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Running the Numbers: Romo, Randomness & Week 6 Pick
Tony Romo’s Week 5 performance was one of the all-time great games by any quarterback. Since 1970, only 13 quarterbacks have ever thrown for 500 yards in a single game. Every single one of them threw at least 45 passes, except Romo. With just 36 attempts, he recorded perhaps the greatest combination of bulk stats and passing efficiency that the NFL has ever seen. It was a truly jaw-dropping performance.
But how likely is it that Romo can carry that sensational play into Week 6? Probably not as likely as you might think. That has nothing to do with Romo and everything to do with how we perceive randomness.
Most sports are filled with randomness, football even more so than others. A lot of weird things can happen when you have an odd-shaped ball and 22 men colliding into one another.
But our brains are hardwired to detect patterns, even when there’s nothing there. That’s why we perceive in-game momentum when, for the most part, it doesn’t exist. It’s also why we perceive players or teams as “getting hot” when that’s typically not the case.
To give you an idea of how this can happen, I created a random number generator to simulate Romo’s potential touchdowns in a game. The simple generator was built to randomly provide a number – either one, two or three. I ran the simulation 160 times to simulate 10 full NFL seasons. Read
If we were to assume that Romo has an even chance to throw either one, two or three touchdowns in every game he plays, we could expect results relatively similar to this over the course of 10 seasons. The more games Romo plays, the closer his stats would get to reflecting the “real” Romo, which would of course be an even distribution of one, two and three-touchdown games.
But in the short-term, we can see lots of weird things. I broke down my simulation into 10 distinct seasons, and here’s the touchdown distribution in one of them:
1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1.
That’s 16 straight games without a single three-touchdown performance, even though we know that, in this simulation, a three-touchdown game is just as likely as a one or two-touchdown outing. We also see five straight games with one touchdown, even though there was just a 33.33 percent chance of that happening each time.
In that particular “season,” Romo threw 22 touchdowns. In the average season, though, we’d expect 32 touchdowns from Romo. So that’s one heck of an “underachieving” year, despite the fact that we know the results were completely random. Read
But imagine if we saw this sort of outcome in real life. If Romo came out and threw one touchdown (or even none) in five straight games, we’d say he’s playing without confidence. We’d say he’s lost his ability to lead the team. We’d say Jerry Jones made a huge mistake in re-signing him to a huge contract extension.
We’d come up with any and every narrative that it would take to explain the patterns we’re built to detect. Everything, of course, except that it just kind of happened and, maybe, there’s not a great reason behind it.
None of this is to say that football is completely random. There are lots of non-random factors that can affect an individual or team’s performance, such as confidence, for example. But looking at the big picture, the results we see aren’t too far from what we’d expect out of a totally random sequence.
That doesn’t make the game unpredictable, though. Actually, random outcomes can paradoxically become extremely predictable over large samples. In my example, we know beyond a shadow of a doubt that if we could simulate one million games, we’d expect Romo’s percentage of one, two and three-touchdown contests to all come very close to 33.3 percent.
Let’s look at Romo’s potential performance in Week 6. Even though we don’t have an overly firm grasp on how many yards he’ll compile, I bet you’d be willing to wager a pretty penny that he won’t repeat last week’s stats, right?
Far more difficult than making predictions in random environments is trying to discern between actual non-random play – performances that are caused by repeatable factors – and randomness. Certainly Romo’s Week 5 performance could be the start of a hot streak for him. But how could we possibly know that? How could we tell if he’s ready to break out or if Week 5 was just a fluky outlier when, in the short-term, it’s so difficult to predict performances?
In short, if we know we can see very strange outcomes that seemingly contradict the numbers in the short-term, should we really be using short-term results as the sole basis for our predictions?
Trying to predict Romo’s exact touchdown total is kind of like predicting short-term fluctuations in stock price. Over the course of a few hours, a stock will bob and weave in a way that has very, very little to do with its true value. The same is true of Romo (or any player’s) output; it’s extremely random over the course of a game or even a handful of games, but over the course a season, that changes. Read