Bondonomics! Sky-High Expectations for new 007 Flick

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I finally published some thoughts on the ‘Bond, James Bond 007’ movie franchise business model via an opinion piece, which ran in the Australian Financial Review (today, Monday 9 November), titled: “Bond Formula Ensures Franchise will Die Another Day” on p.35.

With the new movie (number 24) opening in Australian cinemas on Thursday, it is a timely piece for those of you wanting your Bond fix before then.

More on Optimal Sequencing: Soccer Edition

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[Cross-posted at: Wages of Wins Journal, 7 August 2014]

This earlier Wages of Wins piece by Shane Sanders (July 29, 2014) generated plenty of discussion. It highlighted the problem of Triathlon deaths in the swim leg. One crucial point to make with many economic policy analogies on which to draw is that sequencing of the legs (or phases) matters – all other considerations aside, the ‘best’ sequence of phases can be optimized according to some objective (in this case, minimizing fatalities).

One such possible economic policy analogy is with respect to unemployment benefits. Imagine a two-phase policy, where in the first six months the recipient is eligible to a relatively unrestricted entitlement of an amount according to some predefined percentage (say 40%) of some benchmark (average weekly earnings or minimum full-time wage). If the recipient is still unemployed after the 6 months have elapsed, a second phase kicks in at which the benefit is now highly restricted thereafter (having to satisfy minimum job search requirements, etc.) and/or reduced in value. Now, many people will disagree as to whether this two-phase policy is too generous or too miserly (or even on the basis of something else entirely). However, one aspect most of us would agree on is that swapping the sequence of these two phases would make absolutely no sense whatsoever.

It got me thinking about other such analogies about sequencing from sport that could be useful in policy circles. Recently, I published an article in the December 2013 issue of Journal of Sports Economics [gated], along with Jan Libich (my colleague at La Trobe) and Petr Stehlίk (University of Western Bohemia, Czech Republic). We took on soccer’s penalty shoot-out problem.  In knock-out matches that are tied after 90 minutes, the following 30 minutes of overtime is often beset with overly-defensive play due to insufficient incentive to attack.   This means that overtimes often finishes goalless, and that nearly 50% of the time, the match is decided via penalty kicks anyway (put differently: in nearly one of every two ties, overtime fails to achieve the one and only thing it is fundamentally there to do).

We show that an alternative sequence – regulation time followed by a penalty shoot-out followed by overtime – improves attacking outcomes. The qualification is that, while the shootout produces a winner – you still play overtime, with the winner of that winning the contest as currently. It is only when overtime fails to resolve the deadlock that the winner becomes the team that had won the shootout already (think of winning the shootout as worth half-a-goal lead at the start of overtime).

Specifically, we show that the probability of at least one goal being scored in overtime rises by approximately 50% (depending on the underlying characteristics of the match). Exactly how we estimate the effect of a policy that’s never existed is outlined in the paper for those of you who are interested to read further.

Coming back to sequencing, why the simple economic intuition (as well as the data) says this rule change will likely work is the following: there will always be one team chasing the next goal, because they will be eliminated unless they do – they have little else to lose. While the other team may correspondingly become more defensive, we show the net effect to be overwhelmingly positive. Furthermore, what you will no longer get are those overtimes where both teams sit back having jointly overestimated the probability that they will win if it goes to a shootout.

Had Mario Götze spurned that chance just minutes from time in the recent World Cup final, and it had have instead gone to spot kicks, the penalty shootout problem would now be far higher on the soccer agenda. Nonetheless, better public policy (optimal sequencing included) should never be far from the agenda, so I hope to see more studies like this make some impact in the broader public policy debate.

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!

James Reade on Tennis Home-Advantage

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My co-author, James Reade (University of Reading) published an excellent piece today in The Conversation (UK edition) on our joint work using pro-tennis data, focusing on home-court advantage in the sport. This is of topical interest in Britain right now owing to Andy Murray’s defense of his Wimbledon title currently being in full swing.

Read: Hard Evidence: Does Home Support Help or Hinder Murray’s Wimbledon Chances?

We are interested primarily in other aspects of the data; nonetheless, home advantage is a nice little scientific problem that the average fan can sink their teeth into – nice one, Jimmy!

