What Match Fixing Tells Us About Luck And Skill In Football.

How you identify and separate the contribution of luck from the component of skill in football has been a recurring theme on this blog and so it was refreshing to see the issue addressed during some of the discussion groups at Sloan earlier this month. The impact of luck on both player and team performance metrics influences how these metrics correlate across seasons and has implications if we then use these measurements in a predictive way. Modelling luck instead of likely skill can inflate the worth of the "good" but temporarily lucky at the expense of equally good, but latterly unfortunate. Recognizing that luck exists in a sporting environment, where cause and effect makes for a more appealing and satisfactory narrative, is half the battle.

Luck in the most rawest of forms was on show on Tuesday night, when Nani's dismissal for a waist high challenge after an hour not only reset the game probabilities to near pre kick off levels, but also split the opinions of Twitter users and former professional referees alike. Of the latter group, some thought the decision harsh and others sided with the call that was made on the night. Similar incidents have resulted in widely different outcomes for the perpetrator. De Jong's assault on Xabi Alonso in a World Cup final saw Howard Webb produce a yellow and last weekend, Peter Crouch's unintentional, full bloodied kick to the head of West Ham's Matthew Taylor merely saw the Hammer being led unsteadily to the dressing room and no further action being taken.

In each incident a whole raft of minor incidents ranging from the reaction of the players, the importance or otherwise of the match, to the the mood and viewpoint of the official, combined to produce three entirely different conclusions to, by the letter of the law, three near identical events. Holland and Stoke possibly got lucky, although both ultimately lost the game, with Stoke fortunate to remain with 11 players, only to be beaten by a goal from Taylor's enforced replacement, Jack Collison.

More often randomness in the process is harder to spot, a ball that could have beaten the last defender instead fails through a slight lack of zip on the pass or a goalscorer distributing his talent to produce consolation rather than match meaningful strikes. Single incidents such as these, if we are lucky enough to spot them, can influence the outcome of individual matches, but over a season the signal shines through enough for Manchester United to finish near to the top of the league and West Ham or Stoke to finish slightly above 18th spot. The good or bad random content, that was so keenly felt at the time in a single match is often forgotten because a team usually finishes close to where their talent levels decree they should. Although the bitter taste lingers longer in knockout football.

Which finally brings us to match fixing. Teams or individuals have little control over luck or Nani would have chosen to get sent off in the last minute rather than the 58th and Peter Crouch would have poleaxed a defender instead of an attacking midfielder with an able and talented young replacement on the bench.

In games of pure chance an individual has no control over the result. You cannot "fix" a fair coin toss by paying off the person tossing the coin because they have no (or very little) way of influencing the outcome in either the short or longterm.

But football is different, Nani was unlucky in the current environment where "intent" is tacitly acknowledged by many officials, even if it isn't written into the rule book. So reluctantly, he has become the standard bearer for random misfortune. Skill, however has a choice. A player can do his utmost to find the top left hand corner with a shot or if he wishes, harness his skill to deliberately hook the ball wide and the current Europol list of allegedly fixed games implies that some do.

The revelation that both skill and luck coexist in football shouldn't need constantly restating, but much of the current analysis ignores the latter entirely. If Nani's dismissal helps to reinforce an acceptance that some some events are beyond the control of the participants, then his sacrifice won't have been in vain.

Newcastle's 2011/12 "Lucky" Season.

There's little doubt that Newcastle's 2011/12 season was a huge success for both the players and management. They finished five points and one place shy of the fourth place that in any typical year would have guaranteed Champions League football at the historic Sports Direct Arena. Their success was built on an impressive strike force of Cisse and Ba and a tactical approach that largely shunned possession, while remaining pleasing on the eye.

It's therefore understandable that many should take issue when their lofty finishing position is attributed to luck. Much of the debate revolves around a confusion of terminology. Luck implies a reward reaped by someone, whether deserving or not, through events that they have no ability to influence and that doesn't really seem to apply wholly to the results of a series of football matches. Cisse's wonder goal against Chelsea at the tailend of last season certainly appeared to have a component of luck about it, but there was no doubting the skill involved in striking a ball with such venom and swerve, while also avoiding a severe dislocation of the right knee.

So how should we define luck in sporting contests ? Again a coin analogy is the best starting point. A fair coin has the talent to land on heads 50% of the time, but that doesn't mean that in every 4 tosses, two win be heads and two tails. The rate at which a coin displays it's "talent" only becomes apparent after a much larger number of trials and the proportions of heads begin to trend towards 50%. The distribution of successful tosses in much smaller runs will jump about alot, sometimes hitting lots of heads, giving the appearance of being in form and sometimes not. That's all part of the random nature of events.

The same randomness that prevents a coin from continually alternating between a head and a tail is also present during a football match. It pays to have the best talent available to you, but if your star striker lines up a last minute spot kick where history tells you he converts such chances at a rate of 78%, he cannot guarantee you a goal. His success rate would have to be a bona fide 100% for that to be the case.

