Predicting Penalties.

Nothing illustrates the seemingly random nature of penalty awards than the experience of Stoke over the last month when they have been awarded and have conceded precisely zero spot kicks, but could have possibly accumulated nearly half their recent average seasonal total in each category over that timescale.

The first non decision came early in the match against Fulham as Ireland was felled yards from goal by a clumsy Hangeland lunge from behind. More a penalty than not in my unbiased eyes, not so in the judgement of Roger East. An opinion backed up by the innumerate, self styled refereeing expert, Graham Poll, who cited Ireland's "theatrical" fall as justification for East turning down appeal. A clear case of artistic impression nullifying a 80% goal scoring chance.

Jonathan Walters was then allowed the benefit of the advantage rule to ride an Amorebieta foul outside the box, only to be fouled a second time inside the area. Having blown for the second foul, East then convened an NFL style brains trust meeting of officialdom before returning to the spot of the first offence.

Almost inevitably East then denied Fulham a clear spot kick, when Stoke's Marc Wilson took the easier option of kicking the opposing forward rather than the ball. Minutes later East blew for halftime, mentally plotting his route to London Road, Peterborough, the reward for his eccentric application of the game's laws.

Following the now obligatory complaint to the refereeing assessors, Stoke were rewarded for their unfortunate Craven Cottage experience with the appointment of World Cup final referee, Howard Webb for their following home match with WBA.

The Baggies have long been Stoke's punching bag and the Potters have amassed win after win over their near rivals. But on this occasion, WBA more than held their own, especially in one second half period when Youssouf Mulumbu powered into the box in a move reminiscent of Ireland's dart against Fulham. As with Hangeland, Mulumbu's pursuer, the fleet footed Charlie Adam chose to end the danger by raking his studs down the calf of the opponent.

Mulumbu's fall was much less theatrical than Ireland's, although the contact was comparable. Adam flung his arms wide in an expression that footballers take to signify innocence, but is interpreted by everyone else as a cast iron admission of guilt. In short, the incident passed every criteria for a penalty to be given, but in the October spirit of non application of the Laws, Webb awarded Stoke a goal kick instead.

Webb cannily apologized to WBA after the goalless match, citing being un-sighted as mitigation, hanging out to dry his nearside assistant, but avoiding a potential visit to the wilds of Huish Park, rather than the plusher surroundings of Stamford Bridge.

Four, cherry picked incidents, all of which would result in a penalty kick more often than not, but on these particular, actual occasions, none were awarded.

Penalties are extremely valuable events in a low scoring sport, such as football. Their very award has a longterm expectation of nearly eight tenths of a goal, it is then up to either the taker to drive the favourable probabilities to 1.0 or the keeper to redeem a flawed teammate. They are also fairly rare events, a team rarely manages to receive or concede double figure spot kicks and occasionally the penalty spot remains unused by a side over an entire 38 game season.

Incidents of award or non award are rarely as clear cut as the compromised decision making that has followed Stoke around during October, but the often used phrase of "that would have been a free kick anywhere else on the pitch" is not entirely without merit. An official, I would imagine is naturally reluctant to exert as much influence on a match result as a penalty award does unless he is confident of his decision. Making a decision that merely restarts play in a non dangerous area is far removed from making one that usually, directly and visibly, contributes to the final result.

Penalties, therefore have all the ingredients of being extremely difficult to predict. They are rare, contentious and important decisions. The forward correlation from one season to the next is very poor. Tottenham, complete with the game's biggest "flop" can go 38 EPL matches in 2012/13 without being awarded a penalty, but then make penalty goals a primary method of acquiring points in the following season, where six points have come directly from successfully converted kicks so far in 2013/14.

The causes for Spurs' barren spell in 2012/13 may (or may not) have been partly particular and unique to that season. The media perception of Gareth Bale as a diver is as simplistic and as lacking in nuance as is the current branding of him as a flop by Spain's finest. But the widely reported perception may have influenced refereeing decisions when he was apparently fouled inside the box during his last season at the Lane.

Similarly, in the more usual case of Stoke, if they continue to draw or commit reckless and clumsy challenges inside the box, their penalty ledger will start to see entries both on the credit and debit side of the book, although it may take longer than 38 matches to be seen in their raw penalty record.

In short, a single season is insufficient for luck, bias, incompetence, competence, excellence or play acting on an Olivier-like scale to even out and consequently the number of penalties awarded in year N is a very unreliable indicator of likely penalties next term.

Stoke and Spurs do their best to combine for a near penalty kick.

However, lack of correlation between outcomes across the seasons does not mean that there is no strong correlation, merely that the timescale and the rarity of the events prevents that correlation from showing itself. Broadly speaking, the better attacking teams get more penalties and they attain those levels mainly, but not exclusively by possessing the ball inside the box. All four of the cited incidents of non penalties in this post saw the man in possession getting kicked off the ball by a defending player.

Therefore, whenever an attacking player has the ball inside the box, there is potential for a spot kick should the defender be unkindly and the referee kindly disposed. These events are much more numerous than penalty kicks. The best sides touch the ball over a thousand times inside the box over a season compared to around 600 for the Premiership's perennial struggling teams. Any penalties awarded are likely to be a random draw from the individual interpretation of potential incidents that may occur where a side has possession in the box and a defender is trying to deprive them of the ball.

Creating opportunities to induce a lunge from an opponent in the box is therefore a much more common event than an actual penalty kick award. How often the attacking team cashes out that lottery ticket depends on the ebb and flow of a multitude of different factors over a single season ranging from the timing and venue of the event, to an official's desire for more diverse and interesting travel opportunities. But season on season the same type of sides "buy " more tickets by their repeatable level of possession of the ball inside the box. Even if their yearly penalty kick return doesn't always fully reflect their "outlay" in the short term.

In short, penalties don't correlate well over seasons, but the underlying cause of why they are awarded (using touches inside the box as a decent proxy) probably do. So if we want a guide as to how many penalties a side will get to take next season, looking at this season's final tally is not the best place to start. The relationship between touches inside the box and penalty kicks awarded provides an avenue to produce the expected number of spot kicks a side might have won, devoid of particular, situational and largely unrepeatable, random factors, such as minor aberrations from either player or official (also known as the reasons we avidly watch sport).

Data is now an even rarer resource than was previously the case with the enforced closure of many re-sellers, so this study is partly compromised by lack of numbers. But the 1000+ touches inside the box by Arsenal and Manchester United in 2011/12 implied expected penalty counts of around six each rather than the recorded respective totals of 3 and 11. In 2012/13 their respective totals were 6 and 7. Overall a penalty prediction based on expected figures from touches in the box gave better N+1 estimates than actual figures in around 75% of cases, although, quite naturally neither actual or expected penalty totals for Spurs in 2011/12 came close to predicting their duck egg in 2012/13.

Overall though, penalties represent another case where in looking to predict rare events, the more numerous cause or causes of the required outcome and the relationship between the two is almost always the best point of reference, rather than the actual event frequency itself.