Where Have All The Strikers Gone.

Having written around 318 posts loosely based around the effects of random variation on sports data in general and football stats in particular, yesterday's post, which tentatively suggested that the lack of early season goals may have various causes in addition to the ubiquitous fluctuations of real time events, attracted the second most daily views in the life of this blog.

C'est la vie.

So as a rapid follow up, I will go through both the thought processes and methodology that went into posting yesterday's post.

Around November 2011, it suddenly dawned on everyone that the Premiership was seeing lots of goals. The big clubs were handing out the type of beatings to their own kind that they usually reserved for lesser teams. Manchester United put 8 past Arsenal, were then tonked 6-1 by City, who had already put 5 past Spurs, before Arsenal replied to Chesea's three with five of their own. And so it went on.

By the time 100 matches had been played, the average number of goals per game was very nearly three. To satisfy myself that we were seeing mostly random variation I simulated the 2011/12 season's first 100 matches to see how often you should expect to see 295 goals if the goal expectancy for each individual match was similar to recent historical levels for the 20 EPL sides.

Unfortunately, Liverpool's Ian Graham beat me to it and posted this when he was still at Decision Tech. Ian's a nice guy, so I'm sure he won't mind me using his post as an example of what I also did back in 2011 and latterly in 2013.

Having been beaten to the post in 2011, I repeated the process using the first 40 matches of the 2013/14 season, fully expecting the results to show that 74 (now 78 goals) in 39 (now 40) matches was likely to arrive about 20% of the time in a simulation using normal, for the current time, goal expectancy. There was a similar 17% chance that a "normal" group of EPL sides had produced 295 goals up to November 2011 purely through random variation and I fully expected to finally get to post my 2011 effort, two years late.

Instead I got a figure of 0.5%.

You are of course free to set the bar of "proof" as high or as low as you wish, but the 17% chance of 295 goals appearing in 100 EPL matches if we assume scoring is around historical levels, strongly implies short term fluctuation is the most likely, major cause. There is no need to speculate on why the art of defending is in decline or striking is in the ascendancy. The 0.5% figure for the first 40 matches of 2013/14 to produce 78 goals due to short term fluctuations of a typically higher recent goal expectation, however carries a much larger requirement for blind faith.

An alternative viewpoint may be that for various reasons, the current EPL over the course of the first 40 games has been played out by teams that may only be capable (or intend) to score less goals. If you simulate a 40 game run of matches where the average goal expectancy for each match is just below 2.5 goals, the chances of a total of 78 goals appearing jumps from 0.5% (using the historically higher goal expectancy) to around 10%. This figure is a much easier "sell"

The last four EPL seasons have averaged around 2.8 goals per game, prior to that and further back into the 90's, figures in the region of 2.5 over a whole season aren't uncommon. The French premier league regularly throws up total goal averages over a season that are even lower at around 2.3 goals per game. The opening group matches for the last five European Championships (conveniently totaling 40 games) has produced 2.25 goals per game compared to 2.78 goals per game for the final group matches. So lower average goal totals aren't unusual in top flight football and France.

So we may be seeing random variation (we always will), but around a lower expected goal scoring average. And that is where observation becomes as important as statistical analysis based around assumptions of what has passed for recent normality in the EPL.

It has been suggested that nothing short of a mass suicide of strikers could account for the expected goals total falling to 1.95 a game. But it need not fall to that level, it just has to fall compared to previous highs and then experience short term variation to arrive at a figure that sits to the left of the true average, but happens with enough frequency (say around 10%) to provide a believable explanation for real events.

Minutes Played out of a Possible Maximum of 3240 By the Major Scorers for Eight EPL Sides in 2013/14.

Team.	Player(s).	Goals scored in 2012/13.	Goals as a Percentage of Team Total.	Minutes Played in 2013/14.
Tottenham	Bale/Defoe	32	51%	37
Crystal Palace.	Murray.	30	41%	0
Liverpool.	Suarez.	23	34%	0
WBA (Loan).	Lukaku.	17	34%	40
Newcastle.	Ba.	13	30%	65
Norwich.	Holt.	8	20%	0
Manchester City.	Tevez.	11	17%	0
West Ham.	Carroll.	7	16%	0

All EPL goal scoring strikers are currently alive and well, but many are in new (non) Premiership surroundings or idle.

Bale is of course in Madrid and Defoe, with whom he combined to score over half of Spurs' goals in 2012/13 is an occasional late substitute. Palace's 30 goal striker, Glen Murray is still recuperating from an injury sustained in the playoff semi final. Holt is now in the Championship, Suarez is completing an anger management course, Lukaku is largely practicing penalties on Chelsea's training ground prior to his loan to Everton and Ba is similarly underused, Carroll is injured and Tevez has departed.

So we can chose between random, short term variation around a historically high goal expectation leading to a very rare run of scorelines or (and not necessarily the only alternative), short term random variation around a slightly lower goal expectation caused by the temporary or permanent unavailability of 141 goals worth of talent, but likely to occur much more frequently.

The general opinion is that levels at the end of the year will return to more normal totals, but that won't validate the opinion that everything was "normal" in August and September. The conditions of the trials (games) will inevitably be different also. Suarez can return in a week, Lukaku will be unleashed on defences by Everton as he was by WBA in 2012/13, Carroll and Murray will return from injury and Ba, another talented scorer with little appreciation at Chelsea, may even get to wear in anger that Stoke shirt he wore for his (failed) 2011 medical.

I'm a huge advocate of accounting for short term, random variation, but it shouldn't be used exclusively to solve every conundrum.