrees it is the best side in the country. Then it goes out of the cup in the fourth round to a team three divisions below, and the newspapers call it a shock, a humiliation, a collapse of standards.

But consider: how surprised should we actually have been? The league record and the cup exit are measurements of the same team by two very different instruments. Before reaching for explanations about complacency or the magic of the cup, it is worth asking what each instrument can and cannot measure.

Start with what a single match is. Two sides meet; one wins. The result depends on their true qualities, and also on the bounce of a ball off a post, a linesman's judgement, an injury in the eleventh minute, the weather. Call the second group noise — not because it is unimportant, but because it does not repeat.

So a match is one sample from a noisy process, and a season is many samples of it. Which do you expect to reveal the underlying quality more reliably? The season, obviously — and that is the whole answer in embryo. The league table is not a better opinion than the cup result. It is a larger sample.

Now put a number on it, because the intuition is badly calibrated here. Suppose our team is genuinely strong enough to beat any given opponent three times in four — an enormous edge, far larger than most real favourites enjoy. What is its chance of winning a thirty-two-team knockout? It must win five consecutive matches, so three-quarters raised to the fifth power: about twenty-four percent. A team that is overwhelmingly the best loses the tournament three years in four.

Sit with that. Nothing went wrong in the three-quarters of cases where it lost. No collapse, no complacency, no explanation is required at all. The format simply asks for five consecutive successes from a process that fails a quarter of the time.

Why does the knockout compound so brutally? Because failure is absorbing. In a league, a bad afternoon costs two points and you play again next week; the errors average out. In a knockout, one bad afternoon ends the tournament, and no amount of subsequent excellence can undo it. The structure keeps every piece of bad luck and discards every piece of good luck beyond what was needed to survive.

That suggests the remedy, and sport found it long ago: play more matches per opponent. A best-of-seven series is simply a bigger sample of the same comparison, so the better side's chance of advancing rises well above its chance of winning any single game. Basketball and baseball settle championships this way; knockout cups do not, largely for reasons of fixture congestion and drama rather than fairness.

One more question. Does a single match contain the same amount of luck in every sport? Clearly not, and the difference is enormous. Football produces a handful of goals per match, so a single deflection can decide it and the underdog needs only one moment. Basketball produces well over a hundred possessions per side, and a favourite's per-possession edge gets many chances to express itself, which is why upsets in a single professional basketball game are far rarer than in football or ice hockey. This is measurable, not a matter of opinion: compare how well past results predict future ones in each sport.

It would be a mistake to read this as saying upsets are meaningless noise and the favourite was always the better side. Two refinements.

First, the model treats the per-match win probability as fixed, and it is not. Early rounds are easier than late ones, so a favourite's real path is a rising sequence of difficulties. Home advantage, travel, fatigue and squad rotation all shift the number match by match. The five-consecutive-wins calculation is a clarifying idealisation, not a forecast.

Second, and more interestingly, the noise is not a defect of the sport — it is much of the point. A format in which the best entrant always won would hardly be worth playing, and competitions choose their position on this dial deliberately. Knockouts are cheap, dramatic and decisive, and are chosen partly because they generate upsets. Seeding is the compromise: it does not reduce the luck in any one match, but keeps the strongest entrants apart early so fewer are eliminated by each other.

So the honest conclusion is not that the favourite deserved to win. It is that a knockout was never an instrument capable of reliably identifying the best side, and reading its result as a verdict on quality misuses the measurement.

• How seeding and draw structure change a favourite's odds without changing any match.
• Why some sports adopted best-of-seven finals while others kept one-off deciders.

Every term the collection defines is gathered in the glossary.