On Sunday afternoon, the Green Bay Packers made an impressive second-half comeback to defeat the Dallas Cowboys. But was it a “miracle?” (More)

Squirrels invented rugby when Bearach MacLongtufts and his cousins tried to sneak a nut past the MacWhiskers clan. It was an almond, which explains the shape of the rugby ball. Later, American football grew out of rugby. Admittedly, squirrels don’t touch each others’ tails during the game because our tails can pull off and won’t grow back. So that football-tail-patting is a human thing.

Still, we invented rugby and that grew into American football, so that makes me an expert on Sunday’s game … and despite press reports like this and this, the Packers’ comeback was not a miracle. In fact, I predicted the Packers would play better in the second half:

That wasn’t because I’m psychic. It was simple statistics. The Cowboys’ offense set a franchise record for yardage in the first half, while the Packers were way below their season average scoring pace.

The law of large numbers is a mathematical principle that predicts a large sample of random events is more likely to aggregate near the mean. If you’re flipping a fair coin, it’s not unlikely get heads twice in a row; that should happen about once per four series of two flips. But to get heads 10 times in a row is another story; that should only happen once in 1024 series of 10 flips.

And as it happened, the the Packers set a franchise comeback record in the second half. Each of those – the Cowboys’ first-half yardage record and the Packers’ second-half comeback record – seems so unlikely on its own that for both to happen in the same game feels miraculous. But it isn’t.

In the NFL, on average, the home team scores about 12 points per half and the visiting team scores about 10 points per half. But that’s just an average, and a look at NFL team scoring records shows that:

  • At least three teams have come back to win from greater deficits (San Francisco from 28 points down, Buffalo from 26 points down, St. Louis from 25 points down).
  • Neither the Cowboys’ 26 first-half points nor the Packers 34 second-half points were anywhere near league records (Green Bay once scored 49 first-half points, and Chicago once scored 49 second-half points).
  • Green Bay once scored 41 points in a single quarter, and once gave up 37 points in a single quarter.

So it’s not that unusual for an NFL team to score 30-ish points in a single half. What made this game feel “miraculous” is that Dallas did it in the first half, and Green Bay did it in the second. Yet that’s not so surprising either, really.

The Packers and Cowboys came into the game with almost identical records, so it’s fair to assume they were roughly evenly-matched teams. Both coaches use their best lineups and call from a list of their best plays in each situation, so on any given play it comes down to one coach out-guessed the other and how well the players anticipate and react to the action of the play.

In other words, with evenly-matched and well-coached teams, the outcome of any play is essentially random. On 3rd and 6 at the 40-yard-line, Coach O picked a good offensive play for that situation from his game plan chart. But Coach X happened to pick the best defense – against that particular offensive play – from his game plan chart. Or a key defensive player happened to see and react perfectly. Or the quarterback put a fraction too much or too little on the throw. Or the quarterback threw it perfectly but the receiver slipped. Or….

A drive is a series of offensive plays by one team, and in a typical NFL game, each team has the ball about 11 times. That’s only 5-6 possessions per half, few enough that one team could “outplay” an evenly-matched opponent over a single half, by mere random chance. But that’s much less likely to happen over an entire game.

The Packers’ comeback felt like a miracle because of a common fallacy: the tendency to think that what’s happening right now will continue to happen in the future. But that’s only likely if what’s happening right now is pretty much the norm. If what’s happening right now is exceptional – good or bad – then it’s unlikely to continue unless you get cocky (when it’s good) or get down (when it’s bad) and start behaving differently.

So if two NFL teams are evenly-matched and keep playing to their abilities, you’re safe to predict that the team who lit it up in the first half won’t play as well in the second, and the team who stunk it out in the first half won’t play as poorly in the second. Not because of stirring halftime speeches or brilliant adjustments, but merely because both teams will tend to revert to their usual levels of performance.

And that’s a good lesson to keep in mind when pundits talk about the latest news cycle as if it’s the new pattern for What Will Happen From Now On. They’re usually as wrong as fans who thought the Cowboys had won the game by halftime.

Good day and good nuts.