Conventional Tennis Strategy Wins Out.

Aside from partnering John McEnroe to seven Grand Slam doubles titles, Peter Fleming was also noted for his uncompromising second serve in which accuracy was sacrificed for power. Although the tactic of using power on both first and second serves is open to anyone, it is seldom used apart from as an occasional surprise, or desperation tactic. The payoff between a reduced second serve success rate and an increased chance of winning the subsequent rally because of the greater power of the initial shot of that rally has yet to be tested in top class competition.

The changed aesthetics of the game that would result from a likely shorter, serve volley spectacle, especially on the faster grass courts of Wimbledon would probably not be welcomed by spectators, but we can use maths to see how close the current game has come to make the adoption of such a tactic potentially profitable.

To calculate the likelihood of winning a point under the two different serving scenarios, the traditional fast serve followed by a slower one and one using two full bloodied "first" serves, we need to know four things.
These are;

The Probability of a Fast Serve not being a Fault, (F(nf)).
The Probability of a Slower Serve not being a Fault, (S(nf)).
The Probability of winning the point following a successful Fast Serve, (F(wp))
The Probability of winning the point following a successful Slower Serve, (S(wp)).

These probabilities are easily pulled for the top players from the various tennis stats websites. For F(nf) the top ranked players hit around 64%, S(nf) is in the region of 90% and F(wp) and S(wp) are 75% and 56% respectively.

Now we need to map out the two routes for each scenario that lead to a player winning a point. For the traditional fast/slow routine she can serve a successful fast serve (with probability of 0.64) and win the subsequent point (with probability of 0.75). The probability of this occurring is 0.48

In addition she can serve a first serve fault (with probability (1-0.64)) followed by a successful slower second serve (with probability of 0.9) and then win that subsequent point (with a probability of 0.56). Overall, a probability of 0.18 for this route to a winning point for a combined likelihood for both routes of 0.66.

The adventurous use of two fast serves follows the same sequence as above except that the slower second serve is replaced by a fast, conventional first serve (with probability of 0.64) and an enhanced probability of winning the point of 0.75 instead of just 0.56. Overall this commitment to speed and brevity gives the generic, top class player a point winning probability of a marginally inferior 0.65.

Wimbledon can look forward to longish rallies for the moment.

Therefore, by happy accident rather than design the current court dimensions and tennis equipment leads to the conventional, more rally friendly serving strategy having a small, but cumulative and often repeated advantage over a power orientated alternative. Federer's dominance may be declining, but longer, second serve induced rallies, especially in the men's game and on the faster courts are still hanging on in there.

I've added some player specific figures from 2013 here.

Efficiency Stats and Team Talent .

It is relatively easy to obtain quite detailed team or individual statistics for most of the major European leagues, most notably the Premiership. Sources and interpretations do vary, therefore it is important that consistency of source is ensured before conclusions are made. The new data is at it's most useful when presented in the form of efficiency figures. The margins within the Premiership are often extremely tight and a team that can perform a task a couple of percentage points better than their rivals may have a decisive edge in fulfilling their aims.

Team style and tactics of course vary greatly between teams in the same division and so looking at how effective side A is when hitting the target with their goal attempts compared to team B is likely to be because of a clash of styles rather than a raw talent differential. Side A may merely engineer shooting or heading opportunities from closer to the goal or in markedly different proportions to side B. Therefore if we look at such figures across all teams, inevitably a difference will be apparent, but often the resolution will require detailed knowledge of the approach favoured by each side.

A much simpler method is to look at efficiency stats, such as the ability of one single side to hit the target, spread over multiple seasons to see if there is a significant, attributable change in this rate over time.

The rate at which a side performs tasks such as getting their shots to hit the desired target will of course fluctuate over multiple seasons through random variation, even if there is no change in the side's inherent talent levels. However, if the seasonal rates change to a larger extent than should be expected due to simply chance fluctuations we can begin to suspect that something or someone within the side has engineered this change. Looking for possibly significant changes in a largely stable team format over a limited number of seasons, should be possible.

I've used simple "success/fail" shooting data for the twelve ever present Premiership teams over the last five seasons, so the teams involved are as follows. Manchester City, United, Everton, Liverpool, Spurs, Arsenal, Chelsea, Wigan, Sunderland, Fulham, Villa and Stoke. All data looks at each side from an attacking perspective, because, unfortunately defensive shooting numbers are much less easy to come by or collect.

Attempts On Target.

Half of the sides appeared to show seasonal fluctuations that weren't wholly consistent with the usual random fluctuation in their ability to find the target with all of their goal attempts given their average success rate over the five seasons. The biggest likelihood that we are seeing a real effect came at Manchester United, where the change in accuracy was accompanied by a near relentless improvement from a likely true accuracy of just under 32% in 2008/09 to 37% in 2012/13. The first major improvement came in 2010/11, this was repeated in 2011/12 and consolidated at peak levels in 2012/13.

