Tuesday 2 May 2017

ABBA Instead of ABAB? What’s the Fuss?

At this year’s annual International Football Association Board (IFAB) meeting, the body in charge of the Laws of the Game decided to start experimenting with an alternative sequence for taking penalties during a shootout. Instead of having both teams take turns (i.e. ABABABABAB), as they have always done in football, a sequence akin to the one of serving in a tiebreak in tennis (i.e. ABBAABBAAB) will be tried out. Could this have any impact on who is to win a shootout, really? The answer is an unequivocal ‘yes’. And science helps us understand why.

In 2010, two Basque economists, Ignacio Palacios-Huerta and José Apesteguía, showed that in actual penalty shootouts in football, the team shooting first ends up winning in approx. 60% of cases; the team going second only in about 40%. This is quite a difference with both teams winning half, which is what would have been both expected and desirable. These findings imply that the toss deciding which team could go first imparts an enormous competitive advantage.

The mechanism behind this advantage is the so-called “lagging-behind effect”. The lagging-behind effect represents the simple fact that it is more difficult to convert a given penalty if one's team is behind in the score at the point of taking the kick than when not behind, due to the enhanced pressure such a “near-to-losing” situation creates as one “has to score” to keep one's team in the game.

Source: diariosdefutbol.com

It is easy to see why such a lagging-behind effect, under the current sequence, results in an advantage for the team going first, simply by considering both teams' first kick. What is the probability that team A is lagging behind at the time of their first kick? Naturally, this is zero as all’s square at that point. Now it is up to team B to take their first kick. Their chance of lagging-behind at this point? With penalties being converted at a rate of approx. 75%, there’s about a 75% chance team A will just have scored and thus a 75% chance that team B are lagging behind when taking their own first kick. So a 0% vs. a 75% chance of lagging behind on the very same kick. Under the current ABAB-sequence, in which every time team A get to act and team B to react, this pattern will be preserved and the resulting lagging-behind effect knocked on till the end.

In case of applying an ABBA-sequence, as in a tennis tiebreak, instead, the advantage of having the opportunity to force the lagging-behind effect upon the opponent rather shifts from one team to the other: it, again, starts with team A, but then moves to team B as they get to go twice; then to team A that get to go twice, etc. The whole idea being that the influence of whoever may win the coin toss and thus be able to go first will have only minimal impact on who will win.

In addition to the abovementioned empirical research uncovering the lagging-behind effect, together with Profs. Brian McCann and Govert Vroom, we were able to prove, through theoretical (mathematical) research, soon to appear in the Journal of Sports Economics, that, in case of a lagging-behind effect, the ABBA-sequence substantially reduces the advantage of winning the toss relative to the current sequence. However, we also prove that there is yet another “natural” sequence, known as “Prouhet-Thue-Morse”, which reduces this advantage even more than the ABBA-sequence does. Perhaps something to add to next year’s IFAB meeting’s agenda J

Saturday 1 April 2017

Why We Should All Hope FIFA’s 2026 World Cup Slot Allocation Will Be Rejected, for the Good of the Game

In 2026, for the first time, the FIFA World Cup will feature 48 contestants; a 50% increase from the current format of 32 participating nations. On the one hand, this is good news as – as the rationale for the expansion goes – now 50% more peoples will be able to join the party. On the other hand, there can be obvious concern about maintaining the level of quality delivered on the pitch – after all, the World Cup is not just any party: it’s a football tournament. The severity of the latter risk is naturally linked with the competitiveness of the nations additionally to qualify for the 2026 and subsequent world cups. This, in turn, depends a great deal on how the slots are divided among confederations.

Before going into the newly proposed slot allocation, which will be voted on in May, I will present two alternatives, mainly for the purpose of benchmarking: a "pareto-optimal" one and one based on the current FIFA World Ranking. Pareto-optimality is an economic concept indicating a state in which it is impossible to reallocate resources in a way that will benefit at least one agent without leaving any agent worse off. This corresponds to each confederation’s number of slots growing proportionately with the growth of the pie, i.e. by 50%, so that proportions represented by each remain unchanged. The result is as follows:

*The host nation currently completes the 32; as of 2026, the host nation will count towards the total of allocated slots per confederation
** UEFA-affiliated associations additionally include Turkey, Israel and Russia
*** Australia is currently affiliated to AFC, not OFC

