By David Butler

Last week I presented some data relating to prize money allocations in golf and horse racing. As a corollary, below is a Lorenz curve showing the distribution of prize money for 534 professional snooker players competing in 57 international tournaments over 23 years from 1992-2014.  

In Economics the Lorenz curve is a graphical illustration of an income distribution. This curve originated from the works of Economist Max Lorenz in 1905. The red line in the graph below is called the line of equality. The bowed line beneath is the Lorenz curve. The difference between both lines gives an indication of how unequal the distribution of winnings in snooker have been.  

The top 20% of snooker players over 23 years have claimed £65,339,628. That’s 95% of the entire earnings. England's Ronnie O Sullivan is the highest earner. He’s won 6.5% of the total prize money available. The Scots, John Higgins and Stephen Hendry are 2nd and 3rd while Wales’ Mark Williams is 4th in the list. The highest ranked Irishman is Ken Doherty in 13th position. There are only 3 players from outside the British Isles in the top 30 earners; Neil Robertson (Australia, 6th), Ding Junhui (China, 8th) and Marco Fu (Hong Kong, 17th).

For the more technically inclined, one can specify the degree of inequality in prize money by calculating what’s called a Gini coefficient. This is a measure of dispersion and is the ratio of the area between the red line (perfect equality) and the Lorenz curve, to the area between the black line and the line of perfect inequality.  The higher the Gini coefficient (0-1), the more unequal the distribution is. For international snooker the Gini coefficient is 0.88 indicating a high degree of inequality in prize money allocations in professional snooker.

By David Butler

The Pareto distribution is quite famous in Economics and is named after the Italian polymath Vilfredo Pareto (1848-1923). Mathematically,  the distribution is referred to as a power law probability distribution (see graph) and it is applicable to phenomena in both the natural and social sciences.

The distribution has its origins in the income data Pareto  published in 1897 when he explored how wealth across society was allocated. Pareto found that the income distribution was not a bell shaped curve. There was many people at the bottom end of the wealth distribution, a wide middle class and some super wealthy individuals. His distribution is usually explained through the 80-20 rule of thumb.  80% of the wealth is usually owned by 20% of the people. This is usually a good approximation.

A fun and accessible way to  learn about the Pareto (and Pareto-like) distribution is through sports data.

The graph below shows the PGA Tour Earnings for Golfers in 2015. Out of the 385 golfers on the tour Jordan Spieth has the highest earnings.  Like Spieth, there are a few very high earners but these are in the minority (e.g. Jason Day, Bubba Watson, Rickie Fowler, Dustin Johnson, Justin Rose and Rory McIlroy). There are some golfers earning a reasonable sum, the middle-class,  and then a glut of lower earners. The top 20% (77 Golfers) earned $218,010,501 together, that’s 68% of the total earnings. The remaining 80% (308) golfers divided the remaining $101,434,093 between them.

What about a different sport? The second graph shows the prize money earned by Irish National Hunt Jockey's (all race types) for the 2014-2015 season. While the earnings are far less than in golf, we still see a similar pattern. Ruby Walsh tops the list out of 152 jockeys. Bryan Cooper, Jonathon Burke,  Paul Townend and  Paul Carberry all perform very well too.  The top 20% (30) of the jockeys shared €18,785,125 between them. That’s 78% of the pie.  This left only €5,211,170 worth of earnings for the other 122 jockeys.

Of course, the more interesting question is why do such patterns emerge? The answer to this question has puzzled social scientists for years and is far too complex to address in detail here. To hazard a guess, these outcomes are not unicausal; no exclusive factor is probably causing the outcomes above. Albeit somewhat of a weasel word, the skewed distributions are often referred to as an ‘emergent property' of a system. Small, random differences at the start can amplify themselves and lead to significant differences down the road.

By David Butler

Last week the Southampton manager Ronald Koeman expressed his unhappiness with Martin O’Neill’s decision to use Shane Long in Ireland’s second leg play-off win against Bosnia.  Koeman was “very surprised he played 40 minutes. The player didn't train for five or six weeks, [and] had only one training session on the Sunday”.

Such instances are becoming increasingly common in modern football where a tension exists between parent clubs and home countries.  This outcome of the problem is often moral hazard. This is some form of after the fact opportunism; you take on an amount of risk while someone else pays the costs if things go wrong. For example, you may be more likely to drive your car dangerously or live an unhealthy lifestyle if you have car and life insurance respectively. 

