More on Penalty Shoot-out Alternative

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Following on from my post on 2 July, I had another newspaper piece in the Australian Financial Review (today, Tuesday 15 July), called: “GOAL! A Better Alternative to Penalty Shootouts“. The link is gated as usual (see p.43 of the hard copy if you have it, or e-mail me a request). It further delineates the economic case for shifting the penalty shoot-out to before extra-time.

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!

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.

Football Penalties BEFORE Extra-Time? Dr Jan Libich and I Assess the Proposal

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I recently recorded a video (description below) that follows from a previous post on 16 July 2010.

WATCH ON YouTube.

FIFA President Sepp Blatter called penalty shootouts in football (soccer) a “tragedy”. Dr Jan Libich interviews me about our study (also co-authored by Dr Petr Stehlik) assessing an alternative rule: to stage the penalty shootout BEFORE (rather than after) extra-time. The study can be downloaded at www.janlibich.com/penalties.pdf. This video was recorded on 31 August 2012.

The First Two Data Points Say “…mmm, I’m Not Sure Yet”

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[Archived from: The Sports Economist, 23 January 2012]

The new NFL overtime rule, see page 111 (introduced last season for playoff games only) finally became binding in the current playoff series two weeks ago, and then for a second time yesterday. Of most interest to economists about the rule change is its potential for teams to alter their overtime strategies in response to the element of the rule that both teams are now guaranteed a direct opportunity to score.

While it’s far too early to make firm inferences about this, it’s worth recounting that the primary intention of the rule was for the result of the coin toss determining which team gets to receive the kick-off (and consequently first possession) to have less power in determining the match winner (previously almost 60% of the nearly 500 overtime games since 1974). At the margin, we might also expect touchdowns to be the winning method of scoring slightly more often than previously, since it is now the only way that the team with first possession can effectively kill the game without the opposition getting the chance to equalize.

On the basis of these first two observations, it is interesting to note that the qualitative outcomes were very different – while winning the toss allowed Denver and Tim Tebow to end the contest on the first play via a touchdown, both NY Giants and San Fransisco each failed to score on their first possession, triggering reversion to sudden death as previously, which was won eventually by the former. [Disclaimer: I have only recently followed the sport, so feel free to critique this via comments.]

While this (admittedly premature) anecdotal evidence suggests that the coin toss is more influential than before, the reality is about as mixed as could have been expected. Someday – perhaps in a few decades or even within the decade should the rule be extended to the regular season, one of our esteemed TSE colleagues will no doubt crunch the numbers on this rule change when there is a sufficient (presuming due restraint exercised) sample size.

IRB Rugby World Cup Statistics

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[Archived from: The Sports Economist, 30 November 2011]

The International Rugby Board (IRB) report on the analysis of match statistics from the 2011 World Cup was released recently (see the report here). It paints a flattering picture of various game specifics in comparison to the 2007 and 2003 World Cups, including competitive balance (see my earlier post on this issue):

…Tier 2 teams were competitive for all 80 minutes of the game. The Tier 1 teams did not pull away over the last 20 minutes which was frequently the case in previous World Cups.

 
…as well as tactical dynamics and aesthetic appeal of the games:
 

…fewer set pieces, a substantial reduction in kicks from hand and many more passes, Rugby World Cup 2011 saw a renewed emphasis on running rugby.

On the latter, Bret Harris from The Australian newspaper (1 December) is not convinced, citing (perhaps unknowingly) what economists would refer to as selection biases (insofar that the sample of World Cup matches are, on average, less competitively balanced than the population of professional matches):

What was that? Running rugby? If the World Cup was a festival of running rugby, then I’m missing something. Certainly, there were some big scores when the super powers of the Tri-Nations and the Six Nations played the minnows, but in the crucial pool matches and the knockout stages, teams played not to lose rather than to win. There was not a lot of expansive, attacking rugby when the top-tier teams played each other.

For rugby fans, be advised to read the report and make your own decision. My feeling was that the 2011 World Cup (overall) was a marginal improvement on 2007 in terms of attacking/attractive Rugby.

Bonus Points and Incentives in Rugby

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[Archived from: The Sports Economist, 23 October 2011]

The 2011 Rugby World Cup has climaxed with hosts New Zealand being crowned champions for the second time last night (joining Australia and South Africa, while England has won it once). They did so by defeating France 8-7 in a tense affair in the Final at Auckland’s Eden Park, in front of (a capacity) 60,000 supporters – certainly not the easy way as most expected, but having endured 24 years of angst since their last title in 1987, all Kiwis will still take it nonetheless! As a tribute to the ‘Shaky Isles’, another post on Rugby seems in order.

