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Why the heck did the Detroit Lions go for 2 down 8? Math.

We explain why it actually makes a fair amount of sense that the Lions went for two late in the game.

Dallas Cowboys v Detroit Lions Photo by Leon Halip/Getty Images

The Detroit Lions made a puzzling decision to go for two late in their game against the Dallas Cowboys.

Here’s the situation: Having just scored a touchdown with 5:49 remaining, the Lions pulled the score to an eight-point differential: 35-27. Common sense says kick the extra point, pull the score to seven points, and then you’re just a touchdown and an extra point away from tying the game.

But, instead, the Lions went for two, trying to get the game to a six-point differential, but risking it becoming an eight-point game with a failed conversion.

The Lions failed to convert, and it ended up not mattering at all, because Detroit would not score again in the game. However, many criticized the Lions for the risky play, thinking they put themselves in a tougher position to win the game.

However, basic game probability suggests the Lions took the right strategy here.

Going for two down eight points is becoming a more and more accepted strategy around the NFL and in all levels of football. PredictiveFootball.com has a great explainer of why, and you can read it right here. But to put it in very basic terms, here’s how it works:

This chart makes three statistical presumptions based on previous data: Two-point conversions are converted about 50 percent of the time, extra points are good 100 percent of the time, and if you enter overtime, each team has a 50 percent chance of winning.

Obviously, that math is a little crude. Going into Week 11, NFL teams have converted 31 of 64 two-point conversions in 2019, or 48.4 percent. Extra points have been converted 653 out of 699 attempts, or 93.4 percent of the time. It’s close, but not exact.

While that doesn’t exactly match the number from the chart above, what’s important here is that two consecutive two-point conversion attempts result in about the exact same points as two consecutive extra point attempts. Here’s the math:

2 points x 48.4 percent chance = 0.97 expected points x 2 attempts = 1.94 expected point

1 point x 93.4 percent change = 0.934 expected points x 2 attempts = 1.87 expected points

So two-point attempts actually make sense for the majority of the game, but in this late-game scenario, the two-point conversion attempt gives you an extra benefit when down eight late in the game. If converted, it gives you the opportunity to score that second touchdown and only need an extra point to take the lead. If you miss, you still have the opportunity to tie, with a 50-50(ish) shot to convert.

As the chart above points out, that extra benefit is worth an approximate 12.5 percent in win percentage. That’s because you win about 62.5 percent of the time using these scenarios. If you go extra point both times, you go into overtime, where your win probability is just 50 percent (crudely).

Of course, there are a ton of other in-game factors to consider. How is the offense playing? How is your red-zone offense? How good is your kicker? All of those things were also part of the equation, according to Detroit Lions head coach Matt Patricia.

“It’s one of those things where you try to judge momentum swing through the fourth quarter,” Patricia said. “Figure out what’s going in which direction. And certainly at that point if we were able to score those touchdowns and be in those positions, than the offense, probably, would have swung things in their favor at that point.”

So while the decision looked unorthodox, a lot of game-theory experts and probability analysts will applaud Patricia’s decision. Obviously, none of this ended up mattering in the end, but it’s an interesting choice that Detroit made that could have a huge impact on a future outcome.