If penalties are to be missed you would prefer them to be missed 86 minutes into a 6-0 romp, rather than in the last seconds of a stalemate, but the random component of a skill means that you are largely powerless to ensure that the best case scenario always happens. Being skillful is plainly good, but being skillful and have random manifestations of that skill fall in a fortuitous pattern, (as may have happened at Newcastle) is an extremely potent mix.

One way to look at how "randomly blessed" Newcastle were in 2011/12 is to look at the high and low points from each game during the season. Games states are constantly changing, usually only slightly by dint of time elapsing and sometimes dramatically through goals or red cards and at any point in a match a team will have an associated points expectation derived from their likelihood of winning or drawing the game. By looking at these highs and lows we can better see what the average seasonal up and downside was for a side. One of the biggest swings against Newcastle came at home to Wolves. Leading 2-0 going into the 50th minute, the home team would average 2.95 points from that position, but at full time their points expectation had collapsed to 1.

Newcastle's High & Low Points During Each 2011/12 Game.

Opponent.	Highest Points Expectation	Lowest Points Expectation.
Arsenal.	1.07	1
@Sunderland.	3	1.09
Fulham.	3	1.92
@QPR.	1.23	1
@Aston Villa.	1.06	0.30
Blackburn.	3	2.24
@Wolves.	3	1.25
Tottenham.	1.25	0.18
Wigan.	3	1.45
@Stoke.	3	1.02
Everton.	3	1.60
@Man City.	0.61	0
@ Man Utd.	1	0.13
Chelsea.	1.11	0
@Norwich.	1.29	0
Swansea.	1.90	1
WBA.	1.72	0
@Bolton.	3	1.25
@Liverpool.	1.56	0
Man Utd.	3	0.83
QPR.	3	1.79
@Fulham.	2.11	0
@Blackburn.	3	1.36
Aston Villa.	3	1.43
@Tottenham.	0.54	0
Wolves.	2.95	1
Sunderland.	1.65	0.15
@Arsenal.	1.39	0
Norwich.	3	1.81
@WBA.	3	1.21
Liverpool.	3	1.23
@Swansea.	3	1.23
Bolton.	3	1.59
Stoke.	3	1.88
@Wigan.	1.41	0
@Chelsea.	3	0.63
Man City.	0.95	0
@Everton	1.16	0
Actual Points Total.	Best Case Average.	Worst Case Average.
65	83	31.5

The first point to make is that these game states are purely theoretical. You can't take 1.16 points from a single game against Everton. But if you replayed enough scenarios from that particular game state, then your average points haul would be around 1.16 points. So by summing the various game states to get a best and worst case points total we have combined both real and theoretical points totals. It is a useful device to get an average indication for what might have occurred had the cards fallen more or less kindly for Newcastle last term.

If everything had gone right last year, Newcastle could have probably secured Champions League football with an average of 83 points. Their actual points haul in each "lucky" season would be centred around 83 points, even  including the slimmest of slim possibilities that they may have won all 38 games.

Of much more relevance to the 2012/13 Magpies is the range between last year's best and worst case scenarios. The mid point is 57 points compared to their actual total in 2011/12 of 64. Might the 57 points be a better indication of what Newcastle "should" have got during last season's campaign and might that be a better indication of what a luck neutral Toon side may achieve this term ?

We can repeat the process for Chelsea, the team who finished just behind Newcastle, but are legitimate title contenders and top four constants, as well as being the current holders of the Champions League trophy.

Chelsea's Best & Worst Case Averages for 2011/12.

Actual Points For Chelsea.	Best Case Points Average.	Worst Case Points Average.
64	93	45

Chelsea's best and worst case averages are over 10 points above Newcastle's respective totals, despite the London side gaining one less actual point than Newcastle and their midpoint is 69 points. So despite finishing line abreast with Newcastle, "in game" situations may indicate that bad luck, much of it self inflicted may have prevented Chelsea from gaining a more representative 69 points. 

Perhaps tellingly,current points projections for 2012/13 have Chelsea ending the campaign with 74 points and Newcastle with just 54, numbers that are closer to their expected midpoints from last year than their actual figures recorded in May.

Every team experiences random variation from their true ability over a short 38 game season and a team which finishes just outside the top four and isn't part of the EPL's major six sides has very likely benefited from some good fortune combined with excellent play. 

Further supporting evidence is present in the records of teams who finish just out of the top four positions. Over Premiership history, the average goal difference for sides finishing 5th to 8th who aren't one of Man Utd, Man City, Chelsea, Arsenal, Liverpool or Spurs is plus 7. The average points total is just over 58 and the average finishing position is 6.6. In the following season, average goal difference drops to minus 3, points total is 50 and finishing position is 11th. Four such teams were actually relegated and 75% of them recorded lower final points totals. So the overwhelming evidence is for a return to earth following an over achieving season previously.

If Newcastle of 2012/13 manage to breach even the 50 point barrier, they will have bucked a very strong trend.

  

Spotting Genius is Easy, But what about The Rest.