One of the most distinctive nuances about the game lies in how in some tournaments (including the World Cup and Super Rugby), there exists a system of ‘bonus’ competition points (in round-robin stages). Specifically, in addition to the standard four competition points for a win (two each for a draw), either team is rewarded with one bonus point if they score four or more tries in a match (irrespective of how many tries the opposition scores). Furthermore, the loser receives an additional (narrow-loss) bonus point if they lose by seven or fewer (match) points. The purpose of these bonus points is to reward attacking Rugby by encouraging teams to score more tries (for example, by running the ball more and kicking it less), and to maintain interest in the game longer in situations where the result has already become highly certain.

A co-author of mine, Niven Winchester (these days at MIT), is a native New Zealander who will no doubt be ecstatic after having been at the game in person. He is primarily a Trade Economist, but also has a penchant for modeling predictions and ranking systems in sport. His 2008 paper in JQAS (abstract here) concludes that the current bonus points system is sub-optimal at his defined objective of revealing the best quality teams over the duration of the season. Instead, he favors altering the narrow-loss bonus threshold from seven to five match points, and changing the try bonus to either a minimum of eight tries, or alternatively, for scoring at least three more tries than the opponent does. The last of these recommendations is particularly compelling when recalling some of the pivotal results from the previous World Cup in 2007. To quote the paper:

Anecdotal evidence also supports our assertion that defensive capability should be included in a try bonus decision rule. In the quarterfinals of the 2007 Rugby World Cup, New Zealand and Australia, two teams heavily favored to advance to the next round, lost to France and England respectively. Several rugby experts, including Australian coach John Connolly, suggested that the attacking style adopted by the two favorites was partly responsible for the unexpected results. In turn, incentive structures in place in the competitions that these teams regularly participate in may influence playing styles. Specifically, New Zealand and Australia compete in the Tri-Nations competition where a (four-or-more) try bonus point is offered, and France and England participate in the Six Nations tournament, where try bonuses are not awarded.

Niven has since adapted this methodology with further modeling improvements to consider a similar question using data for the Australian Football League (AFL) and the National Football League (NFL), with some interesting findings for both.

Perhaps one of the most fascinating questions yet to be explored with Rugby match data is the degree to which such a system effects within-match team and player behavior, compared to what would be observed in the absence of bonus points. In terms of the try bonus, a very simple way to do this would be to look at the distribution of the number of tries scored by teams in matches, and determine whether the frequency of ‘4’s is greater than that suggested by a fitted or stylized distribution. If we look at a histogram of tries scored in all Super Rugby regular-season matches from 1996-2011 (see here), we see that it is not easy to tell from a simple ‘eyeball’ whether this is indeed the case. Even if so, one still needs to control for match-specific factors that may be driving the observed distribution.

As for the narrow-loss bonus, a similar exercise is possible, though arguably more difficult to validate, since there are other factors skewing the incentives simultaneously, and also given the discrete nature of the scoring system. Nevertheless, this is a nice little example of how sports data provides much potential to the Economics profession with respect to the ability to test for incentives and strategies in games.

Brazil Bleg

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[Archived from: The Sports Economist, 11 November 2010]

Bitter football enemies Argentina and Brazil (combined 7-time World Champions) square-off yet again in a friendly next Wednesday.  The match is in (of all places) Doha – since the match coincides with the final evaluation of Qatar’s ‘no expense spared’ 2022 FIFA World Cup bid, it is hard to imagine the reasons for the choice of location are anything other than economic! It will be the 90th all-time meeting between the two giants of South America, with the previous 89 failing to separate them, at 33 wins apiece and 23 draws (Argentina are ahead slightly on goals scored, 143-137), though Brazil have had the better of the results in recent times. The game will also be a useful tune-up for both sides ahead of next year’s Copa América, hosted on this occasion by the Argentines.

Owing to my girlfriend being from Buenos Aires, one’s loyalties in this game are cast clearly in favor of La Albiceleste.  However, I have recently been working on testing an old myth that it is unwise tactically to score too early in the game when playing against Brazil. The underlying intuition here is that doing so merely makes the Brazilian players angry (waking the sleeping giant), giving them extra incentive to attack and score freely thereafter as a ‘lesson’ to the opposition. This is not a frivolous applied microeconomic exercise, as it provides further evidence about the choice of timing of effort exertion by an underdog in a finite-length bilateral (but asymmetric) industry contest against a more favoured opponent, drawing upon inspiration from Avinash Dixit’s seminal 1987 piece in American Economic Review.

Despite an ardent belief that this myth is well-known to many fans of the game (at least in the Anglo-sphere), finding hard-source material validating it is proving more difficult than imagined. The only successes thus far are a quote in the 2000 autobiography by former Liverpool and Scotland centre-back Alan Hansen, as well as an old video of an SBS1 TV (Australia) telecast of a 1997 Confederations Cup group-stage match, where the English commentator states it explicitly.

If anyone knows off-hand of any citeable source on this one, please share with TSE readers via the comment section above. For the record, using data from 267 full ‘A’ internationals involving the Seleção between 1993 and 2010, the myth is found to be, in the words of Adam Savage and Jamie Hyneman: ‘totally busted’!