For those of you who haven’t been following the World Cup, there are three notable features this time around: vuvuzelas, Landon Donovan (*swoon*) and bad calls by referees. (If you ever turned it on and wondered why it sounded like there was a swarm of bees in the stadium, now you know. Note that the sound is due to the vuvuzelas, not the bad calls.) For example, referees failed to see a shot go over the line in England’s 4-1 loss to Germany. As a result, FIFA- or more specifically the International Football Association Board- is considering adding goal judges to its arsenal of referees. I can only imagine that this would appease Bill Simmons to some degree, since he has seemed less than pleased with the World Cup officiating. For example, he tweeted the following during the England-Germany game:
Wow!!!! Was that the worst botched call in the history of sports??? How do they not have refs behind each goal? I’m in shock.
FIFA statement: “So you know, by not putting goal referees behind each net, we save upwards of $500 per game. We stand by our decision.”
I can only assume that he was being sarcastic with the quote in the second tweet, but who knows. In any case, let’s think about how FIFA could decide whether the extra officials would be worthwhile under those circumstances.
It’s all too tempting to say “well, getting the outcome of a game right is clearly worth $500, so FIFA is just being stubborn,” but that’s not really what the tradeoff is. If you stop and ponder for a second, you will probably realize that the above tradeoff assumes that people can know which games will have officiating problems and only pay for the extra referees for those games. Unfortunately, scientists have failed to develop a reliable crystal ball thus far, so FIFA realistically only has the options of “hire goal judges for all games” and “don’t hire goal judges.”
The real tradeoff looks something like this:
This is sort of hard- how are we supposed to know the value of a correct outcome or the probability that the extra official will matter? For the latter measure, we can at least approximate to some degree by looking at how many bad calls have been made historically divided by the number of games. (You could limit the time frame here to a period that looks reasonably similar to the present.) Note that I didn’t say that we could look at how many bad calls have actually changed the game outcome, since we can’t really know that. (I am also assuming to some degree that the extra referees would eliminate all errors, which isn’t necessarily the case but at least provides a starting point for discussion.) For example, England was denied one goal and lost to Germany 4-1, so one could argue that the denied goal was irrelevant. However, this doesn’t take into account the notion that the denied goal might have affected play in the rest of the game. (People are, after all, human.) If we are counting all bad calls made, we are probably overstating the true probability, and if we count only those bad calls that directly affected the game’s outcome, we are probably understating the true probability, but at least we can use these two numbers to get bounds on what the right number should be.
The value of a correct outcome is a more difficult problem to think about- after all, who really knows what dollar figure to place on a legitimate sports outcome? Does legitimacy impact viewship or fandom? Probably, but again, it’s hard to quantify. Does it affect sponsorship? There are a lot of similar questions that I wouldn’t even know how to approach. Luckily, I can avoid the issue by turning the underlying question on its head a little and instead asking “how much would a correct game outcome have to be worth in order for the benefits to outweigh the costs?” In this sense, if I end up with an outlandishly high or low number, I can pretty confidently answer the original question without thinking about lost merchandise sales and ad revenue directly.
For example, let’s say hypothetically that there is one (correctable) bad call in every 5 games (even that seems like a low estimate given current circumstances) and half of these actually affect the game outcome directly. This means that the probability of a bad call in a game is 1/5 and the probability of getting the wrong outcome in a game is 1/10. These numbers would imply that a correct game outcome would have to be worth between $2500 (since $2500 * 1/5 = $500) and $5000 (since $5000 * 1/10 = $500) in order to wake the $500 cost worthwhile. If nothing else, I would venture to guess that the losing team would be willing to pony up five grand to not have unfairly lost, so these estimates appear to show that the benefits of the extra officials would outweigh the costs.
Note, however, that it could be the case that the actual number of officiating errors is much smaller- I’m not quite in the mood to go and do historical research on this matter. If the number of game-changing errors is 1 every 1000 games, then the value of a correct game outcome would have to be much higher ($500,000) in order to justify the $500 per game cost. In general, when the chance of error with the existing referees is lower(or the marginal benefit of the extra referees lower), the value of a correct outcome has to be higher in order to justify the cost of trying to ensure that outcome.
Or…you could just make the case that the $500 per game amounts to the cost of somewhere between 3.6 and 25 tickets out of 40,000, depending on whether the ticket-holders are from South Africa. And that, people, is called price discrimination.