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Yellow Card: A unique problem

April 27, 2012

Yellow Card is a recurring feature about penalties in sports. Today, I discuss the conditions that make penalties a necessary part of sports design.

Games are defined by rules, and in most cases, the rules are absolute. If you’re playing chess and you decide to break the rules by, say, moving a rook diagonally, then you’re either cheating, or you’re no longer playing Chess. There’s no provision for what happens when you decide that maybe this time, I’ll move the pawn 2 spaces, and hope nobody notices. There’s an implicit assumption that the rules are inviolate, and the game’s rules are enforced as such.

These assumptions are even more pronounced in computer gaming. The rules of a computer game, that is, the program, are actually unbreakable. Within the magic circle of the game world, it’s actually impossible to do something that isn’t accounted for by the original game design. There may be bugs, cases where the implemented rules don’t match the designer’s intent, but the rules of the game itself are unbreakable.

So, sports and other physical games have a unique problem. They’re games played in real space, in the real world where literally anything is possible. There’s no implicit assurance that the rules will be maintained. Further confounding the problem is the fact that in a physical game, many rules are defined as a matter of degree: it’s okay to do a little of this, but not a lot. So, you need an enforcement mechanism. You need penalties. The study and design of penalties is a wide open field.

When considering sports, I group rules into 2 different categories: procedural and administrative rules.

Procedural (or mechanical) rules define what the game is. A basketball court is 94 feet long. A football team has 11 players. A baseball inning consists of 3 outs. Generally speaking, there’s no advantage to be gained by breaking these rules.

Administrative (or enforcement) rules define how the game is played. Roughing the passer in football. Personal fouls in basketball. These rules are often called according to the referee’s discretion. They’re distinguished with words like “excessive” and “unnecessary”. Of course, the line between the two classes of rules isn’t hard and fast, but it’s still a useful framework to use to think about the design of these games.

Violations of procedural rules are typically not that interesting. If a player is able to gain an advantage by breaking a procedural rule, it’s typically a hallmark of poor design. It doesn’t happen often, but it does happen. Generally, attentive officiating can resolve the few cases where it does occur. Violations of administrative rules, however are very interesting, because they’re impossible to eliminate: they’re inherent to the sports design. And because these penalties usually exist because the proscribed activity confers an unfair advantage, it is to the player’s benefit to push the rule as far as it will go. In fact, the player’s ideal outcome is to break the rule every time, by as much as possible, but never have anybody notice.

But as the Polish Goal Line proves, it may be worth it even if somebody notices. The players’ calculus becomes weighing the cost of committing the penalty vs. the expected value of breaking the rule. If he’s caught 1/3 of the time, and it gets 3 points, the penalty has to be worth more than -1 point. Otherwise, the players are going to break that rule every time. So it’s not hard to enforce rules, if that’s what you want to do, you just adjust the severity of the penalty. You just need to make sure that you understand what incentives you’re creating for the players, and make sure those align with your rule enforcement goals.

Of course, officials aren’t the only way that rules get enforced.

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From → Features, Yellow Card

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