NFL Scheduling and Competitive Balance

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[Archived from: The Sports Economist, 2 January 2014]

In this paper (now forthcoming, JSE: doi: 10.1177/1527002512471538), it was shown that for every single year after the expansion to 32 teams in 2002 (until 2011), the NFL was even more competitively balanced when the strength of schedule was accounted for, without exception, using four common CB measures. Previous The Sports Economist posts on this are here and here.

Since the 2013 regular season has just been completed, we crunched the numbers on the two most recent seasons. The streak remains unbroken, once again demonstrating the importance of adjusting CB measures for unbalanced schedules.

2012:

Standard Deviation Ratio: 1.5245 (unadjusted); 1.4645 (adjusted)

Herfindahl Index of CB:  1.1453 (unadjusted); 1.1340 (adjusted)

Concentration (12) Ratio:  1.4010 (unadjusted); 1.3889 (adjusted)

Gini Coefficient:  0.2776 (unadjusted); 0.2647 (adjusted)

Home Advantage Omen for Ashes Whitewash

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[Archived from: The Sports Economist, 2 January 2014]

With cricket’s latest ‘Ashes‘ series having been decided more than a fortnight ago, much of the remaining interest in the final Test, just underway, centres purely on whether Australia can complete a 5-0 Ashes whitewash for only the third time in history (following 1920/21 and 2006/07). Most ‘key performance indicators’ for Sydney are pointing in that direction – the newly-rediscovered ferocity of the Australian pace attack, not to mention the unexpected feebleness of England’s batting top-order (and middle-order, for that matter). England have also selected three debutants.

Moreover, there is an additional factor that, given recent history, points fairly and squarely in Australia’s favour – merely that they are the home side. The calendar year of 2013 was a stellar one for home teams in Tests. Specifically, of the 44 Tests played last year, a remarkable 30 were won by the home team, 10 were drawn and only 3 won by the away team (Pakistan looks likely to make that 31 against Sri Lanka in the Test that started on New Year’s Eve).

The surprising element of this occurrence, according to some pundits, was that it came after a period, from 2010-2012, in which away teams performed quite admirably against the tide of home-ground advantage. At least on the basis of raw numbers – in these years, a combined 124 Tests resulted in 48 home wins, with the number away wins almost at parity (43). This apparent ‘trend’ towards away teams did not go unnoticed by sports journalists and other non-academic writers. For example, Gideon Haigh remarked to this effect (“The quiet revolution: home ground advantage begins to fade away”, The Australian, 20/12/2012).

However, as economists know all too well, looking at just the raw figures is too parsimonious an analysis for making claims that the nature of home-ground advantage – a phenomenon so well researched, understood and entrenched in sporting culture – has diminished so fundamentally and suddenly. What needs to be understood about the sample of Tests in those years were that they were correlated with factors that skew the chances of victory in favour of the home team to begin with, most obviously on the basis of relative strength of both teams.

For example, easily the best team of 2012, South Africa, played 10 Tests that year. All but one of them were played away from home, with an unbeaten record (4 wins, 5 draws) befitting a World number one. This is a nice example of what in economics (and some other scientific disciplines) is called a ‘selection bias’ – such biases have to be accounted for, since it is not difficult to imagine how the figures would have more-highly favoured home teams at an aggregate level if the Proteas had instead been scheduled to play 9 Tests at home. Another example (this time for 2011) is that minnows Bangladesh and Zimbabwe played a combined total of 8 Tests, 7 of which were on home soil, again skewing the overall record in favour of away teams. With such a small sample of teams and Tests, these selection biases are important and should not be ignored.

Likewise, the stunning reversal back towards home teams in 2013 has to be taken with caution – (the again rampant) South Africa played 7 of its 9 Tests at home, winning 6 and drawing the other. Second-ranked India also played the majority (6 of 8) of its Tests at home, completing a perfect record, not to mention third-ranked England’s impressive Northern summer record (5 wins, 2 draws), prior to their almost inexplicable slide in the current series.

