Why Abramovich Sacked Villas-Boas.

Expectation is everything in football and fans and owners often share a common trait of impatience and recency bias.The impatience arises when the manager and the team fails to deliver in a timely manner the proper level of success commensurate with the level of support provided.Be it financial in the the case of the owner or financial and vocal in the case of the supporters.This slightly unfair bargain often ignores the many uncontrollable factors that make the difference between winning or losing a game of football.Injuries and luck being two such factors.

Recency bias can cut both ways for a manager,as a recent good run can elevate him to the heady heights of hero status,while a run of winless matches can quickly see the terraces and boardroom calling for his head.A prime example of this is the current situation at Stoke where the team currently have their best post February points total,are FA Cup Quarter finalists again,have enjoyed 3 and a half years of Premiership football and have played 44 matches so far including a run to the knockout stages of the Europa Cup.For a club of Stoke's limited resources this is success beyond most people's expectations.Yet despite this enviably record there is a minority of fans who are calling for a change at the top.A run of consecutive losses is the usual catalyst for the unrest.Follow that up with complaints about team selection and a disagreement about prioritising the Premiership over the Europa adventure and you soon have a manager under siege.Although fortunately for Stoke,their owners are made of stronger and more sensible stuff.

Pulis' near neighbour,Harry Rednapp at Tottenham has also just this weekend discovered that third place in the Premiership offers no protection in the face of back to back high profile losses to fellow high flyers,especially if fan's favourites are left on the bench.

Fans are fickle and there's no reason to suppose that owners are much different

One man who failed to survive a dip in expectations was of course Andre Villas-Boas at Chelsea,who experienced the same fate as befell his double winning predecessor,Carlo Ancelotti.The bar is set much higher at Chelsea than at most other clubs,but the same factors that conspire to make all managers vulnerable exist at Stamford Bridge.

Owner,player and manager relationships play some part in how partnerships fracture,but reliable information on these factors will never make the public domain,but we can quantify the publicly displayed interactions between the manger and his players.Fan satisfaction with the manager on match day can be broken down into three easily digestible pieces.Firstly,what was the starting eleven and how did they perform? Next,did his substitutions help the team to the best possible result and lastly,what was the final score and did the result come close to meeting expectations.

To quantify these three factors I've used my Expected Points model to look at every Chelsea EPL game from Ancelotti's last season in charge of Chelsea and all 27 of AVB's EPL games before he was axed after defeat to WBA on Saturday.

Chelsea "Heat Map" Under Ancelotti 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.
WBA	60	65	70	2.65	3.00	3.00	3.00	3
@Wigan	63	70	79	2.56	3.00	3.00	3.00	3
Stoke	72	81	85	2.75	2.95	3.00	3.00	3
@WHU	76	82	83	2.46	2.99	2.99	3.00	3
Blackpool	72	75	78	2.75	3.00	3.00	3.00	3
@ManC	69	75	81	1.65	0.44	0.36	0.28	0
Arsenal	73	83	89	1.99	2.69	2.77	2.99	3
@Villa	45	76	76	1.99	1.78	1.49	1.49	1
Wolves	72	79	82	2.75	2.94	3.00	3.00	3
@Blackburn	72	89	-	2.24	1.68	2.89	-	3
@Liverpool	45	70	76	1.72	0.24	0.10	0.07	0
Fulham	78	85	89	2.73	2.95	2.96	2.97	3
Sunderland	58	69	75	2.56	0.50	0.30	0.21	0
@Birmingham	65	72	-	1.99	0.62	0.52	-	0
@Newcastle	80	-	-	1.99	1.43	-	-	1
Everton	65	78	88	2.40	2.80	2.84	1.37	1
@Spurs	45	68	78	1.44	0.54	0.37	1.23	1
@Arsenal	45	56	61	1.33	0.49	0.02	0.08	0
Bolton	89	89	-	2.46	2.92	2.92	-	3
Villa	57	73	79	2.53	1.03	0.68	0.53	1
@Wolves	66	72	79	2.24	0.76	0.64	0.48	0
Blackburn	80	80	87	2.50	2.99	2.99	3.00	3
@Bolton	72	77	-	2.06	3.00	3.00	-	3
@Sunderland	77	82	89	2.06	2.75	2.79	2.87	3
Liverpool	75	84	-	2.06	0.48	0.28	-	0
@Fulham	66	71	-	1.95	1.59	1.54	-	1
ManU	61	71	81	1.65	1.45	1.38	2.68	3
@Blackpool	55	72	75	2.50	2.83	3.00	3.00	3
ManC	70	71	77	2.06	1.60	1.59	1.50	3
@Stoke	61	61	80	2.05	1.70	1.70	1.45	1
Wigan	45	59	75	2.55	2.25	2.09	2.87	3
@WBA	63	77	82	1.99	2.94	2.97	2.98	3
Birmingham	57	67	68	2.68	2.99	3.00	3.00	3
WHU	57	70	77	2.68	2.91	2.91	2.92	3
Spurs	57	63	73	2.29	1.91	1.84	1.69	3
@ManU	45	45	62	1.29	0.12	0.12	0.08	0
Newcastle	64	64	64	2.59	2.05	2.05	2.05	1
@Everton	61	70	78	1.51	1.36	1.32	0.29	0

At every point in a match a team will have a probability of winning the match and a probability of drawing.These probabilities will depend on the relative merits of both sides,the current score,time remaining and less common outcomes such as red cards.This allows us to calculate how many league points a team should gain on average for any point from the first whistle in August to the last one in May.It also allows us to see how the manager's starting 11 fare each week and how able a manager is to  improve the fate of his team by the introduction of substitutes.By seeing if a team's Expected Points rose or fell with every managerial decision we can gauge how pleased both the fans and more importantly the owner would have been with their coaches actions.