Nearly forty years on and it is still a vivid memory. The Blue shirted Swedish defender appears to be in control of the situation. Notwithstanding the instant control, the attacker seems to have few options, he's got the ball wide on his team's left flank, about ten yards from his opponents goalline, but he's facing back down the touchline towards his own half of the pitch. His only real choice is to lay the ball back to a supporting colleague or at best lift a hopeful inswinging cross with his right foot into the congested area. And for a split second he seems to have chosen the latter. The defender sticks out a half hearted left leg to block the expected response. He's induced the cross from the attacker and from that angle and with no real intended target it's almost certain to be cleared or claimed by his keeper.

But then it happens. Instead of the cross, the attacker deftly caresses the ball back through his own legs with his right instep. Instantly he pivots on his standing, left leg and sprints after his own pass towards the now undefended byeline, showing only his black number 14 on his Orange shirt and a blur of attacking intent to his bemused marker.

Ladies and gentlemen, the Cruyff Turn.

Genius.

A moment of supreme skill as well as theatre and recognisable as such to anyone who saw it. Unfortunately, it's not always as easy to separate the skill from the mere mundane in football as the talent shows itself in minute improvements in efficiency of passing, quickness of brain or variation in power or placement.

Increasingly analysis is turning to rate statistics to attempt the classify a pecking order for talent based footballing actions. Every transfer target now comes with his numbers attached, shot conversion rate, cross conversion rate, pass conversion rate, the list goes on. So it's vitally important that we have some level of confidence in these type of figures.

How, why and even if the quoted statistics are causatively correlated to match outcome would appear to be the most obvious course of the initial investigation and that should be followed by how much strength we should attach to players who have recorded impressive or not so impressive records from limited sample sizes. However, there is one stage we need to evaluate before these processes are even applied to the raw numbers.

The most fundamental question that is rarely asked is "Is the factor we are measuring even a skill"? or are we simply seeing random fluctuations in performance rates that are entirely down to chance. Once we have confirmed our intuition and found evidence that we are indeed looking at a skill, we next need to know how much of a skill it is. Only then can we start to begin to know how many observations we need to make of a group of players before that skill begins to shine through.

Solving the "is it a skill and how much of a skill is it" ? problem would seem straightforward. The natural starting point is the player's raw conversion rate. So imagine you've identified an attribute that you've seen on a pitch and you want to purchase a player who displays that attribute. I don't want to confuse things by picking an obscure skill that may or may not be almost entirely luck based, so we'll just call it "The Attribute".

The success rate at completing our particular attribute in a group of similar players averages exactly 10%. Let's imagine you've got a list of 50 prospective purchases and their success rate over their last 100 occasions of attempting to perform your team's desired footballing task. Below I've listed the top 5 and bottom 5 performers.

How many Success Were Recorded by Player's Performing "The Attribute".

Player.	Number of Successes in 100 Attempts.	Success Rate.	Price ?
1st Ranked.	17	17%
2nd Ranked.	16	16%
3rd Ranked.	16	16%
4th Ranked.	15	15%
5th Ranked.	15	15%
46th Ranked.	6	6%
47th Ranked.	6	6%
48th Ranked.	5	5%
49th Ranked.	5	5%
50th Ranked.	3	3%

So who do you buy? If you're Manchester City or Chelsea and money is no problem, you buy one of the top five, probably driving up the price to unrealistically high level. If you're Stoke you pick up number 48 on a free transfer, possibly with a history of off field problems.

The catch is that the group from which the above table is just a part, was actually generated randomly. I set the success rate to 10% and over 100 different observations for 50 different players, this is the range of outcomes that appear solely through chance. If you broke the bank to buy the top ranked player, then you're out of luck because he doesn't have any skill when it comes to excelling at the attribute, because no one has. The table makes it appear that skill is involved because that is the kind of distribution of successes and failures that people expect to see if skill is a factor. Player 1's 17 successes came about entirely by chance, as did Player 50's mere three successes.

Fortunately, it's possible to take a mathematical look at the spread of the distribution of successes and failures for a group of players and be able to tell if it has likely arisen through chance alone or if it has been skewed by external factors that could be attributed to a varying level of skills within the group. Applying these methods to the tabulated numbers above confirms that I generated the distribution randomly.

However, if I use the same methods to look at such attributes as a players ability to create chances that are converted in open play, you find that the distribution of converted chances that are turned into goals doesn't resemble a random distribution. Another factor, such as a combination of skills spread between the provider and the scorer is present. If we further look at the ability of players to provide clear cut chances for their team mates, we find that not only does that appear to be a talent, but it is a much rarer talent than any other that I have currently looked at.

This was intended as an excuse to post a photo of my Cruyff shirt and discuss chance creation. Instead it's turned into a post on the steps needed to validate, analyse and produce reliable and credible static player rate statistics that are beginning to flood the blogosphere. Knowing the spread of talent within a group of players is vital to giving you an idea about the reliability of your conclusions over a limited number of observations. In short, you need to know if you're likely buying a lucky or a talented player and how much of your desired skill  is down to player talent.

I'll deal with chance creation later, but at least I kept in the Cruyff reference.