Most Australian cricket supporters will  hope that the aberration of 2013 does not continue past this week – their next series is away to South Africa. Otherwise, that tour could prove to be a sobering experience following the current euphoria. Nevertheless, the influence of home-ground advantage in Test cricket does not appear to be under any immediate threat. To this end, if one was the betting type, I would not be shy in punting on a home victory at the SCG.

Media Misses Point on Cricket’s Decision Review System

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[Archived from: The Conversation, 15 July 2013]

The first Ashes Test was indeed a veritable thriller. England edged Australia by a mere 14 runs, after an absorbing four-and-a-half days of action to go one-up in the best-of-five series. For those not well versed on the sport, only a dozen or so of more than 2,000 Tests dating back to 1877 have been decided by fewer runs.

Partly because of the closeness of the match, much of the media focus has centred on decision outcomes arising from the Decision Review System (DRS). This system, which allows up to two incorrect challenges per innings, is in economic terms a resource like any other – a scarce one, and one to be used, lest it be lost.

Opening with a disclaimer, I have absolutely no sympathy for my team here. No Australian cricket fans were complaining back in the pre-DRS era in 2008 when the Andrew Symonds incident in Sydney arguably turned the entire series against India in Australia’s favour. I could even excuse Doug Bollinger for his infamous dummy spit in Adelaide a couple of summers later against the West Indies when the system was still in its infancy, but by now there is no longer any excuse for such irrationality.

What is not in dispute is that the DRS has significantly reduced the incidents of incorrect umpiring decisions being allowed to effectively stand, relative to the previous status quo. This is also true in tennis, yet the consensus is that it works perfectly well in that sport. This helps tell the economist in me that there is very little, if anything at all, wrong with the system itself in cricket. But try telling that to various print and broadcast journalists.

Many local scribes over the weekend into today have sadly succumbed to the temptation to pander to the masses of their readership. Since Australian fans want to have our spleen vented in one united voice right now (among other ways) by reading what we want to hear – that “we woz robbed” – sports writers have a strong incentive to serve up precisely that, even if it misses the entire point.

As an economist, of ultimate policy-related importance is that what the DRS did was to re-assign some (albeit small) proportion of decision-making power from the umpires to the players themselves. But what is being ignored in the DRS discourse is the commensurate responsibility that comes with that power.

Sure, Aleem Dar’s third-day call on Stuart Broad was indeed a howler, and that wasn’t the only injustice served up by the men in white during this Test either. But why is it that no-one seems to be willing to give Australian captain Michael Clarke and his men the unconditional lambasting they deserve for willfully squandering their unsuccessful challenges like a bunch of drunken sailors on tour?

An argument here might be to say that (former Australian wicket-keeper Adam Gilchrist’s views on walking aside) professional athletes cannot be trusted for complete honesty anyway. So why bother holding them to account like we have always done to the umpires?

However, this argument is weak at best. In fact, if I were Stuart Broad, I too would have defiantly stood my ground. What’s more, rather than looking sheepish about it, I would have backed it up by giving the Australian players a right old bollocking – or perhaps sledging – telling them (in laymen’s terms) that if they were not so systematically and profligately quick on the trigger with their challenges, I’d be back in the pavilion by now…so suck it up, laddies!

Even more worrying was that the harsh lessons from the third innings of the match were not heeded in the final innings, when Australia once again exhausted their challenges early on (though they had already benefited once from one correct challenge). Imagine if Brad Haddin had not actually nicked the ball, yet were incorrectly shown the index finger.

Economics, particularly on the micro side, is about decision-making. I am yet to meet a cricket-loving microeconomist who thinks the DRS is anything but a solid system with an appropriate treatment given to incentives and strategy.

It is just a pity that the Australian cricketers have not yet woken up to their responsibility of mastering the art of rationality around it, and that commentators and writers have not yet learned to correctly apportion the fair share of the blame on the players for the so-called injustices that can still arise under the system.

‘Old Urn’ Itself Could Alter Aussie Ashes Tactics

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[Archived from: The Sports Economist, 10 July 2013]

The oldest prize in Test cricket is once again up for grabs. Commencing earlier today, Australia is taking on England away from its own backyard in an attempt to regain the Ashes. Michael Clarke’s men have shown transparently that this one is the series they have the greatest desire to win, despite the old urn’s grossly underwhelming aesthetic stature.

