How Wenger Rang The Changes in 2010/11.

Once the starting eleven walk on to the pitch at kickoff time, the manger has already played a large part of his hand. "In game" tactical rearrangements and of course substitutions are his only recourse if the game situation turns against him or if he wants to consolidate a strong position. We saw here and here how the course of a season's worth of games were altered by the introduction of substitutes for teams such as Chelsea and Stoke. By mapping the expected points situation for sides pre and post their phase of substitutions, we gained a broad picture of how successful (or lucky) AVB and Tony Pulis had been with their tinkering.

Of course the introduction of one or a group of replacements being immediately followed by an upturn in game fortune doesn't necessarily mean that all of the credit should be immediately heaped on the substitutes. Nor should they shoulder all the blame should things go from bad to even worse. Credit or debit should be shared between the 90 minute players as well as the manager for deciding to make adjustments. So in this follow up post, I've tried to isolate some of the individual attacking contributions made by the Arsenal substitutions employed by Wenger during the 2010/11 league season.

Much of the easily available data can be used to give a general picture of Wenger's approach to substitutions, but it's probably best not to read too much into these numbers because they may be determined by a multitude of different and competing factors. Injury replacements are obviously enforced, but game situation, depth of squad and upcoming games may also partly determine gameday rotations. Unused bench duty is also a favoured punishment for player misdemeanors by at least one EPL boss.

Instead I'll use Wenger's 2010/11 substitution tendencies merely to set the scene. 107 players were substituted into Arsenal's 2010/11 EPL season, so that's an average of just over 2.8 a game. 61% were midfielders, 33% strikers and  only 6% defenders. Game position didn't really seem to change Wenger's average response, he was as likely to sub in attackers or midfielders to protect a lead as he was to chase a deficit. The average time of a substitution was just past the 70th minute and the most active 10 minute segment was from the 80th to the 89th minute. 6.5% of the subbed players received the bad news whilst eating their half time orange. Bendtner (14), Rosicky (13) and Arshavin (12) were the most frequently called upon replacements.

70th Minute.......All Change.

Goal tally is the most recognised measure of individual offensive production, but it's also a very crude one especially over limited sample sizes. Goal attempts allows a slightly more precise estimation of a player's contribution to his sides's attacking intentions and this approach can be bettered still if we can factor in the quality of chances a substitute is producing in combination with his teammates.

Nineteen different substitutes of which 16 were either midfielders or strikers managed only three goals for Wenger in 2010/11, one each from Vela, Arshavin and Walcott. However, if we look instead at the goal attempts of the group, we now have 66 events to analyse.

Goal Attempts of Arsenal Subs, 2010/11, Sorted as Strikers, Midfielders and Defenders.

Player (mins played as sub) 2010/11.	Goal Attempts.	Cumulative Goal Expectancy.	Cumulative Shot Accuracy Expectancy.	Actual No. of Goals.	Actual No. of Shots on Target.
Bendtner (281)	8	1.1	3.2	0	2
Chamakh (350)	8	1.3	3.2	0	2
Denilson (217)	6	0.3	1.7	0	1
E-Thomas (13)	0	0	0	0	0
van Persie (173)	2	0.1	0.4	0	1
Vela (48)	3	0.3	1.0	1	0
A Diaby (70)	3	0.4	1.2	0	0
Arshavin (347)	7	0.5	2.3	1	2
Eboue (70)	0	0	0	0	0
Fabregas (98)	3	0.2	0.8	0	0
Nasri (16)	2	0.1	0.6	0	0
Ramsey (15)	0	0	0	0	0
Rosicky (341)	12	1.2	4.0	0	4
Song (13)	1	0.3	0.5	0	0
Walcott (198)	9	0.5	2.8	1	3
Wilshere (90)	2	0.2	0.7	0	1
Djourou (66)	0	0	0	0	0
Gibbs (22)	0	0	0	0	0
Squillaci (70)	0	0	0	0	0

At once we see how little information is conveyed by a "goals only" approach. Even simply adding the number of shots on target and total goal attempts begins to enhance the picture of the impact made by each substitute. If we record the pitch co ordinates from where each individual shot originated from we can compare the figures to the goal expectancy model described here and calculate a goal expectancy and accuracy expectancy for each effort. Cumulative totals for each individual player's attempts can begin to be used to estimate a longterm average expectation should the player's 2010/11 shooting exploits prove typical of their future performance.

Naturally goal attempts are very limited for individual players. It would be extremely optimistic to expect Song's eyecatchingly high goal expectancy per minute to continue in larger samples, based as it is on just 13 minutes of substitute action, during which he conjured up one shot with a comparatively high chance of success. Similarly, Vela out performed his goal expectancy with one goal from three shots that had a cumulative predicted expectancy of well below half a goal. His figures would almost certainly regress with increased attempts.

The most prolific individual shooters, namely Rosicky, Chamakh and Bendtner are seeing their shot accuracy figures trending towards their predicted numbers, but their goal totals are stuck firmly on zero and the figures above do illustrate the problems involved when analysis is done on relatively small sub samples. We can add definition to opinion by summing goal expectancies from a dozen or so shots, but trying to derive certainty from only a handful of individual efforts is ultimately self defeating. To be able to talk with more authority we need to pool the substitutes performances together and compare their performance as a group to that of Arsenal's starters over roughly the same time scale.


The Offensive Output of Arsenal's Starters over the Last 20 Minutes compared to that of their Subs.

	Cumulative Goal Expectancy for All Shots.	Actual Number of Goals.
Shooting Record of Arsenal Subs. 2010/11	6.3	3
Shooting Record of Arsenal Starters 70th Min Onwards. 2010/11.	18.3	18

Arsenal's subs underperfom their goal expectancy from their 66 attempts by nearly half despite their fresh legs, while the starters perform very close to their expectation over a roughly comparable portion of the match, namely the last 20 minutes when subs are most likely to also be active. If this kind of split performance repeats itself over larger Arsenal populations and is seen in samples of other teams, it may provide evidence that the attacking output from substitutes fails to match those of the starters who play through the entire game. They may be subs for a reason, or it may a quirk of this particular set of samples.

Goal expectancy and accuracy estimates are just the start in assessing individual player contribution, the quality of assists is the logical next step. This post should be looked on as a methodology to begin to sort the good player from the not so good and habitual substitutes would logically fall into the latter category. The results of this preliminary trial would suggest that Wenger well knew where his goal generating talent lay in 2010/11.

Data for this post was variously gathered from chalkboards, 442's EPL ipad app and an especial thanks to OptaPro.