Last night's match between Arsenal and Liverpool seems merely the latest in a new pattern of 4-4 thrillers. (I didn't see the game; its deadline week here at Prospect. Most us were in the office late, although our assistant editor Mary Fitzgerald snuck out in time to see all seven second half goals.) On the way home, I saw someone had posted an open question on my twitter feed: "is this the best football season ever?" If it is, it must be because the championship race remains open, and all of the top four teams have something to play for in at least one of the remaining competitions. The consensus in the papers this morning seems to be that so much was at stake last night that once-steady players began to panic, especially towards the end. Certainly, the Guardian's minute-by-minute gives this impression. Having unwisely declared "AND THAT MUST BE THE WINNER! YES. YES, IT IS!" with 7 minutes and 2 goals to go, the reviewer concludes: "this was a brilliantly ridiculous match played at a cracking tempo and featuring some fabulous interplay. But ultimately its defining characteristic was rubbish defending. Manchester United are going to win the league not because they are the best attackers - they palpably are not - but because they make fewer mistakes at the back."
Why so many mistakes? The result reminded me of a fascinating recent paper from the LSE's Center for Economic Performance, concerning the economics of tournament theory - and Olympic wrestlers.
Economist's developed tournament theory in the 1980s as a way of thinking about how people behaved, be they sports stars of regular joes, if their incentives were structured like a sports contest, with huge prizes for first place, and very little for those after. (Think gladiators.) Economists Christos Genakos and Mario Pagliero, in their paper "Risk Taking and Performance in Tournaments: Evidence from Weightlifting Competitions", looked at the performance of professional weightlifters in competitions, including the Olympics, for the last twenty years, to see if they took more risks if they thought they'd win, and in turn choked under pressure. They found that:
risk-taking exhibits an inverted U-relationship with rank: risk-taking increases up to rank six and then monotonically decreases moving towards the bottom of the ranking. In other words, the same athlete will attempt to lift a heavier weight (0.8kg or 51% more than the average discretionary incremental announcement) if he is ranked sixth than if he is ranked first higher.In non economist speak: if Romania's finest pile driver moves from the bottom of the heap to the middle, and starts to think he had a sniff of gold, he'll d lift more than he can really manage, and drop it with a clang. Atheletes, in this case, did choke under pressure in part because they rationally decided to take a greater risk. They also found this same behaviour was more likely the more prestigious the competition: while a regional competition might not be worth the both, for olympic gold you'd risk anything. The result of such risktaking tends to injured wrestlers—or, last night, sloppy defending—as much as gold medals. Discussing the research in the journal CentrePiece (PDF) the authors conclude that previous economic wisdom on the wider application of tournament theory—until recently used to justify all manner of bonuses and stock option schemes—needs to be rethought: tournaments, they say "can be too succesful in encouraging risk-taking, leading to excessive risk and lower than average performance." True. Just ask Rafa Benitez.
