Cardiff Shoot Down Manchester City

The most memorable victory of Stoke's inaugural Premiership season took place on the last day of January 2009. A single goal home victory against a Manchester City side managed by Mark Hughes and yet to really flex their new found monetary muscle, may not appear as an obvious high point for a side that also took the bigger scalps of Spurs and Arsenal. But the manner of the 1-0 win epitomized a season.

Reduced to ten men after half an hour, when Delap saw red for first fouling Wright-Philips in full gaze of Martin Atkinson and then smacking the ball at the prostrate City player for good measure, Stoke scored the game's only goal just before the crowd adjourned for halftime pies. Manchester City's inability defend a high ball to the edge of the six yard box was all the encouragement James Beattie required and a raucous crowd, that spawned a myth, saw Stoke home for their first win in 11 long matches.

Judged from the sofa and from testimony from those I know who were there, the more opulent, current version of Manchester City, suffered a similar aerial mugging in a loud and proud stadium in Cardiff on Sunday afternoon.

Provocatively dressed in red, both for the City fans and also for a sizeable minority of their own supporters, the Bluebirds lifted themselves from an even bigger hole than the one faced by Stoke four and a half years ago. Dzeko's 52nd minute opener was cancelled out by Gunnarsson and then well and truly eclipsed by two headed Campbell goals from corners. Negredo's injury time consolation merely held back any early leavers intent on beating the traffic.

Cardiff's classic rearguard action, where territory was ceded, but bodies flooded the defensive third and pressure was relived towards the isolated attacking pace of Bellamy, was a familiar sight for Stoke fans used to Tony Pulis' preferred method of play. But having fallen behind, Cardiff had to go to another Potteries staple, namely the set piece.

Paradoxically, corners should be relatively easy to defend, but if a side can engineer or are allowed a free header from close range, the quality of the opportunity is often excellent.

                                      Cardiff's Attempts on the Manchester City Goal.

                                         Manchester City's Attempts on the Cardiff Goal.

City's possession dominance also gave them a 16-9 shot advantage, but what Cardiff lacked in quantity, they made up for in quality. Nearly half of their opportunities came inside the six yard box, compared to just one, off target injury time effort from Negredo for the visitors.

However, if we sum the goal likelihoods for each side's created chances, City edge back ahead with a expected goal supremacy that is nearly half a goal in front of Cardiff's. The expected situation becomes even less favourable for the hosts if we look closer at each shot.

Gunnarsson's equalising goal came about immediately following Campbell's saved effort from similar close range. It is to Cardiff's credit that they had players ready to react quicker than City's defenders, so they should potentially benefit from creating two such high quality chances inside the six yard box. But, although the caveat that an altered, preceding shooting outcome would inevitably alter the course of the game for any subsequent shot applies to any simulation, it is most keenly apt in the case of follow up efforts.

In short, Cardiff are entitled to score once from either Gunnarsson or Campbell's near simultaneous efforts, but not twice. Therefore, in any simulation, I've allowed that if Campbell scores with the initial shot, Gunnarsson can not repeat the feat a second later.

Simulated Match Outcomes Based on Quality and Quantity of Shots.

Team.	% of Sims Won.	% of Sims Lost.	% of Sims Drawn.
Cardiff City.	26.5	45.5	28
Manchester City.	45.5	26.5	28

Manchester City had a torrid time defending corners. Their poor play began simply by allowing Cardiff an opportunity, especially from such close range. But they also failed to exert any kind of defensive pressure on Campbell when he did evade his markers twice in ten minutes. Once those failures had kicked in, Campbell's likelihood of scoring probably eclipsed the generic, average conversion rates for headers inside the six yard box.

Nevertheless, on a straight reading of the chances created, Cardiff were still lucky winners on the day, despite their excellent, but likely unsustainable accuracy and conversion rates. They probably created enough late game chances to average a one goal return, but managed three and just a third of their shots probably should have required a save, rather that the two thirds in reality.

Manchester City would have won nearly half of the outcomes had they been decided by a repetitive shooting contest and in the reality of the day they failed to take advantage from actually taking a lead on Sunday from one of their least likely opportunities. 

A Cardiff win was the minority outcome from a shot based simulation, but Cardiff will take heart from  a performance that overall belied the expected pregame supremacy that most experts granted to their opponents. Manchester City had an estimated 67% chance of winning prior to the Cardiff City Stadium kicking off their home Premiership adventure.

Manchester City will wonder if defeat was merely down to a bedding in period for a change from zonal to man for man corner marking and will take scant comfort from a likely virtual victory in light of a real life, points costing, defeat.

Stoke 2 Crystal Palace 1. A Shot Analysis.

Crystal Palace's visit to the Britannia Stadium pitted together two of the favourites for a return to Championship football in time for the 2014/15 season. As one of the promoted sides, Palace's position is understandable, especially with the loss of Zaha to the champions, Manchester United and an elevation that came by way of the playoffs. Their chance of an immediate return is currently rated around the 70% mark.