Following its creation as the spoils of victory in series between these combatants in 1882 (though curiously never designated as such formally), its place in the sport as a bilateral trophy (one that can be won only by either of two teams) was unique for almost 80 years.

This changed only during the remarkable 1960/61 West Indies tour in Australia, which was capped with the minting of the Frank Worrell Trophy, to be contested thereafter between those teams. There has more recently been a real proliferation of these trophies, especially since the mid-1990s.

Currently, with 10 Test playing nations involved in World cricket, there are consequently 45 bilateral sets of opponents, and a total of 11 different bilateral trophies (effective since 2008) are now actively played for periodically, with Australia being the ‘worst offenders’, playing for 6 such trophies out of its 9 Test rivals.

Cricket fans – please feel free to disagree, but one’s personal view is that with the Ashes an obvious exception (given its history), many of these other bilateral trophies are surplus to one’s interest above and beyond the simple significance of the Test series and its ultimate result, and often play a role of little more than a shameless gimmick, and a diminution of the actual cricket.

Nonetheless, in any individual Test series, the simple tactical objective is generally to win the series, and if that becomes mathematically impossible or even improbable, a series draw is still better than a loss.

A complicating factor in cricket, however, is that there is no universal consensus – the ICC ranking system aside – on the value of a draw relative to a loss, unlike other sports where league points make this explicit (one-half in many sports, one-third in modern soccer). The existence of a trophy, assuming that ‘holding’ it really matters to players and fans, muddies the tactical waters, as the holder has to be beaten for the ‘silverware’ to change hands.

There is relevance in this setting of interest to microeconomists through incentives and strategy. Sporting contests have much potential to tell us economists more than a thing or two about the way firms behave in duopolistic industries where the competitors are not equally resourced.

Assuming there is some value to holding the trophy, potential follows for this value to skew attacking and defensive tactical decisions of both captains, comparative to the identical series scenario where there is no trophy on the line.

This upcoming series can be used to illustrate a textbook case of how a bilateral trophy being at stake may just alter team behaviour at the margin. However unlikely you think it, suppose the series is level at 1-1 after four Tests, and that late on day five of the fifth test, the final and deciding game is on a knife’s edge (and that a draw is still a comparable possibility).

Since 1-1 is not good enough for Australia to return home with the prize (England currently holds the Ashes), it is easy to envisage how Michael Clarke would throw caution to the wind to give his XI every possible chance of winning the decider, not to mention what Alistair Cook’s ‘game theoretic’ tactical response might be.

In the counterfactual that there exist no Ashes for him to regain, rather it’s purely the series outcome that matters, one might imagine how he may turn defensive to suffice for a draw and (arguably) claim a moral victory in levelling an away series against a significantly more favoured team. The inclination for him to do this might be accentuated if his captaincy and/or personal form were under scrutiny during the series, with equal honours perversely providing him some measure of vindication.

Even if you summarily reject any possibility that Clarke would ever sway toward that tactical inclination, you might be willing to accept how Zimbabwean skipper Brendan Taylor would analogously almost certainly opt for any stalemate within reach at the death of an away series to their neighbours – the World top-ranked South Africans.

At any rate, I suspect that fans of Australian cricket will have a wide range of views about how they will feel about a drawn series. Many will consider it equivalent to a series loss, since the Ashes are not regained either way. Others like me, with the recent 4-0 whitewash in India still fresh in the mind, will still take some matter of pride in averting a third successive series loss against the old enemy.

Forget ‘Fab Four’, Men’s Tennis Still More Competitive

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[Archived from: The Sports Economist, 25 January 2013]

As the Australian Open approaches the business end, this year’s installment has developed a palpable sense of familiarity of recent years about it. Each of the top four seeded men made the semi-finals, and it’s hard to escape the feeling that fourth-ranked Rafael Nadal would have been in the place of his compatriot David Ferrer if he were present. And so we have the familiar trio of Andy Murray, Roger Federer and Novak Djokovic left standing.

The story in the women’s singles has been notably different, and not just to this stage. There were a sprinkling of upsets in the first week – earlier in the tournament only 3 of the top 16 men’s seeds were eliminated before the fourth round, compared to 7 casualties from the top 16 seeded women.

