May 29, 2017

How Not to Fix Soccer

With the World Cup comes the quadrennial ritual in which Americans try to redesign and improve the rules of soccer. As usual, it’s a bad idea to redesign something you don’t understand—and indeed, most of the proposed changes would be harmful. What has surprised me, though, is how rarely anyone explains the rationale behind soccer’s rules. Once you understand the rationale, the rules will make a lot more sense.

So here’s the logic underlying soccer’s rules: the game is supposed to scale down, so that an ordinary youth or recreation-league game can be played under the exact same rules used by the pros. This means that the rules must be designed so that the game can be run by a single referee, without any special equipment such as a scoreboard.

Most of the popular American team sports don’t scale down in this way. American football, basketball, and hockey — the most common inspirations for “reformed” soccer rules — all require multiple referees and special equipment. To scale these sports down, you have to change the rules. For example, playground basketball has no shot clock, no counting of fouls, and nonstandard rules for awarding free throws and handling restarts—it’s fun but it’s not the same game the Lakers play. Baseball is the one popular American spectator sport that does scale down.

The scaling principle accounts for soccer’s seemingly odd timekeeping. The clock isn’t stopped and started, because we can’t assume a separate timekeeping official and we don’t want to burden the referee’s attention with a lot of clock management. The time is not displayed to the players, because we can’t assume the availability of a scoreboard. And because the players don’t know the exact remaining time, the referee gives the players some leeway to finish an attack even if the nominal finishing time has been reached. Most of the scalable sports lack a clock — think of baseball and volleyball — but soccer manages to reconcile a clock with scalability. Americans often want to “fix” this by switching to a scheme that requires a scoreboard and timekeeper.

The scaling principle also explains the system of yellow and red cards. A hockey-style penalty box system requires special timing and (realistically) a special referee to manage the penalty box and timer. Basketball-style foul handling allows penalties to mount up as more fouls are committed by the same player or team, which is good, but it requires elaborate bookkeeping to keep track of fouls committed by each player and team fouls per half. We don’t want to make the soccer referee keep such detailed records, so we simply ask him to record yellow and red cards, which are rare. He uses his judgment to decide when repeated fouls merit a yellow card. This may seem arbitrary in particular cases but it does seem fair on average. (There’s a longer essay that could be written applying the theory of efficient liability regimes to the design of sports penalties.)

It’s no accident, I think, that scalable sports such as soccer and baseball/softball are played by many Americans who typically watch non-scalable sports. There’s something satisfying about playing the same game that the pros play. So, my fellow Americans, if you’re going to fix soccer, please keep the game simple enough that the rest of us can still play it.

Gymnastics Scores and Grade Inflation

The gymnastics scoring in this year’s Olympics has generated some controversy, as usual. Some of the controversy feel manufactured: NBC tried to create a hubbub over Nastia Liukin losing the uneven bars gold medal on the Nth tiebreaker; but top-level sporting events whose rules do not admit ties must sometimes decide contests by tiny margins.

A more interesting discussion relates to a change in the scoring system, moving from the old 0.0 to 10.0 scale, to a new scale that adds together an “A score” measuring the difficulty of the athlete’s moves and a “B score” measuring how well the moves were performed. The B score is on the old 0-10 scale, but the A score is on an open-ended scale with fixed scores for each constituent move and bonuses for continuously connecting a series of moves.

One consequence of the new system is that there is no predetermined maximum score. The old system had a maximum score, the legendary “perfect 10”, whose demise is mourned old-school gymnastics gurus like Bela Karolyi. But of course the perfect 10 wasn’t really perfect, at least not in the sense that a 10.0 performance was unsurpassable. No matter how flawless a gymnast’s performance, it is always possible, at least in principle, to do better, by performing just as flawlessly while adding one more flip or twist to one of the moves. The perfect 10 was in some sense a myth.

What killed the perfect 10, as Jordan Ellenberg explained in Slate, was a steady improvement in gymnastic performance that led to a kind of grade inflation in which the system lost its ability to reward innovators for doing the latest, greatest moves. If a very difficult routine, performed flawlessly, rates 10.0, how can you reward an astonishingly difficult routine, performed just as flawlessly? You have to change the scale somehow. The gymnastics authorities decided to remove the fixed 10.0 limit by creating an open-ended difficulty scale.

There’s an interesting analogy to the “grade inflation” debate in universities. Students’ grades and GPAs have increased slowly over time, and though this is not universally accepted, there is plausible evidence that today’s students are doing better work than past students did. (At the very least, today’s student bodies at top universities are drawn from a much larger pool of applicants than before.) If you want a 3.8 GPA to denote the same absolute level of performance that it denoted in the past, and if you also want to reward the unprecendented performance of today’s very best students, then you have to expand the scale at the top somehow.

But maybe the analogy from gymnastics scores to grades is imperfect. The only purpose of gymnastics scores is to compare athletes, to choose a winner. Grades have other purposes, such as motivating students to pay attention in class, or rewarding students for working hard. Not all of these purposes require consistency in grading over time, or even consistency within a single class. Which grading policy is best depends on which goals we have in mind.

One thing is clear: any discussion of gymnastics scoring or university grading will inevitably be colored by nostalgic attachment to the artists or students of the past.

Why Don't NFL Teams Encrypt Their Signals Better?

Yesterday the National Football League punished the New England Patriots and their coach, Bill Belichick, for videotaping an opposing team’s defensive signals. The signals in question are used by coaches to tell their on-field defensive unit how to line up and which tactics to use for the next play. The coach typically makes hand signals and arm movements that the on-field players know how to interpret. (The offense also needs to send signals to players from the sidelines before each play, but they use radios.) The opposition gets an advantage if they know what play is coming, so they will try to figure out what the signals mean.

This is essentially a weak form of cryptography. The coaches apply a kind of encryption to translate the desired play into a ciphertext, which is a sequence of hand and arm movements. They transmit the ciphertext (by making the indicated movements) to the on-field players, who then decrypt it, recovering the original play that the coaches wanted to send. An adversary who can see the ciphertext is supposed to be unable to recover the original message.

I don’t know what systems NFL teams use, but Belichick and the Patriots apparently thought they had a chance of breaking their opponents’ code.

There’s an interesting technical problem here: how to encrypt defensive plays into sideline signals securely, in a way that’s practical for real coaches and players in a game situation. I can think of at least one solution that is secure and practical. (Exercise for geeky readers: How would you do this?)

You might think that any solution would be too complicated for a mere football player to decode. If you think that, you’re underestimating the players involved. NFL defensive captains already cope with complex information and plans, and their teams’ current signaling systems already require decoding of symbols. Clever solutions can be pretty simple.

Crypto applies not only to designing a team’s signals, but also to analyzing rivals’ signals. Who will be the first NFL team to hire a cryptographer?