Sunderland appeared to show the next highest levels of fluctuation, recording five year highs in 2009/10 of 34.5%, but immediately following  up with lows of 28% the next season. Fulham showed and maintained distinct improvement in shooting accuracy from the start of 2011/12.

Teams Showing Change. (Most Likely to Least)	Season High Accuracy Rate.	Season Low Accuracy Rate.
Manchester United.	37.0% in 2012/13.	32.4% in 2009/10.
Sunderland.	34.6% in 2009/10.	28.6% in 2010/11.
Fulham.	35.2% in 2011/12.	30.2% in 2008/09.
Wigan.	32.9% in 2012/13.	29.1% in 2008/09.
Liverpool.	33.2% in 2010/11.	30.4% in 2009/10.
Spurs.	33.7% in 2012/13.	31.7% in 2010/11.

All of the remaining six sides exhibited shooting accuracy figures over the five seasons that did vary, but not by enough for random chance alone to be ruled out as the sole cause.

Converting On Target Attempts.

If we now move on to conversion rates for on target shots, remembering that we are not looking for the most or least efficient teams, but for a side that has shown greater than expected efficiency fluctuations over a five year period and it may be possible to attempt to isolate some of the potential causes for the observed change.

Only three teams showed sufficient variation to raise suspicion that on field actions or a different squad make up had lead to real, repeatable and controllable change over seasons and they were Liverpool, Chelsea and Manchester City. The best evidence from the raw conversion figures came at Anfield, but there was similarly strong output from the other two sides. The most significant conclusion, here is that the vast majority of sides failed to demonstrate an ability to increase or a failing to decrease their goal expectancy from the shots they did manage to get on target.

Teams Showing Change. (Most Likely to Least)	Season High Conversion Rate.	Season Low Conversion Rate.
Liverpool.	31.5% in 2008/09.	22.3% in 2011/12.
Manchester City.	35.3% in 2011/12.	29.6% in 2012/13.
Chelsea.	33.0% in 2009/10.	27.6% in 2008/09.

Having Attempts Blocked.

In the previous two categories higher percentage rates are desirable, but it is more ambiguous here. Seeing a shot blocked tends to be bad news overall, although if your opponent chooses to block a shot that is going wide at least the ball remains in play and available to all. The likelihood of an effort being blocked is often a function of shot type, shot distance and therefore, also game state. So there are more likely to be causes that may not be directly attributable to mere team approach in this case.

Seven of the sides appeared to be able to alter their opponents blocking ability outside of random variation over the five year period. Again there were no borderline cases, so in these seven cases the fluctuations may  have a cause if you are prepared to look hard enough. In the table below, again remember that a high rate of blocking is probably a bad thing for the team trying to score.

Teams Showing Change. (Most Likely to Least)	Season High Attempt Blocked Rate.	Season Low Attempt Blocked Rate.
Liverpool.	28.1% in 2009/10 and 2012/13.	22.8% in 2008/09.
Chelsea.	28.6% in 2008/09.	24.1% in 2011/12.
Manchester United.	29.7% in 2008/09.	23.5% in 2012/13.
Everton.	29.8% in 2010/11.	23.2% in 2008/09.
Manchester City.	29.2% in 2010/11.	24.1% in 2008/09.
Aston Villa.	27.0% in 2012/13.	23.1% in 2008/09.
Arsenal.	27.8% in 2012/13.	24.6% in 2010/11.

Converting Clear Cut Chances.

Villa took good advantage of clear chances in 2012/13, although this one got away.

We are down to just three years of completed seasonal data in this final category. However, the more restricted definition of a clear cut opportunity may make the smaller sample size similarly valuable because of the more consistent repeatability of each goalscoring "trial". There is very strong evidence that Manchester City's ability to convert so called clear chances has changed even over three season, along with much less convincing clues for Sunderland and Villa, with Arsenal and Liverpool sandwiched in between.

Teams Showing Change. (Most Likely to Least)	Season High Clear Chance Conversion Rate.	Season Low Clear Chance Conversion Rate.
Manchester City.	42.0% in 2011/12.	30.0% in 2012/13.
Liverpool.	42.3% in 2010/11.	31.5% in 2011/12.
Arsenal.	39.6% in 2012/13.	31.3% in 2010/11.
Aston Villa.	38.9% in 2012/13.	31.5% in 2010/11.
Sunderland.	35.9% in 2012/13.	29.5% in 2011/12.

This post is as much about the sides that don't appear in any of the above tables as it is about those that do. Stoke's shooting accuracy ranged from 25% in 2011/12 to 29.5% the previous year, but given their league low shooting attempts, combined with data from the other three seasons, those figures are perfectly consistent with being a product of their average rate over the five season period of 28%. You may be embarking upon a fool's errand if you try too hard to rationalize the drop from the Potters from 2010/11 to 2011/12.