In comparing the sexes, it is worth reflecting how the modern era of tennis is arguably an unusual one in terms of the relative competitiveness in both the men’s and women’s games.

The current prevailing wisdom among occasional observers of the sport is that men’s tennis is highly predictable – at least until the semis where the fab four seem to meet more often than not, and that now, it is the women’s draw that offers a far more balanced and interesting proposition.

Historically, this is unusual – but long-passed are the successive eras of Margaret Court, Chris Evert/Martina Navratilova and Steffi Graf/Monica Seles. Back then, you could almost bet your vital bodily organs that any Grand Slam trophy would end up safely in one of only two or three possible pairs of female hands, even before a ball was served in anger. Meanwhile, the four majors seemed to be far more contestable on the male-side of the draw.

Things began to change in the early-to-mid 1990s – the rise of emerging women, such as Arantxa Sánchez Vicario, Mary Pierce, Martina Hingis and Lindsay Davenport, renewed interest in the women’s game. Concurrently, the Sampras/Agassi duopoly began to hold sway, as it would for the better part of the following decade.

A short period followed in which Jennifer Capriati and the Williams sisters dominated the majors, at a time when the male duopoly loosened its grip and other men, including Lleyton Hewitt, had comparable claims to slam titles.

In the decade since, however, other women such as Justine Henin and Maria Sharapova have once again challenged at the top to produce a more open field, while the ascension of Roger Federer, since joined by the other three members of the quartet, has made the men’s game look like a closed shop.

However, this prevailing wisdom is ill-informed. Many of us will only watch a handful of games on television during the Open. Locals, even certified tennis tragics, who go to Melbourne Park will not see many televised matches in the other months of the year, let alone live overseas.

In fact, the ATP and WTA tours each involve roughly 2,500 matches each year in the top-four tournament tiers (and the season-ending championships), and only an analysis of all of these matches can tell us the complete story of the overall tour, as opposed to merely anecdotal evidence at the very apex of the talent pool.

I was motivated to find whether this conventional wisdom was indeed true over the entire tours, and so having obtained data on all matches (excluding walkovers, retirements and disqualifications), I set out to find the answer. I went back as far as 2007 – the last year in which the fab four did not quadrella the end-of year rankings (Andy Murray would join them in 2008). During this period, Serena Williams found a way to win a further eight slam titles during her post-injury renaissance, but she hasn’t had it all her own way – she has only occupied the top end-of-year ranking spot once (twice finishing outside the top five).

One simple statistic would be the percentage of matches that go to a third set. For this, we would have to exclude best-of-five set men’s matches (mostly grand slam) to circumvent an unclean comparison.

On this score, more men’s matches are competitive, with 33.8% going to a deciding set compared to 31.2% of women’s matches (31.6% if grand slam matches are excluded for closer comparability).

Another sensible statistic is the proportion of matches where the favourite was beaten, as a measure of propensity for upsets. Only matches in which all (at least three) bookmakers odds were unanimous on the favourite were analysed.

Here, slightly more women’s matches were upsets (26.8% to 26.6%), but again, best-of-three and best-of-five matches are not comparable – statistically, the underdog is less likely to beat the favourite when the match is longer.

When grand slam matches are excluded for both sexes (plus a handful of other best-of-five tour event finals), the scales again tip in favour of the men (28.1 to 27.7%). The story was similar with two other metrics I investigated, specifically the median of the log-ratio of the betting odds and the average number of games won by the loser.

It is worth noting that these differences are not statistically significant, but it dispels the prevailing wisdom that elite women’s tennis has been more competitive in recent times.

I emphasise that this result should not be taken as an endorsement of men’s tennis over women’s; rather, it warns of the ever-present danger of various stakeholder groups in sport (or any other industry for that matter) making false inferences due to extrapolating on a small number of matches (or observations) to make crude generalisations without looking at the data in its entirety.

Ultimately, however, the title odds at Melbourne Park were more open on the women’s side two weeks ago. Therefore, next time you have to decide between watching a men’s and women’s match, there are numerous factors that will determine whether or not it will be an exciting and close match, so I would advise to simply use your own discretion.

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.