Twenty-Four Times in a Hundred. This Was One of Them.

By Sean McKnight · Wisconsin alumnus, reluctant bettor

When an underdog wins, was the forecast wrong? Almost everyone says yes without thinking about it. The answer is usually no, and once you see why, you will never hear a pundit the same way again.

I am a Wisconsin alumnus. I always root for the Badgers and I almost never bet on them. Somewhere in the fan part of my brain lives the suspicion that my money causes the missed tackle.

On September 26 that part of my brain had plenty to work with. Wisconsin fell behind No. 13 Penn State 17–0, then won 24–20. Two touchdown passes inside the last 3:31 finished it — an 11-yarder, then a 72-yarder with 1:13 left.

The fan's reaction: unbelievable. The statistician's question: how unlikely was it, really?

The number hiding behind the word “underdog”

Penn State was favored by about ten. Wisconsin to win outright was priced at +300; Penn State at −380.

Translate those. At +300, a winning $100 bet returns $300 profit, so the price breaks even at a 25% win rate — one win covers three losses. Penn State's price breaks even at about 79.2%.

Add them: 104.2%. Not 100. The extra 4.2 points are the house's cut, and you have to remove it before the numbers mean anything. Divide each by the total and Wisconsin lands at 24%, Penn State at 76%.

Now notice what changed. “Ten-point underdog” sounds like a wasted afternoon. “Roughly one chance in four” sounds like a football game worth watching.

What a 24% forecast is actually promising

Calibration asks a simple question of any prediction: when something is given a 24% chance, does it happen about 24 times in 100?

Look at the red squares before you read on. A well-priced 24% underdog is supposed to win two dozen of those hundred games. One of them landing tells you nothing about whether the price was right.

To judge the forecast you need many predictions made before kickoff, and the results that followed. If 24% underdogs kept winning closer to 40% over a large sample, then you would have found something.

Calibration is not the whole of forecasting skill. Someone who gives every game the same probability can be perfectly calibrated and useless; he never separates a mismatch from a coin flip. But it is the right place to start, and it is why a favorite losing discredits nobody.

How often does the underdog actually win?

One analysis of BCS-team games from 1999 to 2010 found these outright underdog win rates:

Treat those as historical benchmarks, not laws. The dataset counts some matchups twice and is not restricted to top-ranked opponents. But the point survives: even a two-touchdown favorite loses roughly one time in six, with nothing supernatural involved.

Keep two distinctions straight while you watch. A ranking and a line answer different questions: being No. 5 is a poll's opinion of a season, while being favored by 14 is a price on one game. A ranked team can be the underdog.

And winning outright is not covering. Wisconsin could have lost by seven and still covered ten. On this Saturday they did both.

The Saturdays we remember

Wisconsin fans carry a long memory for these afternoons. In 1981 the Badgers beat No. 1 Michigan 21–14. In 1984 they beat No. 6 Ohio State 16–14 in Madison. A year later they won 12–7 in Columbus against No. 3.

Those stay with us. The routine losses blur.

And there is the trap. A highlight reel is not a sample. To learn how often ranked teams lose as big favorites you have to count every qualifying game, including all the comfortable wins nobody retells forty years later. The denominator belongs in the story too.

What changes the odds after kickoff

Injuries can be part of it. In 2007 Stanford beat USC 24–23 as a 41-point underdog; the USC quarterback hurt his throwing hand in the second quarter and threw four interceptions, and USC turned it over five times. Stanford was starting a replacement quarterback making his first career start.

That shows an injury can matter. It does not show injuries explain most upsets, and I could not find a reliable figure for how often they do. You would need to compare injured favorites who lost against injured favorites who won, holding opponent strength fixed.

Timing matters too. An absence known beforehand is already in the price. One that happens in the second quarter is not. And an upset needs no single cause: a turnover, a fourth-down stop, a missed kick. Wisconsin won this one while throwing three interceptions.

There is also a real mathematical case for an underdog taking more risk. Accept a worse average result for a wider spread of outcomes, and you raise the chance of the one outcome that counts. That is a reason for calculated aggression. It is not proof that every underdog tries harder.

What to take home

We judge probabilities as though they were promises. A 76% favorite loses and we say the forecast was wrong. A 24% underdog wins and we call it impossible. Neither follows from one game.

Ask the calibration question instead, and you can ask it of anything: when someone says this has a one-in-four chance, how often does it actually happen across all the comparable cases? That works on football, on weather, on a surgeon's odds, on anything anybody tells you about an uncertain future.

My wager cannot make Wisconsin miss a tackle. It can only make me remember the tackle. The Badgers supplied the comeback; the odds had already left room for one.

Where the numbers come from. The 24% is one sportsbook's published game-day price with the margin removed proportionally. It is an estimate from one market, not a measurement of true chances. It is also a pregame number, not Wisconsin's odds once they trailed 17–0. The historical rates are entry-weighted descriptive counts, not sample estimates with intervals. This piece teaches calibration; it does not claim to measure a modern rate of ranked teams losing as double-digit favorites, or how much of that is injuries. Those are separate pieces.

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