[Cross-posted at: Football Perspectives, 25 September 2012]
Last Wednesday in Goiânia, Brazil defeated arch-nemesis Argentina 2-1 in a friendly match to square the all-time head-to-head ledger between the two giants of CONMEBOL at 35 wins apiece from their 94 meetings dating back to 1914.
This was much to my chagrin, as my in-laws are Argentine. Could it be that Juan Manuel Martínez’s sublime 20th minute opener (after a 12 successive-pass move) was a clear tactical mistake, insofar that it ‘awoke the sleeping giant’?
Brazil, urged on by the 40,000-strong fanatical home crowd, attacked furiously from the re-start and equalised only six minutes later, and eventually won by the odd goal in three with a Neymar penalty at the death.
Realistically, any rational individual would have to think that the answer is a resounding ‘no’ – after all, why would any professional footballer deliberately spurn the opportunity to score a goal when they have the chance? However, while doing this would appear to be totally irrational on face value, an old ‘myth’ about Brazil in football – if believed – would provide such a reason.
Formally, the myth that it is that when playing against Brazil, it is unwise tactically to score early in the game. The intuition here is that scoring early merely serves to make the Brazilian eleven angry, providing them with extra incentive to attack furiously and score repeatedly for the remainder of the game, thus handing a football ‘lesson’ to the opposition who dared to go 1-0 up earlier.
As can be imagined, the myth probably owes its existence to a small number of identifiable (and famous) cases where this chain of competitive behaviours played out. In the final of the 1958 World Cup, hosts Sweden went ahead after four minutes, only to have Brazil open the floodgates thereafter; winning 5-2 (and a brace from 17-year old Pelé). Four years later in Santiago, the sense of déjà vu was palpable in the final, when Czechoslovakia scored on 15 minutes, with Brazil equalising two minutes later and winning 3-1. There have also been numerous other such instances.
While it may seem at first to be a frivolous exercise in sports science, it is nevertheless a useful applied microeconomic analogy to a specific (but common) industrial setting. Namely, a finite-length bilateral (but asymmetric) industry contest, in which substantiation of the myth would provide evidence that an underdog over-exerts effort (relative to optimal) early in the contest against a more favoured opponent, and that analogously the favourite under-exerts effort early. Such a conclusion would refute the theoretical findings (that the underdog has an incentive to commit effort early) of Baik and Shogren’s seminal 1992 piece in American Economic Review, and is (kind of) more consistent with Avinash Dixit’s earlier 1987 paper (where the ordering of moves is not endogenised), also in AER.
What does the data tell us?
For the prospective opponent that takes heed of the myth, perhaps the optimal implied strategy is to keep the game at 0-0 until the final few minutes and then score, circumventing Brazil’s scope to react. A casual look at the data suggests that there may be something to this – of Brazil’s 306 ‘A’ international matches since 8 August 1993 (when FIFA rankings were published), Brazil has lost 40 (in regulation time), of which 15 produced a 0-1 score line, and in a disproportionate six out of these 15, the opponent scored the winner in the final 10 minutes (this compares to only four out of Brazil’s 37 victories by 1-0 coming via a goal after the 80th minute), and meanwhile there have been 26 scoreless draws.
One still believed the myth to be an empirical issue. Using a sample of these matches, I set out to compare (only) Brazil’s scoring outcomes, after various ‘early’ cut-offs of 15, 25 and 35 minutes, in a treatment group of matches in which they concede an early goal, to a control group in which the opponent does not score early. On the basis of mean scoring rates (goals divided by minutes played), Brazil scored more frequently after the early cut-offs in the control games, significantly so for the latter cut-offs, in direct contrast to the myth.
Controlling for match-specific factors
However, the comparison of scoring rates did not account for various important match-specific factors that could be driving the results. When ordered probit models were estimated to control for these factors, the point estimate of the treatment game dummy variable became positive – the correct sign required for the myth to hold (except for the 35-minute minute cut-off) – but was insignificant. Here, factors such as home-ground advantage, competitive balance of the teams (according to FIFA ranks) and context of the match (friendly, qualifier, group/knock-out stage of tournament), all became important.
Finally, matches in which Brazil themselves score early before the opponent were removed from the sample, so as to make a cleaner comparison of whether the opponent is either at 0-0 at the early cut-off or 1-0 at/before it. Here, the dummy variable of interest (for the 25-minute cut-off) actually became very close to substantiating the myth, with a p-value close to 10%.
However, the hypothesis was framed in such a way to give the myth ‘every possible chance’ to hold, hence the ruling was that the myth is, to phrase television’s Adam Savage and Jamie Hyneman, ‘totally busted’!
Baik, K. H. and Shogren, J. F. (1992), “Strategic Behavior in Contests: Comment”, American Economic Review, 82 (1), 359-362.
Dixit, A. (1987), “Strategic Behavior in Contests”, American Economic Review, 77 (5), 891-898.
Lenten, L. J. A. (2012), “The Underdog Should Always Fire the First Salvo against Brazil“, Applied Economics Letters, 19 (10), 935-938.