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.

Tuesday 8 November 2016

Best 11 vs. 11 "Best Bang for Your Buck"

With the initial study rounds being a matter of the past, the 2016-2017 season is finally well underway. An appropriate time to assess whose star has been shining. In today's post, I will assemble and compare two line-ups, across all leagues: the best performing one and the one that has so far yielded the best value for money. As performance measure, I will employ the industry standard, i.e. the InStat Index, an overall quality score indicating a player's recent form. 

The InStat Index is based on a detailed breakdown of a player's recent performances along about a dozen relevant performance dimensions, according to the position the player occupies on the field, e.g. finishing for a forward and key passing for a central midfielder. As a measure of a player's value, I use the market value as provided by transfermarkt.com. Both InStat Index scores and market values used are those as of November 8, 2016.

To determine the best-in-form line-up, I checked for each position on the field which of all players on that position has the highest InStat Index score. The resulting team is as follows:
Figure 1: Best 11, based on InStat Index per position
(Top, italicized, number in players' squares is their InStat
Index score; bottom number their market value, in €m)

Observation 1: Although players from all professional leagues across the world are being taken into consideration, the best starting eleven come from as few as three national leagues: La Liga, the Premier League and Ligue 1. Moreover, the Spanish league is host to no less than 9 of the 11. Additionally, apart from PSG's Brazilian skipper Thiago Silva, the only representative of a league other than the Spanish one is David Silva, indeed a 2010 World Cup winner with Spain. In total, there are five Spanish players in the team and three Brazilians.

Observation 2: Spanish champions FC Barcelona provide more than half of the best team: the attacking line is entirely Barça's MSN, with Pep Guardiola's incarnation on the field, Sergio Busquets, forming a link between the attack and a defense featuring both the blaugranas Umtiti and Sergi Roberto.

Observation 3: The two players in the team who are no absolute stars (yet) are Sevilla FC's goalkeeper Sergio Rico and Las Palmas' central midfielder Jonathan Viera. With solid performances both in La Liga and the Champions League, Rico, a 23-year-old local boy from Sevilla, who made his debut for Spain earlier this year, is keeping PSG arrival, Italian international Sirigu behind him on the bench. Those readers for whom virtuoso Jonathan Viera, by far the player with the lowest market value to make it into the squad, may or may not ring a bell, I gladly point to the previous post in this blog.

Observation 4: Apart from who made it to the team, it is also interesting to consider some who did not. In spite of them being the players with the third and fourth highest InStat Index score overall, respectively, neither Real Madrid's Gareth Bale nor Cristiano Ronaldo feature in the 11 best. Their misfortune is that they happen to be playing in the same position as the numbers one and two in terms of InStat Index, Messi and Neymar, respectively. Marcelo is thus the only merengue to make it to the best 11.

As, for most clubs and people, money is a limited resource, it is at least as worthwhile to find out which team yields the best value for money. In terms of our analysis, which players represent the most InStat Index points per euro? Simply dividing a player's InStat Index score by his market value, however, would imply that, say, a player with half Messi's InStat Index score and costing less than half of Messi would be "better value for money". To correct for this, I apply a natural-logarithmic transformation to the players' market value. Thus, the measure I consider here is InStat Index score divided by ln(market value). 

For a player to be withheld, in addition to having the best above measure in his position, he should be part of the top 10 in his position according to InStat Index and he must have featured in at least half of his team's domestic league games this season to date. The resulting "best bang for your buck" 11 are as follows:

Figure 2: "Best bang for your buck" 11,
based on InStat Index and market values
(Top, italicized, number in players' squares is their InStat
Index score; bottom number their market value, in €m)

Observation 5: The dominance of La Liga is similar in case of the "best bang for your buck" 11: 8 players play their football in the Spanish league; one of the "foreigners" in the team, Bayern Munich's Xabi Alonso, is actually a World Cup winner for Spain. Together with Schalke 04's Brazilian centre back Naldo, Alonso is one of two Bundesliga representatives coming into the team. With six players, more than half of the team are Spanish; again there are three Brazilians.

Observation 6: With a market value of just one tenth even of Sergio Rico's and with an InStat Index score that is just marginally lower than his Sevilla FC counterpart, Espanyol's on-loan goalkeeper Diego López, the man in whose favor Mourinho famously dropped San Iker Casillas to the bench when at Real Madrid, comes into the team. Sevilla FC does manage to keep a player in the squad, though, as Sergio Escudero replaces Marcelo on left back.

Observation 7: Expensive Barça options on right back and centre back, Sergi Roberto and Umtiti, are being replaced by the very lowly valued Míchel and David García, both from Las Palmas. As, naturally, Jonathan Viera retains his spot in the team, Las Palmas thus become the only club with as many as three players in the "best bang for your buck" 11! Another player coming in from one of La Liga's smaller teams is Villarreal's promising midfielder Manu Trigueros.

Observation 8: Both Messi and Neymar remain in the team, in spite of their astronomical market value. The rationale is simple: both are so much better (as indicated by the InStat Index differential) than the other players in their position that they still provide the best value for money – in this case a lot of value for a lot of money. As mentioned above, Bale and Cristiano Ronaldo are the ones who come closest to the performance of Messi and Neymar, respectively, but their market value is comparable to their blaugrana counterparts.

Observation 9: A big part of bringing down the cost (i.e. market value) of the team without sacrificing performance much has been achieved by bringing aging stars in, whose market value is at a low, but whose performance is still up to standard. Whereas only two players in the best 11 team are over thirty, with Thiago Silva (32) being the oldest, in the "best bang for your buck" 11, five players are aged 34 or 35. The average age of both teams differs by 3 years.

Observation 10: The best 11, corresponding to a total market value of €520m, managed an accumulated InStat Index score of 3,685. This compares to 3,567 for the "best bang for your buck" 11, valued at €259m. In other words, with only half the budget – and still being able to count with both Messi and Neymar – the "best bang for your buck" 11 represent only a 3% loss in InStat Index score compared to the best possible 11.

However, adding players' individual performances may not provide the right basis for comparison. If football is a "weakest link" rather than a "strongest link" game, as advocated by some of its greatest managerial innovators, such as Lobanovskyi and Sacchi, multiplying individual performances may be the more accurate way to go (see Anderson and Sally's The Numbers Game). This would paint quite a different picture as the product of the individual InStat Index scores of the "best bang for your buck" 11 reaches only 69% of the best 11's – hence a 31% rather than just a 3% loss. So one's philosophy of the game will matter a great deal, also when talking "hard" numbers.