Sunday 23 November 2014

Probability of a Goal from Expected Goal Data

This is a post to share a thing that might be a new way of using expected goal data. Rather than adding up the individual shot probabilities to get a summed total (a.k.a. Expected Goals) we can use the xG values of each individual shot in a match to work out the probability of a team scoring in that game.

This uses the idea of shot quality or chance quality, and that less quantity (shots) and more quality (per shot, aka xG) is a good thing. Sometimes less is more. I dabbled with this idea about a year ago in this post about Manchester United's 2012/13 season. In this I presupposed that United's exceptional shot quality that season was a possible explanation for them scoring considerably more goals than their expected goal total alone would suggest. Presuppose. Possibly. Yeah. The method was a bit of a fudge and from further testing/dabbling didn't go anywhere.

Early this year Mark Taylor took a much better swipe at the idea with his post Twelve Shots Good, Two Shots Better, where he demonstrated by simulation that Team A attempting 2 big chances on goal (xG = 2 * 0.60) would beat Team B who took 12 lesser chances (xG = 12 * 0.10). Both teams have the same total goal expectation from the game (1.20) but from his simulation Team A wins out in 37% of the simulated games versus Team B's 32%.

Here's my method for calculating Probability of a Goal (pG) using a team's individual shot/xG data. For each fixture take the xG values for each individual shot and then determine the probability the team do not score at all from any of those shots.Then subtract this from 1.

pG = 1 - [(1-xG1)*(1-xG2) *...* (1-xGn)]

This is the probability that a team will score 1 goal or more in a match having take n shots, with each shot having an individual probability of xGn. 

To the results, or I should say the differences between Expected Goals and the freshly calculated 'probability of a goal', pG. I'm cautious to say "results" as xG has been well tested and proven to be decent, whereas pG hasn't and is new, to me at least, and will need much more testing and stuffs. As you'll see from the chart though there are some significant differences between these two values even though they are determined from the exact same data.


Below is a plot of average xG vs average pG from the first 11 games of this season. The data does not include penalties or own goals. Beneath the chart I'll go over the key "winners and losers" as I see them.



  • Chelsea are the most significant winner. They go from being placed 5th amongst all teams for xG to first for pG. This means they have a best probability of scoring a goal  in any given match. 
  • Arsenal, City and Southampton lose ground to Chelsea. One reason they may be penalised is for being very good against some teams but at the same time not good enough against others, and this perhaps could be the most relevant thing about pG. It's no good hammering one team and padding out your xG total if you then struggle to create equivalent chances in your other games.. 
  • Some teams could also be accused of not having a real cutting edge this season (relative to Chelsea). When big teams face smaller clubs the underdog will naturally and - importantly - deliberately concede possession and defend deep in numbers. "Big Team" will get lots of ball in their opposition's third, and will be afforded lots of chances... but if they overplay or are not incisive enough then they won't be able to create chances of any real quality.
  • Everton and WBA are also big winners here. Everton draw level (horizontally) with the trio of United, West Ham and Spurs which perhaps reflects their actual goalscoring record so far this season. West Brom..  yeah.. dunno. 
To quickly wrap up, I like that pG uses the same data as xG does but takes advantage of a greater amount of information available in the raw data. I shall have to do some more prodding around of previous season's numbers and see where it takes me.

Monday 5 May 2014

Defensive Errors in Football


Mistakes are a massive part of football. You only have to think back to Kompany's skewed clearance for Coutinho's goal or Gerrard's slip against Chelsea to realise just how important a single error can be to a game, or even final league positions. They can be a big spanner in the works for anybody looking at the stats too, a player might make 29 successful passes on the pitch but the 30th is misplaced straight to the opposing forward - oops... goal. In this post I'm going to go through a few things I've found looking at defensive errors. 


“Football is a game of mistakes. Whoever makes the fewest mistakes wins.”
Johan Cruyff

Error = Big Chance
Since the start of the 2011/12 season there have been 1265 defensive errors that then led to a shot on goal and 491 goals scored. This is a 39% conversion rate, an equivalent rate to a 'Big Chance' or 'Clear Cut Chance' in Opta parlance, that is "a situation where a player should reasonably be expected to score usually in a one-on-one scenario or from very close range".  (see Opta's definitions). In other words, you make a defensive error and let the opposition in on goal, they are going to get a good chance to score. 

The chart below is a plot of errors leading to shots vs. errors leading to goals.  It's not a great R2 value but you can see the trend is definitely there. Each point on the chart represents a individual season for a team. 


This Season
The next chart below is just for this season. Spurs have made a lot of errors and been punished severely! This is one of the biggest outliers in this data. Liverpool have made the most defensive errors that led to a shot on goal of any team and conceded around the league average number of goals from them. City have conceded a similar number of goals from defensive errors but from half the shots. Strong defensive teams such as Chelsea, Hull and Crystal Palace have built their season on rarely making costly mistakes.

Repeatable?
Defensive errors don't look repeatable, for most teams. The chart below shows the plot of each team's 'errors leading to shots' from one season to the next for the clubs that have been in the Premier League for each of the past 3 seasons. Overall, there's no trend to speak of, however, there are some patterns that stick out. It's also worth noting that errors (for either shots or goals) do not correlate with 'regular' shots/goals conceded, i.e. teams who concede a lot of shots don't necessarily make a lot of errors.
Arsenal are shocking, amongst the most error prone of teams each season. They're the only team that has a consistently poor trend with regards to errors and their goals conceded each year  tracks this. You can also see how varied most teams are from one season to the next. Some teams have remarkable seasons. Swansea's 'sterile possession' and defensive strength under Rogers in 2011/12 stand outs out on the plus side.  Ditto WBA under Hodgson in the same year. Last season was the worst of the three here for errors leading to both shots and goals and Newcastle led the calamity. 