While Ireland and Southampton have no formal contractual agreement, Southampton are paying the wages of Shane Long on a weekly basis and it is, of course, in their interest to have a fit performer for the entire Premier League season. Ireland however faced a crucial match where short term success was in their interest. Southampton gave advice to Martin O'Neill but ultimately Ronald Koeman had no decision making power – Ireland were deciding on how much risk to take on, Southampton were carrying the costs if things went badly!

Economists are often interested in designing contracts to ensure that efficient risk bearing occurs between two parties stuck in dilemmas like these. It will be interesting to see whether such mechanisms arrive in football in due course or whether a club will legally challenge an international association if their asset returns as damaged goods from international duty. Should clubs be compensated when an international manager decides to outsource the costs?

As a fan it was great to see Shane Long play for Ireland last week, as an economist I think some of the risk needs to be shifted to international associations.

The lowest position a champion has finished the following season in La Liga was 7th (Valencia 2004-2005) while Werder Bremen (1993-1994) and Wolfsburg (2009-2010) both finished 8th the year after being crowned champions. While approximately 80% of champions in the EPL have returned to win the league or finish runner up the the next season, this rate is lower for La Liga (60%)  and Bundesliga champions (50%).

Something has definitely gone wrong for Mr. Mourinho. In my view Chelsea's fall is a product of many factors coming together: underperforming or burned-out stars, the sale of key personalities in the summer,  aging defenders, transfer failures (not securing the signing of John Stones), fielding young talent that may not  be quite ready, public relation disasters with staff and injuries to key players (such as Costa and Courtois) have all contributed to the 'crisis' .  While the stats would indicate that the champions may well bounce back from 16th, could Chelsea manage to finish worse than 7th?

By David Butler

Over the last months I've reflected on the trade-off Jack Grealish has made by declaring to play international football for England. In short, I think he has weighed up the costs and benefits of a likely briefer, more lucrative career with England, that has the potential to offer more international success, against a longer but less financially beneficial career with Ireland. Sticking with the Boys in Green could have made him a cult hero, albeit for a nation which will likely be less successful in international competitions.

Although Grealish could not be called up to England's squad for the upcoming friendlies, (as he has to wait until the new year to be granted FIFA clearance) it struck me as interesting that Tottenham's Eric Dier, a player quite close to Grealish in age, made the squad for the first time. I asked myself , what age do English midfielders usually begin their senior international career?

Below is a table that shows members of the current England squad and recent call-ups who were capped. They are ordered by their age (excluding Eric Dier who is yet to be capped at a senior level) . The table also shows the age of each player when they made their senior international debut for England.

Alli, Sterling, Barkley, Oxlade-Chamberlain, Wilshere and Carrick will all have been capped at a younger age than Grealish at a senior international level for England. Although it sounds bizarre, at twenty years and one month Jack Grealish  would not be considered 'young' if he is capped by Roy Hodgson. Raheem Sterling is the same age as him and has already chalked up twenty senior international caps. Ross Barkley is one year older and has twenty-one appearances. The Arsenal men Alex Oxlade-Chamberlain and Jack Wilshere, two and three years older respectively, have collected over fifty caps between them.

Some English players are capped at a later age and go on to achieve a high number of caps.  James Milner started at twenty-three and now has over fifty caps, and Jordan Henderson began his international career at approximately the same time Grealish might. The Liverpool midfielder currently has twenty-two caps. These instances are rarer however and, expectedly, players that begin their international career later in life generally collect fewer caps.

Jack Grealish will have to develop significantly to compete with the current crop of English talent. He will probably have to leave Aston Villa - a clear trend is apparent in the clubs the players above are contracted to.  A fair amount of Grealish's competitors are younger and have more senior international experience than him already. What's more, the table above just looks at midfield players, many forwards players such as Theo Walcott can play multiple roles (debuted at seventeen years and two months as England's youngest ever senior international). Neither does the table consider players outside of recent squads that could potentially be recalled (Ashley Young, debuted at twenty-two years  and four months) or  the next wave of English talent. It  probably won't be long before the next batch of young lions such as Jordan Ibe (Liverpool - nineteen years old), Ruben Loftus-Cheek (Chelsea - nineteen years old) and Josh Onomah (Tottenham - eighteen years old) catch Roy Hodgson's eye.

By David Butler

On Wednesday 28th of October from 7pm-8pm in West Wing 5, University College Cork, Robbie Butler and myself gave a joint lecture for the UCC Economics Society entitled, The English Premier League; Media & Sponsorship.  The talk focussed on the football industry in England, how it is perceived by the media and how commercial aspects have evolved over the last 20 years. The talk was intended to be fun yet informative!