The experts are less confident in the prospect of Stoke slipping back down the pyramid come May. In contrast with the pessimism surrounding Saturday's recent opponents, the Potters currently enjoy the considered consensus of a 75 to 80% chance of remaining in the top flight. That number still makes them fourth favourites to be one of the three relegated sides. A sign of the uncertainty surrounding a new manager in Mark Hughes, a seismic change in style and the competitiveness of the lower reaches of the Premiership, rather than an acknowledgement of Stoke as an established EPL team.

So the match on Saturday was an early season opportunity for potential strugglers at the lower end of the table to pick up valuable points, while guaranteeing none for their likely rivals. A nervous 90 minutes awaited both sets of fans, especially Stoke's, who as the home side were reasonably strong pregame favourites and had a manager whom, as a high profile pundit explained "hadn't won a Premiership game since January" (total sample size, one match, away at Anfield).

With the week's marque matchup taking place on Monday night at Old Trafford and the remainder of Saturday's Premiership entertainment providing less than riveting viewing, Stoke's 2-1, come from behind victory appeared second on Match of the Day. As is usual in such truncated highlights, most of the action featured the goals and various goal attempts from each side and initial impressions appear to show that Palace might consider themselves unlucky losers on the balance of attempts.

                                                 Stoke Attempts on the Palace Goal.

                                                 Palace Attempts on the Stoke Goal.

Both sides had 14 attempts on goal with each side requiring the other to make an intervention to a goal bound shot on 5 occasions. So was Stoke outscoring Palace by 2 to 1, not only an absurd use of ratios, but also a fortunate outcome for The Potters and would a share of the spoils been a more appropriate final outcome?

The use of shots and headers to determine the fairness of an actual result is rife with flaws and contradictions. A side tailors their attacking approach to the current game state and that usually means more goal attempts when that state is an unfavourable one. So shot numbers are a function of what actually happened and in which order, on the day. Also a different outcome for one attempt would inevitable lead in reality to later chances being stillborn and others being spawned.

Nevertheless, it  may still be a fruitful and illuminating task to assign each actual attempt a likelihood of it resulting in a score, once factors such as pitch position for the shot, if it was with the boot or the head and if, as was the case for Palace's goal, if it came via a counter attack (or aimless punt down field as it was know when the tactic was extensively used by Pulis' Stoke) are accounted for.


Most Likely Scorelines Given the Quality and Quantity of Palace and Stoke City's Goal Attempts.

Shot Generated Scoreline. (Stoke Score Appears First).	% Frequency.
1-0	25.2
0-0	16.2
2-0	15.5
1-1	11.7
2-1	7.3
0-1	6.7
3-0	6.2
3-1	2.7
1-2	2.1
0-2	1.4
2-2	1.3
4-0	1.3
4-1	0.6
3-2	0.5
1-3	0.3
5-0	0.1
2-3	0.1
4-2	0.1
5-1	0.1
0-3	0.1
3-3	0
5-2	0
0-4	0
4-3	0
2-4	0
6-0	0

* the more unlikely outcomes occurred with such infrequency that they fail to register to one decimal place.

Just over half of Stoke's attempts came inside the box compared to just less than half for their visitors. So initially, even with such a rudimentary classification of attempts, the home side grabs a slight advantage. Better still for Stoke three of their eight penalty area attempts came in an area bounded by two perpendicular lines drawn from each goal post and three others were only marginally outside this lethal shooting area. Once shots from inside the area move towards the lateral extremities of the box, the likelihood of a score begins to fall away. Palace didn't manage one shot from the more profitable central positions.

As a consequence, although numerically equal, Stoke's attempts had a much higher likelihood of a goal resulting from their efforts. The Potters' goal expectancy from their 14 attempts eclipsed that of Palace's 14 efforts by over eight tenths of a goal.

This goal expectancy supremacy, based on the quality of the attempts made by each side on the actual matchday begins to validate the actual one goal margin by which Stoke won the game. But we can go further by simulating the actual outcome of all 28 shots in thousands of possible iterations of Saturday's match. The excitement may be too much for committed Stoke ( @MarkTaylor0) and Palace ( @SimonGleave ) fans to bear!

Over ten thousand iterations, Stoke were by far the most likely winner, judged solely on the quality shot count. They "won" 60% of the simulations, drew 29% and only lost 11% of the time. The five most likely match outcomes all saw Stoke avoiding defeat and the game's actual scoreline was the fifth most likely simulation scoreline, occurring just over 7% of the time. City fans will hope the 25% chance of such a shootout finishing 1-0 doesn't herald a return to the dark, unappealing days of Stoke's binary past.

Overall, less than sparking entertainment, but a fair result in hindsight and three points for Stoke towards their customary 40 point target.

Identifying Penalty Taking Talent Is Hard.

