This summer, I am focused on three things: math, travel (for math and for family), and the World Cup. Not surprisingly, many others are focusing on the World Cup and there are lots of blog posts and articles about World Cup related things. In this post, I wanted to draw attention to all of the math AND World Cup related things that have caught my attention. So here is a list of facts, articles, and blogs, in no particular order.

- Did you know that one of the refs is a former high school math teacher? According to Wikipedia, Mark Geiger, who has been praised as a very fair referee (until perhaps a call earlier today during the Nigeria-France match, in which he may have been a little soft), “became a United States Soccer Federation National Referee in 2003 and has been officiating in Major League Soccer since 2004.” Once I heard this, it seemed like such a reasonable transition! As a high school teacher, you learn to manage a bunch of hormonal young people who mostly dislike you and all of your rules, which seems to me to be the hardest part of being a referee. Well, that and catching every foul and knowing how to sanction them, which I am pretty sure I would be terrible at. And you have to run a lot. I would rather be a high school teacher, I guess, except Geiger probably gets a much better salary.
- There was a very fun article on BBC News recently about the birthday problem (which is also known as the birthday paradox) in the context of the World Cup. This problem is one of my favorite things to teach when I tell my students about probability, and now we have a fun, current-events related version! I don’t want to spoil it, but in essence what you would expect from the birthday problem is represented in the World Cup teams, so that’s pretty nice.
- Fivethirtyeight has been doing some great World Cup coverage. They have crib notes for every day’s matches predicting the results, and more general predictions about the whole tournament (where you can also read about how they came up with their prediction model). They also made predictions for the group round (now over) and they were actually pretty good, as you can read about here. But as we all know, soccer (or futbol) is a pretty unpredictable game, so don’t despair, not-Brazil fans, there is hope for your team yet (as long as it hasn’t already been knocked out).
- By now, even if you could care less about soccer and the World Cup, you may have heard that one player (Luis Suarez from Uruguay) bit another (Giorgio Chiellini from Italy). You may have also heard that Suarez was banned for 9 matches and four months, because it was not his first biting offense. Everyone also seems to have a pretty strong opinion on the matter. But when I heard someone say that there was a higher probability of being bit by Suarez than a shark (as for example in this article in the New Statesman), that’s when I got angry. I mean, talk about a poor use of probability. The more correct statement would be that the chance of being a professional soccer player and being bitten by Suarez is more likely than being a professional soccer player and being bitten by a shark. That’s all you can say. As far as I know, Suarez has not been caught biting people on the street, so even if I did meet him I think I would be safe. I guess maybe the point is that it is very unlikely to be bitten by a shark. Still, even if you hate Suarez and want him to be kicked out of soccer forever, you need to be careful about your use of probabilities. I’m glad to see that at least Ian Steadman (the author of this article) has amended his probabilities (probably given the number of comments from angry mathematicians). But there are many versions of this article being reported elsewhere, and not everyone is making the correction.
- Anna Haensch recently summarized an interesting article about Economics and the World Cup for the AMS Math Digest. You should check that out!
- Finally, for a non-math World Cup item, I have been thoroughly enjoying Slate’s Dive of the Day. This is usually one of the most frustrating parts of soccer (the theatrics) so it’s great that Jeremy Stahl is commemorating these moments in such a humorous way (there is even a score for the dive!).

So dear readers, I hope you enjoy reading and thinking about these things during halftime and the few hours in between matches. Also, maybe don’t watch every match if you want to get anything done.

I like the BBC article on the birthday paradox overall, but am a little upset at their math. Fletcher correctly states the birthday paradox in the bold intro text and later in the article, but blatantly gets it wrong in the hypothetical story involving Hulk and Paulinho at the beginning of the article. The whole point (in a sense) of the birthday paradox is that it only works if you _don’t_ specify two people. As soon as you narrow down your probability space to two particular players chatting in their hotel, the odds of them sharing a birthday is back down to ~1/365.

Grrr. I know I’m preaching to the choir here, but wanted to vent. Anyway, it’s very cool that the mathematical prediction so nicely pans out with WC teams!

Good catch! You are completely correct, sorry I missed that mistake!