Alternatively, we can consider a slot allocation based on the FIFA world ranking. While the FIFA world ranking is no perfect indicator of national teams’ strength, it can be argued that the top-48 of the ranking roughly corresponds to the 48 strongest footballing nations of the moment. According to FIFA's world ranking, as of 01/04/17, the following slot allocation could be taken into account:

* Two slots will be subject to a play-off tournament of six nations, including one delegate from each confederation but UEFA and an additional one from the confederation of the host country. Two of the six participants in the play-off will be seeded, based on their FIFA world ranking. Due to all of its members’ relatively very low ranking, no OFC member could be seeded by any likelihood.

Oddity nr. 1: The cleanest comparison relating the quality of their football and their differential treatment according to the newly proposed slot allocation is the one between AFC and CONMEBOL. Both the Asian and the South-American confederation currently have 4.5 spots each. Over the last 5 editions of the World Cup, i.e. all those featuring 32 contenders, 7 different nations, both of AFC and of CONMEBOL, were able to qualify at least once for the tournament. Interestingly, of those 7 AFC nations, only 3 (so 43%) were able to ever make it through to the Round of 16, as compared to all 7 (so 100%) of the CONMEBOL nations. Moreover, at the previous World Cup, where CONMEBOL had 7 representatives due to Brazil hosting the event, no less than 5 of them made it through to the Round of 16. Not a single member of AFC made it that far. This evidences that while AFC and CONMEBOL have thus far been allotted an exact same number of slots, CONMEBOL has been able to delegate consistently more competitive teams than AFC. Yet, under the new proposal, CONMEBOL’s number of slots allocated is due to increase to only 6.44 as compared to 8.44 for AFC.

Oddity nr. 2: To assess the breadth of competitive teams within each confederation, one may consider how many of their different nations, respectively, were able to qualify for previous World Cups. All confederations but one delegated a number of different countries to the previous 5 World Cups that is at least as large as their minimum allocation for the 2026 World Cup according to the new proposal. The exception being AFC, with 8.44 slots, yet only 7 different nations that managed to qualify so far. This means that even in case all of its members who participated in any of the previous 5 World Cups, viz. Iran, Japan, South Korea, Saudi Arabia, China, Australia and North Korea, are to qualify for the 2026 tournament, then, still, AFC will be able to delegate at least one and possibly two additional nations. As a gentle reminder, in their respective participations in 2002 and 2010, neither China nor North Korea were able to salvage any points from their group. Whereas China also failed to score a single goal, at least North Korea did find their way to the net, once. The cumulative goal average of both nations’ combined 6 games stood at –20. This implies having lost their games, on average, by more than 3 goals difference.

Oddity nr. 3: As evidenced by the changes in the proportions each confederation is able to delegate, the newly proposed allocation implies a loss for UEFA of no less than 9 percentage points (its stake dropping from 42% to 33%), to the relative benefit mostly of the African and Asian confederations. In case of the former, the increase seems granted, based on the FIFA world ranking: CAF is now certain to have at least 9 delegates, with exactly 9 African nations raking within the top-48 of the FIFA world ranking. In case of AFC, however, no more than 2 countries currently rank within the top-48 of that ranking. Concretely, the transfer of slots from UEFA to AFC would imply that the strongest possible countries to potentially make it to the tournament on the side of AFC, according to the FIFA world ranking, will include Uzbekistan (63), UAE (68) and Qatar (84) and that at the very least 10 UEFA countries within the top-48 of FIFA's world ranking will be left out. Furthermore, considering the World Cup's 5 most recent editions, no less than 20 different UEFA delegates (exactly its number of "pareto-optimal" slots) were able, not just to qualify for the tournament – which otherwise could also have been due to too many European slots – but to actually make it through to the last 16 – indicating their genuine ability to compete.

In sum: in the event the proposed slot allocation becomes accepted, in the short term, i.e. at the 2026 World Cup, we can expect more than a few countries to be present that will not, by any standard, have their place among the world’s best 48 footballing nations. In the longer term, we would be likely to witness a number of non-Asian national associations follow Australia’s example by requesting to join AFC, incentivised by the disproportionate number of slots awarded to this confederation relative to the level of competitiveness of its competing members. To conclude with Erasmus' wisdom, prevention is better than cure.