In the previous post on penalty takers in the EPL, I looked at the conversion rates of kickers who were considered to be either the best or worst practitioners from the recent past. However, because of the relative scarcity of opportunities, it is not possible to say with the degree of certainty implied by newspaper headlines if a player is really as good or bad a penalty taker as his raw conversion rate appears to indicate.

Intuitively, you would probably prefer Frank Lampard to be stepping up to take a kick that is vital to your side's chances, rather than Jonathon Walters. But despite their apparently polar opposite conversion rates it is still possible that Lampard is a average taker who has been lucky and Walters is equally average, but has in addition been blessed with bad luck and a lack of colleagues willing to take on the kicking duties.

The intricacies of the problem of teasing random chance from skill in infrequently repeated tasked can possibly be appreciated by using a simulation. If we allow ourselves to know the true penalty taking abilities of a group of players with absolute certainty, we can then via a spreadsheet and random number generator ask them to take as many penalties as we wish to see how the true "Franks" perform against the true "Jonathons".

These trials will inevitably still be somewhat artificial, but we will know in advance which players are really the best and by the range of their actual outcomes we may be able to see how easy or difficult it is to spot that talent differential in typically generated conversion statistics.

I've taken 5 outstanding penalty takers, whom I've given a true conversion rate of 89% and 15 lesser takers each with a rate of 75.6% to maintain the typical EPL penalty conversion rate of 79%. A rand() function complicit with their true conversion rate is then used to simulate a series of penalty kicks and the results are analyzed to see, firstly, if there is evidence for the existence of a talent differential in the group as a whole and secondly, can we spot if the five best takers are noticeably better than the rest.

Penalties, unlike other shooting opportunities are rigorous in their repeatability. The distance is always 12 yards, no defenders can intervene until the shot is taken and the keeper also has to observe the same restrictions at every kick (and sometimes they even comply with those restrictions). By comparison to open play shots, where game state, and hence defensive pressure, shot position, keeper readiness and mode of execution to name but a few, can vary greatly. We almost have a laboratory experiment.

The first trial consists of each individual player taking 6 penalties. By looking at the spread of the conversion rates of the group as a whole in comparison to that expected from a group of twenty players, each of whom was a dead eye, average penalty converter, we can give an opinion as to if there is a skill differential within the group.

In around half of the trials there was good evidence that skill exists, the spread of successful conversion rates was greater than that expected from a group of kickers whom shared the same conversion rate. Similarly, the average rate for the best five takers once an appropriate amount of mean regression had been applied was above that of the inferior takers in most cases. So the evidence for a skill differential mostly originating from the better kickers outscoring their inferior colleagues appears apparent.

Shootout Between Five 89% and Fifteen 75.6% Penalty Takers.

Number of Shots Each per Trial.	Evidence of Skill Differential.	Did the Best 5 Have A Superior Conversion Rate
6	~50% of Trials.	Almost Always.
12	~80% of Trials.	Almost Always.
50	~90+% of Trials.	Always.

The trend continues as we increase the number of shots taken by each player. At 12 shots by each of the 20 players, we can find evidence for players having differing conversion talent in around 80% of the trials. However, we can still in some cases, erroneously conclude that the two different groups have near identical average conversion rates because the evidence for a skill differential arises from unusual random patterns appearing within those two distinct groups.

For example, in one particular trial the top two penalty converters in that trial both came from the lesser true talent group. They were followed by two from the best group, but the elite group, over a limited test involving 12 individual kicks also saw one of their number tie for 19th spot.

It is only when we get to 50 kicks, a whole career's worth for the most frequent of takers, that evidence of a talent differential occurs in over 90% of the trials and the elite five, as a group have sufficient opportunity to always beat the rest.

In reality, a true talent differential of 89% compared to 75.6% is likely to be an unrealistically large gap and even at these levels a single less talented kicker can still out convert some of his more talented colleagues on occasion, (even if the group always wins through, overall).

If we shrink the true conversion differential between the best five and the rest down to just one percentage point, even 50 trials only identifies possible evidence for the existence of that real gap between groups around 20% of the time and the frequency with which a lesser kicker can top the twenty also greatly increases.

What penalties gain in uniformity of execution they give up due to rarity, few teams or players get to take more than a handful per season. Penalty taking ability has almost certainly a tighter range than the one used in this contrived simulation, yet it was only possible to speculate that such a talent existed around half the time with these likely inflated differences in trials with typical seasonal numbers.

Prior knowledge of the true conversion rates that had been baked into the simulation, along with which kickers had been so blessed, was also needed to simply separate the two distinct groups. Moving to an individual player level at such low sample sizes in reality and with any degree of certainty would likely prove a near impossible task.

If we want to look at possible talent displayed in conversion rates, we need to look at much more frequent, open play goal attempts, for teams and then perhaps onto individual players. But we then have to look also at the factors that make such attempts a much less structured experiment than a set piece penalty kick.

Next post, maybe.