Superb World Cup ‘Selection Bias’ Example

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[Cross-posted at: The Sports Economist, 4 July 2014]

For all those economics professors and tutors out there who struggle to explain the crucial concept of ‘selection bias’, a nice illustration can be found in FIFA World Cup finals records. With students (at least those who do not loathe sport) currently in soccer-crazy mode, they may be more motivated to understand this concept through the following trivia question:

Q: In World Cup (finals) history, which team has the highest goal-scoring ratio (goals scored divided by games played)?

Scroll below for the answer, which may be surprising to many, except the amateur World Cup historians among you.

Most people would instinctively say Brazil; however, they appear second on this list at 2.16 per game (218 from 101 games, inclusive of the second-round of the 2014 edition). Germany follows at a very-close third with 2.15 (221 from 103).

The record-holders are…wait for it…Hungary! Yes, those ‘Mighty Magyars’ top the list and (get this) by a comfortable margin, too – indeed a chasm – their 87 goals in 32 games comes in at an astonishing 2.72 goals per game.

If you don’t believe me (and you’re more than entitled not to), check the figures here. Hungary has never won the World Cup, but have twice reached the final: in 1938, when they lost to Italy; and again in 1954, with legends Puskás and Kocsis (et al.) in their ‘Golden Team’, which came into that World Cup undefeated in more than 4 years, only to squander a two-goal lead (which they had after only 8′) to (the then-West) Germany, who incidentally they had annihilated in the first round by the incredible scoreline of 8-3.

OK, so what is the selection bias here? Well, look at the chart below, which displays average goals per game by World Cup. The flags I added at the top of the bars denote the World Cup finals that Hungary both entered and qualified for.

goals by world cup

From this, it is easy to see that scoring outcomes were lower from 1962 compared to earlier, with a further decline (albeit slight) since then. Hungary is but one of a number of national football teams that were among the best handful in the World for considerable periods at any time since the inaugural World Cup in 1930 (according to retrospective Elo ratings, they were ranked number one as late as 1965). However, of all national teams in this category, Hungary is the one that played the highest proportion of its matches in higher-scoring World Cups.

For all you Magyars out there lamenting your boys’ extended absence from the big stage (28 years now and counting), rest assured that (since it’s unlikely that Brazil and Germany will ever get anywhere near 2.72) the only way to guarantee holding this highly-prestigious record in perpetuity is to continue to NOT qualify for the finals – proof that there is indeed success in failure!

UPDATE: OK, Germany (2.181) now overtake Brazil (2.146) for second-place after that unbelievable semi-final; but Hungary’s place at the summit still looking just as safe in the bank vault as before!

Solution to World Cup Penalty Shoot-out Problem: ABC Interview with Waleed Aly

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I returned to ABC Radio National’s Drive program with Waleed Aly, yesterday evening (Tuesday 1 July, go to link for audio).

The 2014 World Cup now in its knock-out phase (which brings with it the inevitable problem of extra-time and penalty shoot-outs, as well as perverse incentive effects to both teams to over-defend). Shining a light on this, Waleed and I discussed a simple rule-change proposal, based on economic principles, which we believe would produce better scoring outcomes in extra-time and diminish reliance on the game’s cruel version of Russian roulette to decide the winner (among numerous other improvements).

If you’re interested in the economics behind the proposal, you can see the abstract of the article from Journal of Sports Economics (December 2013 issue), on which it’s based, here.

Why Oz Soccer Fans Should Cheer for the Chinese Economy

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My latest Australian Financial Review piece: “Sleepless in Skipton: Long Slog for Local Soccer Fans” appeared in today’s edition (Friday 27 June). The link is gated; though it’s on p.43 of the hard copy if you can get your hands on one.

If you’re an Australian World Cup tragic who has been horrendously sleep-deprived over the previous fortnight, you get a lot of sympathy from me in it.

Brazil 0, Economics 2

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My work on the Brazil myth and a general description of my research profile is in the newspapers again. This time, discussed in this piece by Peter Martin: “Can Soccernomics Save the Socceroos?“, which appeared in The Sunday Age two days ago (15 June). The online version is linked (p.35 in hard copy).

UPDATE: Brazil held to a goalless draw in the second match of group phase by none other than their bogey-team, México (as indicated in my earlier Australian Financial Review piece)! How, you may ask? The myth tells us that México not scoring early circumvented having Brazil run up a cricket score against them – hats off to the insightful tactics of master coach, Miguel Herrera.

Brazil 0, Economics 1

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My piece: “Economics Lends Little Support to the Socceroos” appeared in today’s Australian Financial Review (Thursday 12 June). Link gated; but it is on p.43 of the hard copy if you have access to that. I draw an analogy between the optimal tactics for beating Brazil at the World Cup and upstaging a larger business rival in industry.

The abstract of the original 2012 journal article from Applied Economics Letters on which it is based can be found here.

UPDATE: Brazil wins the tournament opener 3-1 after Croatia failed to heed the myth and opened the scoring on 11′ (albeit through an own-goal). By admission, while on paper it looks like a substantiation of the myth, on the balance of play it was anything but!

Symposium: Brazil at the Centre of the Sporting World

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Today, La Trobe University hosted an important symposium at its brand new City Campus, called: Brazil at the Centre of the Sporting World. This event was organised jointly by Centre for Sport and Social Impact (CSSI, of which I am a member) and the Institute of Latin American Studies (ILAS, administrated by our Faculty of Humanities and Social Sciences), and included such luminaries as H. E. Rubem Barbossa (the Brazilian Ambassador to Australia) and Craig Foster (SBS Chief Football Analyst and Presenter).

I made a 15-minute presentation as part of panel discussion, based on my paper (now published, see link): “The Underdog Should Always Fire the First Salvo Against Brazil”, from Applied Economics Letters, which I have blogged about here previously.

Busting the Brazil ‘Myth’

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[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.

The myth

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’!

Further reading

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.