Goal Expectancy Per Minute.

Top of most manager or fan's wishlist in the January window is a 15 goal a season striker. But what actually constitutes such a potential purchase?

In terms of goals scored, a penalty or free kick taking striker in a moderately successful side could easily reach half way to this benchmark from dead ball goals alone.

If they are also the intended target for other set piece plays, have bolstered their recent tallies with a couple of deflected chances (that are extremely difficult to save, but may not be repeatable in the long term) and benefited from the occasional goal keeping error, then the bulk of their recent record may be deceptive.

We therefore may chose to just look at goals that are scored from open play as a more revealing statistics, sieved of wrong footed keepers as well as the added advantage of regularly striking a dead ball.

However, this approach merely invites the other inherent uncertainty of random variation.

Expected goals models hope to illustrate how likely an average player is to score with a shot or header. Over or under performance against this cumulative expectation is often taken to be a sign of above or below average finishing talent, but is far more likely to be mostly down to simple variance within relatively small numbers of probabilistic events.

A fair coin exhibits no skill by falling heads up six times out of ten.

By looking at a player's expected goals from open play, we may eliminate the inbuilt advantage of being the chosen one for set pieces, as well a move to a probabilistic, rather than outcome based assessment. But we still need to adjust for time on the field.

Christian Benteke's 2012/13 season at Aston Villa was rewarded with nine actual goals from open play in 2820 minutes of playing time from chances that had a cumulative goal expectancy of 5.5 goals.

An impressive over performance,

He had required the keeper to save on target attempts that would yield an average player 0.00195 expected goals from open play per minute, but he was actually scoring at a rate of 0.0032 open play goals per minute.

His over performance in converting his attempts in 2012/13 placed him statistically alongside potential superstars, such as Bale, solid Premier League performers, such as Walcott and Cazorla and someone called Michu.

However, it is a simple exercise to simulate the likelihood that an average finisher scores at least nine goals from the chances Benteke put on target in 2012/13 (it's around 8%). So it was eminently possible that his actual over performance in converting chances was simply due to good luck.

Benteke laments the influence of random variation on his actual goal tally.

Anyone who might have considered Benteke as an acquisition capable of 15 goals a season (or perhaps 9 open play goals) may have waited until the 2013/14 January window to pounce, rather than pay an inflate fee for a player who may have visibly, if misleadingly demonstrated his potential.

Up to January 1st of the following season, Benteke had fared less well in open play. Scoring just once in 1145 minutes of play (0.0009 actual goals per minute) compared to a goal expectancy of 1.8 or 0.0016 expected goals per minute.

This time he under performed rather than over performed against his goal expectation based on where and how he took his shots.

But again it may have just been a less extreme dose of random variation. It was a 47% chance that an average finisher would score one or zero goals from Benteke's on target attempts in the first half of 2013/14.

Benteke's open play goal expectation per minute is relatively consistent from 2012/13 to 2013/14, more so than his actual goals per minute. And the latter could reasonably have occurred as a random draw from the former.

This correlation for goal expectation per minute from open play is also stronger across seasons for attacking players as a group than is their actual scoring rate per minute.

Improvements in estimating a player's goal expectation is relatively easy, if data hungry.

Allowances for goal scoring environment which particularly impacts frequent substitutes and allowing for ageing (goal expectation appears to follow the typical ageing curve with a peak in a players late 20's).

Rather than looking at a players actual scoring record, which has less connection with his future scoring feats, it may be wiser to look at his goal expectation per minute in his more recent seasons.

And what fans really want as a late Christmas present might just be a 0.005 goal expectancy per minute striker, preferably in his early to mid 20's.