How Effective were Stoke's Substitutions in 2010/11.

Substitutions provide the manager with his biggest single weapon to alter or consolidate the path a match has taken once under way.Although some substitutions are obviously forced changes because of injury,many more are tactical adjustments based on such factors as historical data relating to tiredness of starters,current score and time remaining.It's therefore understandable that teams will have a genuine interest in assessing the impact their replacements make to the final match outcome.


Attacking substitutions inevitably attract most of the attention because a replacement who grabs an important goal will live long in the memory.However,just as many changes are made with the intention of preserving a lead or a hard earned point away from home and therefore taking a merely goal based approach can fail to capture a large proportion of the effect of juggling your troops.

Hajduk Split Prepare to Ring the Changes at the Brit.

My Expected Points model tracks the average number of league points a team can expect gain in any match up,at any time in the game and under any scoreline.Large changes to each team's current EP totals occur when a goal is scored and I regularly produce game graphs for EPL matches and use the plots to put an Expected Points value each goalscorer's effort.

As an extension of this approach,these graphs can also be used to chart the effect each successive substitution has had on a side's chances of being successful on the field.By recording the EP value at the start of the game for a team and then recording the values at the introduction of each substitute and again at the final whistle,we can see how the EP points has declined or increased during each separate stage of that team's on field make up.

Below I've charted the change in EP for Stoke City over all 38 games of the 2010/11 season.I've recorded the current EP for the team at the time of each substitution,so anyone can easily see by how much the EP changed while the team was playing with the original starting eleven and compare that figure to the change that occurred for example when the team played with two subs on the field.

Sunderland at home must rank as Tony Pulis' most inspired tactical switch of the season.An initial EP of 1.79 points had declined to 0.46 points as they trailed after 67 minutes.However,a single substitution of Andy Wilkinson(a defender) for John Walters( an attacker) resulted in three points with a late winner.This example is one of the memorable,but atypical times when a switch leads to spectacular,goal driven success,but it must be put along side the times when the result isn't as positive.The following week at Birmingham,two late substitutions presumably made to protect a goalless draw ended with a 92nd minute Birmingham winner.
Enforced substitutions are included in this example for completeness,as we can assume that Pulis would not have voluntarily replaced his record signing after just 14 minutes of the season in the away fixture at Wolves.Similarly,Pennant's removal after 12 minutes at the Hawthorns was down to a clash of bodies and not a clash of personalities.

How Stoke's Expected Points Changed with Each Substitution.2010/11 EPL Season.

Opponent.	Time of 1st Sub	Time of 2nd Sub	Time of 3rd Sub.	EP@Start	EP@1st Sub.	EP@2nd Sub.	EP @3rd Sub.	Final Points.
@Wolves.	14	51	67	1.22	1.22	0.10	0.32	0
Spurs.	64	85	88	1.15	0.34	0.16	0.12	0
@Chelsea.	51	68	86	0.27	0.07	0.07	0.00	0
Villa.	61	65	87	1.51	0.46	0.42	1.16	3
WHU.	66	73	83	1.79	1.49	1.43	1.30	1
@Newcastle.	50	57	67	0.96	0.32	0.29	0.25	3
Blackburn.	77	89	89	1.58	2.62	2.81	2.81	3
@Bolton.	67	86	-	1.15	1.11	1.07	-	0
ManU.	57	66	79	0.78	0.24	0.21	0.15	0
@Everton.	74	77	-	0.73	015	0.14	-	0
@Sunderland.	58	75	-	1.09	0.33	0.23	-	0
Birmingham.	73	89	89	1.79	2.95	2.82	2.82	3
Liverpool.	88	89	-	1.09	2.71	2.74	-	3
@WBA.	12	79	83	1.15	1.10	2.50	2.58	3
ManCity.	45	63	76	1.15	1.12	1.11	1.10	1
@Wigan.	71	83	-	1.44	1.27	1.19	-	1
Blackpool.	70	70	83	2.11	0.60	0.60	0.35	0
@Blackburn.	75	84	89	1.22	2.48	2.64	2.76	3
Fulham.	55	69	80	1.92	0.23	0.13	0.06	0
Everton.	59	80	84	1.44	2.40	2.95	2.97	3
@ManU.	69	69	76	0.37	0.11	0.11	0.10	0
Bolton.	71	81	88	1.79	2.94	2.97	2.99	3
@Fulham.	58	59	63	1.15	0.07	0.06	0.06	0
@Liverpool.	62	65	67	0.74	0.22	0.22	0.21	0
Sunderland.	67	-	-	1.79	0.46	-	-	3
@Birmingham.	79	81	-	1.29	1.16	1.16	-	0
@Arsenal.	78	88	-	0.46	0.10	0.06	-	0
WBA.	65	78	83	1.79	2.57	2.67	2.73	1
@WHU.	52	65	69	1.22	0.15	0.10	0.40	0
Newcastle.	60	81	88	1.65	2.99	3.00	3.00	3
Chelsea.	85	89	89	0.78	0.99	0.99	0.99	1
@Tottenham.	76	76	76	0.84	0.17	0.17	0.17	0
@Villa.	73	75	88	0.96	1.04	1.04	1.03	1
Wolves.	31	72	80	1.91	2.47	3.00	3.00	3
@Blackpool.	56	81	89	1.44	1.29	1.18	1.11	1
Arsenal.	51	73	84	0.78	2.60	2.83	2.93	3
@ManCity.	73	74	-	0.51	0.00	0.00	-	0
Wigan.	72	77	-	1.42	1.20	1.18	-	0

To account for these extreme outcomes and also incorporate the many games when the subs trot on and games meander to a less dramatic conclusion,I've averaged the change in EP per minute for the first choice Stoke and the Stoke side comprising various numbers of substitutes.It's doubtful that a single season is sufficient to allow for any extravagant predictive claims to be made about the astuteness of Pulis' tactics (high value EP goals such as winners late in a match will overhang such small sample sizes),but they do provide an interesting descriptive narrative to that season.

If we take the EP value at a certain point in a match and compare that value to a later point in the match,the two numbers are unlikely to be the same.Sometimes the later value will be higher,sometimes lower,but if the model is valid,on average over a large number of games these individual in game fluctuations will cancel out.If we therefore average the change in EP for a team's starting 11 and find that average is positive,we could conclude that the starting team out performs the model.This could be for any number of reasons.Small sample size is the most obvious,but alternatively the starting 11 could just be better than the substitute laden units that by necessity carry the team to the final whistle and the excess EP is "given back" later in the match.

How Stoke's Starting 11 Compared to Stoke Sides Containing Various Combinations of Substitutes. EPL Season 2010/11.

Average EP change  per minute for Starting 11.	Average EP change per minute for Team with 1 Sub.	Average EP change per minute for Team with 2 Subs.	Average EP change per minute for Team with 3 Subs.
-0.00115	0.00122	-0.00853	0.00425

From a purely narrative stand point,Stoke's starting 11 under performed the model in 2010/11.Playing with one substitute on the pitch they over performed,partly as a result of Walters' lone appearance against Sunderland.On average they under performed with two replacements but bounced back when all three took centre stage.

As a starting point this approach quantifies a team's performance with and without it's substitutes on the park without relying on the actual replacement player doing something noteworthy,such as scoring and it provides an individual game narrative.

* A bold Pulis double substitution today when Crouch and Walters made way for Jones and Jerome with twenty minutes left and the game still scoreless against Norwich.The move paid almost instant reward when soon afterwards Matty Etherington beat Ruddy at his near post for the only goal of the game.Another example of the potency of Stoke when they have all three subs on the pitch or just another data point?