Whether it’s rock-paper-scissors or NFL play calling, one certain way to lose is to be predictable. It’s well established that people believe that true randomness alternates more often than it does. People believe that flipping coins should result in heads, tails, heads, tails more often than it really does. Four heads in a row is just as likely as heads, tails, heads, tails.

NFL coordinators are not immune to this instinct for alternation. This can be seen in play calls on 2nd down and 10. Second and 10 situations are universally far more likely to be running plays than 2nd and 11, 9, or 8 yards to go. This aberration is caused by coaches’ tendencies to alternate play types — run, pass, run, pass. Second and 10 plays are much more likely to have been preceded by incomplete 1st down passes than runs stuffed for no gain.

Kyle Shanahan’s Redskins offense of the past two seasons leans heavily toward the pass on second down, but it still shows the same predictable pattern. Second down and 10 plays are passes 60 percent of the time, but 2nd and 9 plays are passes 82 percent of the time, despite there being no appreciable difference in the down/distance situation. In fact, we would expect runs to be more common, and not less so, as the to-go distances decrease, as is the case from 8 yards down to 1 yard to go. This shouldn’t be too surprising, given that Mike Shanahan’s Broncos were among the most predictable in the league on 2nd and 10.

There are other detectable trends. One of the most prominent tendencies, bucking the alternation pattern, is that following a successful 1st down conversion, Kyle Shanahan tends to call the same play type. If a pass is what moved the chains, the subsequent 1st down play will also be a pass 81 percent of the time.

As much time, film study, and preparation coaches put into play design and play calling, they may be too clever for their own good. The numbers suggest there are too many sub-optimum plays called. By that, I mean mostly run plays that have too low of an expected payoff to be worthwhile. I suspect these are mostly “setup” plays, designed to lull defenses into a pattern that can be exploited later with play-action and other tactics. That’s all well and good, but offenses league-wide appear to run these seup plays too often than they need to, which is costing them precious downs.

The laws of zero-sum game theory say that there are only two requirements for optimizing payoffs. First, plays should be called relative to their expected effectiveness. Offenses should proportionately favor their own strengths relative to its opposition’s weaknesses. And second, play calls should be unpredictably random. There could be no play caller in the league as unpredictable as a spinner from the game Twister. As silly as it sounds, whenever people are making decisions, they can’t help but create predictable patterns — patterns that can be exploited by the opposition. But even the most prescient defensive coordinator in the world can’t predict a Twister spinner.

Brian Burke is former Navy pilot who has given up his F/A-18 for the less dangerous hobby of football analysis. He is the creator of Advanced NFL Stats, a website about football, statistics, and and game theory.