The slides from the lecture can be accessed below

By David Butler

Recently, I asked whether the  League of Ireland was the most complex football league in the world. The graphic in that entry provided a preview of work I’m conducting with Dr.Robbie Butler that analyses the changing incentive structures in the League of Ireland – here’s another one.  The chart below shows the average number of goals per game in the league from the 1971 to 2014.

The average number of goals per game  is on a downward trajectory over these years. In the League of Ireland, as in other football leagues worldwide, goals are becoming scarcer.

Since the 1993 season (where the lowest average number of goals per game is observed), the average has slightly increased. This coincided with a change in the competition design; 3 points, instead of 2, were awarded for a win. You could interpret this rule change as an incentive for teams to increase attacking play and the switch to a 3 point system may have stemmed the decrease somewhat.
 
If readers are interested in the idea of goals being under threat, I would encourage them to check out Anderson and Sally’s excellent book The Numbers Game.

By David Butler

Last week I came across an interesting story* that explained why Pelé tied his boots just before the start of a 1970 World Cup quarter final match against Peru. What seemed an innocent act by the Brazilian was actually a key juncture in the ‘sneaker wars’  that was on-going during the second half of the 20th century between sports wear firms Puma and Adidas. The narrative provides another nice example of how concepts from game theory can be applied to the sports industry.

As the story goes, the two shoe manufacturers went through a period of intense rivalry in the 1960’s.  Both firms vied for a greater market share on the back of growing demand for sneakers, and endorsing athletes became an important advertising tool for the firms. Financially savvy athletes soon wised up to this rivalry and began demanding increasingly significant sums to wear their products. In response to these rising demands, Adidas and Puma began to cooperate with each other, attempting to scale down what had become an arms race for the top sports stars.  The most notable form of cooperation at the time was the Pelé Pact; both Adidas and Puma agreed that neither would endorse the world’s greatest footballer for the upcoming 1970 World Cup.

Was the cooperative Pele Pact  stable? Well, when Pelé asked the referee for those extra few seconds before kick-off to lace his boots (isn’t it amazing how he decided to tie them just then?), the camera zoomed in to show him wearing a shiny new pair of Puma's.

Apparently, Puma sent a company representative to the Brazil squad and after some negotiations Pelé accepted a lucrative deal to wear the Puma’s. Adidas were naturally furious that Puma breached the Pelé Pact and the fierce rivalry between the two firms recommenced. If Adidas had known that the pure conditions necessary for cooperation were absent they may not have acted so naïvely. The rational Puma scooped the prize!

My first thoughts when I heard this was that it was an urban legend but with a little research it seems the story checks out.  For those that want to explore the sneaker wars between Adidas and Puma further, see Barbara Smit's 2009  book  Sneaker Wars: The Enemy Brothers Who Founded Adidas and Puma and the Family Feud That Forever Changed the Business of Sports.

*thanks to Sportseconomics.org contributor Gary Burns for introducing this story to me. 

By David Butler

The penalty shootout is a mechanism to decide tied matches in soccer. It was sanctioned by FIFA on the 27th of June 1970. While the idea of a penalty kick was an invention of the Irish, the first major international competition decided through the shootout was the 1976 European Championship final between Czechoslovakia and West Germany. The inaugural penalty shootout in the World Cup finals occurred in 1982 between West Germany and France.

There are many factors associated with the success of individual penalty kicks that are specific to each player. These include psychology (player anxiety, stress and coping levels), ability (particularly shooting ability) and chance. Empirical analyses that consider shooting strategies for players have shown that penalties shot towards the upper left-hand side of the goal represent the most difficult shots to stop (Bar-Eli & Azar, 2009).

Below is data on 97 penalty shootouts (1033 penalty kicks) for six major international competitions from 1976 to 2015.In total for every three penalties scored, one is missed.  Penalty takers in the European Championships have had the most success (discounting the small sample from the Confederations Cup).

Substitutes are precisely no better or worse at scoring penalty kicks than players that start a match. What’s more, no evidence exists to support the argument that introducing a substitute in extra-time leads to improved performance in penalty shootouts. Fresh legs don’t matter too much when it comes to penalties and the performance of kickers is really independent of the time they spend on the field.

For more on this issue it would be wise to start with two papers by Jordet et al in (2007) and (2009).