This post has been about where and when to look and where not to look for substantial change in teams and it also highlights that an apparent drop in efficient output may be simply down to random chance with little change in team ability. A side my appear to falter in a recorded stat, but underlying talent remains if it is given more time to show itself.

The Difficulty of the Double Save.

Just after the turning of the new millennium, Stoke found themselves striving to escape from the third tier of English football, preferably by way of promotion. Therefore, visits from the likes of Liverpool required pre-season largess or a favourable cup draw and both occasions transpired in the 2000-01 season. Of the two games, the November meeting at the Britannia stadium in the League cup proved to be the most memorable. Unfortunately, for all the wrong reasons from the Stoke City viewpoint.

An 8-0 defeat was scant reward for a Stoke team that had struck the visitor's post after barely a minute and such was Liverpool's displeasure at a narrow pre-season defeat, that the Merseysiders were still pouring forward with the game well won. There is no mercy rule in football, so an inept Stoke offside trap ensured more goals and Stoke's misery was further compounded when a confused City scoreboard operator awarded the Premiership team an extra ninth goal for effort.

It is perhaps a measure of Liverpool's fall from the top table that, along with Arsenal from the elite, that they have found Stoke a much tougher nut to crack in the Potters' Premiership career. Anfield wins have been relatively rare and outside of the League cup, Liverpool have yet to redress any of Stoke's three home wins with an away victory of their own. Stoke Liverpool matches have followed the now discarded Pulis blueprint to the extreme. Little Stoke possession, almost always outshot, defence to the fore, but seldom defeated.

City's 1-0 win at the Britannia in 2011-12 was typical fare. Stoke led when referee Clattenburg decided that Jamie Carragher rather than gravity had sent John Walters to ground in the penalty area and then the home side survived a shot differential of nearly 20-2 to claim three points.

One particularly noteworthy shot sequence occurred after 61 minutes. Stoke were caught exposed by an Enrique long ball, leaving Henderson a free run at Begovic in the home goal. Three shots, two saves and a Shawcross block later, the ball broke to Adam. Two shots, one block and another save later and Stoke were spared the consequences of their uncharacteristic attacking ambition.

The Reds had used up a quarter of their shots in barely ten seconds of continuous play and to the two sets of watching fans the sequence of play had been either hugely frustrating or nerve wracking, roughly in equal measure.

The shot sequence invites many questions surrounding the use of goal attempts when analysing games and matches, but the most obvious revolves around the increased difficulty faced by keepers as they attempt to keep out secondary efforts. Certainly the ovation that Begovic and Shawcross received following their efforts demonstrated that the Stoke fans recognized a magnificent feat of defensive football.

Intuitively, a keeper should be best prepared to face an initial shot, but less so if another attempt rapidly follows on. A keeper would appear to have limited control over where he palms away a shot (or he would never provide an opposing forward with a follow up opportunity), so he is likely to be away from his ideal saving position and often recovering from having to go to ground when attempting to counter a rapidfire , second attempt.

To test the theory I used the familiar shot location model to compared the actual outcome of goal attempts, whilst including a term to signify if the shot was an initial attempt or followed on almost immediately from a save by the keeper.

Once again the added factor does appear to significantly alter the likelihood of success. In my dataset comprising 1,000's of normal shots and 100's of rebounded efforts, if the keeper has been involved in the previous save, the striker has around a 30% greater chance of scoring from the rebound compared to an identical "normal" attempt. This figure may not hold in larger samples, but an advantage seems likely to persist.

Secondly, it would appear that the wholehearted involvement of the goalkeeper is required to elevate the conversion probability of the second chance. Rebounded efforts that result from a defender blocking the initial chance don't show a statistical difference from normal, first shots. A blocking defender appears to allow the keeper much more time to set and prepare himself for any follow up shot.

So this, potentially adds another layer of complexity to a location based shot model. It also adds to the ability to more accurately evaluate a keeper. For example a keeper who benefits from a defence that is adept at clearing or blocking the secondary opportunities that he provides for the opposing strikers may not be similarly lucky with his defensive colleagues should he change clubs. We may also be able to better appreciate a striker's skill (if it exists) at anticipating rebounds and bagging himself numerous gilt edged chances along the way. Anticipation, while others merely look on may set some strikers apart from teammates.

Therefore, it would appear that a double save is significantly more than the sum of the individual parts, a fact already appreciated by fans worldwide. For the best example of such a skill, showcased on the then biggest domestic stage of the FA Cup final, check out the legendary Jim Montgomery moment against Trevor Cherry and Peter Lorimer from 1973.

http://www.youtube.com/watch?v=PZmFoo4payA