In the table above and below I've labelled a rise in EP in blue and a fall in red and the numbers relate to the performance of the starting 11,followed by that of the team with first one,then two,then three substitutes.

To demonstrate look at AVB's second game in charge below at home to WBA.At kickoff Chelsea would expect to get an average of 2.5 points from such games,by the time of the first substitution,WBA led 1-0 and the Blues' EP had fallen to 1.42.Therefore,the red number 1.42 indicates that the starting 11 under performed.

During the time Chelsea were playing with just one substitute,Anelka equalises via a deflection in the 53rd minute and when the second substitute appears after 60 minutes their EP has risen from 1.42 points to 2.02 points.Thus the blue 2.02 figure indicates that the first substitution has had a positive impact on the team's EP and presumably the fans are happy with AVB's course of action.

Chelsea play with two subs for just six minutes from the 60th minute to the 66th,but no more goals are scored and the clock has ticked nearer to full time and their EP has started to track towards one point for the draw.So a negative period of play for the two sub combination denoted by the red 1.93 in the three subs column,albeit only slightly.The final sub appears after 66 minutes and Chelsea grab the winner about 20 minutes later.The three sub combination is highly productive raising the Expected Points from 1.93 points after 66 minutes to the (blue) 3 points at full time.AVB is a tactical genius and everyone is happy,although 2 of the four playing periods were negative and things could have ended differently.

Chelsea "Heat Map" under Andre Villas-Boas 2011/12 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.
@Stoke	66	76	89	1.99	1.61	1.49	1.23	1
WBA	35	60	66	2.50	1.42	2.02	1.93	3
Norwich	68	71	83	2.62	2.00	1.94	2.96	3
@Sunderland	62	74	79	1.99	2.94	2.96	2.97	3
@ManU	45	68	79	0.96	0.07	0.04	0.02	0
Swansea	60	79	83	2.62	2.91	3.00	3.00	3
@Bolton	54	56	73	2.17	2.99	2.99	3.00	3
Everton	65	77	77	2.40	3.00	3.00	3.00	3
@QPR	36	47	72	2.40	0.65	0.49	0.27	0
Arsenal	62	72	76	2.06	0.69	0.53	0.46	0
@Blackburn	45	83	89	2.29	2.02	2.83	2.89	3
Liverpool	45	84	84	1.92	0.84	1.33	1.33	1
Wolves	70	77	78	2.59	3.00	3.00	3.00	3
@Newcastle	61	75	79	1.65	2.50	2.61	2.65	3
ManC	73	84	88	1.51	1.76	2.90	2.92	3
@Wigan	45	66	80	2.39	2.12	2.80	2.84	1
@Spurs	33	48	78	1.36	1.33	1.31	1.20	1
Fulham	62	71	81	2.48	1.98	1.83	1.60	1
Villa	57	63	75	2.50	2.06	1.98	1.76	0
@Wolves	84	-	-	2.11	2.80	-	-	3
Sunderland	73	85	-	2.33	2.80	2.87	-	3
@Norwich	37	77	79	2.11	1.93	1.53	1.50	1
@Swansea	65	80	-	1.75	0.53	0.32	-	1
ManU	71	-	-	1.47	2.51	-	-	1
@Everton	69	77	78	1.59	0.41	0.05	0.04	0
Bolton	76	80	88	2.47	2.99	3.00	3.00	3
@WBA	64	76	84	1.81	1.52	1.41	0.26	0

The amount by which the Expected Points value change are of course important,but we can get a feel for how both Ancelotti's and Villas-Boas' team selections and tactical substitution were likely to have been received both on the ground and in the luxury boxes by looking at the percentage and grouping of the negative decisions.The red areas of the tables are times in a match and during the season when both managers were probably feeling the heat both from fans and from Abramovich.Hence I've called them "Heat Maps".

Red figures in the final columns are particularly bad news for top teams such as Chelsea,because they also  represent a real average loss of league points over fan and owner expectation,but intra match red numbers can also make the boss appear powerless to influence on field events while the contest is in progress.

Overall in 2010/11 Ancelotti had 68 positive and 76 negative passages of team play and 16 out of 38 occasions when the actual final points haul fell below that expected from pre game estimates.So he hovered around a 50% success rate under this analysis and did extremely poorly over the last four games prior to his sacking immediately after the loss to Everton.Villas-Boas exceeded those figures,scoring a 52% failure rate in both categories and also performed very poorly in both areas over the last six games of his reign.

In doing so he obviously exceeded Abramovich's tolerance threshold as well.