15% of all Goals from Errors
In the past season's there have been around 160 goals as a result of an error, which is about 15% of the total goals scored. This is a fair chunk, and not to be sniffed at. However, it's not the be all and end all of a team's defensive performance, far from it. Liverpool had an excellent defence and the most clean sheets last season (43 GA, 16 CS) despite conceding a lot of errors (leading to 10 goals). When and in what context these errors occur is clearly important. They are perhaps particularly telling for clubs battling relegation. Last season Wigan conceded 17 goals (the most ) from 36 shots from errors (the most). It was their undoing. They were pretty sound defensively otherwise.

Regarding Other Defensive Stats
As mentioned at the start, errors like these can really throw a spanner in the works of any analyst looking at a team's or player's defensive performance. One loss of possession or misplaced pass can quickly undo a whole game's worth of stoic defending. I spent almost a full month of evenings a few summers ago trying to 'unlock' the secret of clean sheets, looking at every defensive stat I could, including time in/out of possession, opponent pass accuracy, final third passes conceded, shots conceded, lots. 

Whilst all of these metrics pointed roughly in the right direction there was always a few teams facing completely the wrong way, similar to what StatsBomb found themselves this week looking at opponent pass accuracy. That errors are not generally repeatable means as an analyst we can ignore them as 'real' to some degree, but we'll have to accept that they are a permanent source of noise.

Further work on errors would involve reversing the data to see if certain teams force a lot of errors which then lead to shots or goals (e.g. gegenpressing). It also be good to take a closer look at some of the stand-out data points from this and recent seasons: Why do Arsenal conceded so many? What did Newcastle do wrong last year? What did Rogers do so well at Swansea? For now though, one more thought from Johan...

“Actually I never make a mistake, because it takes a huge effort for me to be wrong.”
Johan Cruyff



Wednesday 2 April 2014

Player Impact on Expected Goals Difference

I'm pretty happy with 'Expected Goals Difference' (xGD) as a underlying measure of a team's ability. I used it in my last post to compare Man United's season this year to last. StatsBomb have done a similar thing with West Ham today, successfully debunking the Carroll effect on the Hammers apparent resurgence. I also found that xGD was amongst the best forecaster of future success (points and goals) in some testing I did a few weeks back.

A logical next step for me is to see how individual players impact a team's xGD. Goal Impact do this already with real goals instead of expected goals. They do an absolute incredible job, tracking the impact on their team's goal difference for players around the world right from their earliest youth games. Their system looks very robust indeed. I'm sure they've got some clever stuff going behind the scenes but it's a simple premise: A top down model that doesn't care for the actions a player does on the pitch, but just the output of those actions. Whatever it is, whether it's successful passing, dribbling, tackling, interceptions -  if it leads to or prevents goals for their team then it counts. 

Below is my first stab at the same principle but using expected goals - quality and quantity of chances created and conceded. I am in no position to replicate what Goal Impact have done with their system. They track goal impact and playing time by the minute so can accurately evaluate subs appearances, they have data from numerous seasons from which to correlate plus/minus effect on a team with and without a player. I've had to use a >60 minute playing time cut-off and for now have just processed this season's data. But it's a start. 

With low games played for some players compared to others I have normalised each team's xGD in each fixture against the typical result expected against an opposition. E.G. If Arsenal play Aston Villa at home I'd expect them to achieve an xGD of +0.4 if they performed at an average level for the league. If Arsenal achieved +1.0 then their normalised result would be +0.6.

In the table you'll see I've also included actual goal difference (GD) as a comparison with expected goals, again normalised against opposition. First here's a look at how xGD and GD correlate for players with >1000 minutes played this season.

A pretty healthy and reassuring relationship. That the correlation is 'looser' around the zero marks is a perhaps a useful insight into the advantage of using expected goals over goals. When teams aren't that good scoring is rarer and hence measuring anything/nothing becomes difficult. The best example of this is when a teams score 0 goals. xG's measure of chances created give a better indication of which teams/players were actually the better team.

On to the table then. You'll also see I've included a '+Team' value for both xGD and GD. This is the player's plus or minus difference from their team average. This does produce some wacky result with a lot of players on the worst teams looking strong, particularly the xGD version. There's clearly some sample size issues with this, as there is with the data in general based on just 31 available games. I'm not going to make any comment on the players and values in the table at this time. I'll follow up with some remarks in a separate post at a later date. Suffice to say, there's some interesting stuff thrown out. As usual this table is sortable and searchable. Click on a column header to sort. Type a team code (e.g. 'LIV') in the Search box to search. By default the table is sorted by xGD.


PlayerTeamMins>60 MP0-59 MP0 MPxGD+Team (xGD)GD+Team (GD)
1NavasMCI1510131341.220.282.200.67
2ClichyMCI1212132151.210.282.210.68
3DemichelisMCI1530170101.170.241.980.44
4KompanyMCI1463162121.110.171.610.04
5NegredoMCI159716951.050.111.630.07
6AgueroMCI1191134131.020.071.940.39
7FernandinhoMCI199322171.000.062.130.60
8SilvaMCI1581190110.990.051.860.31
9AllenLIV98298140.970.352.290.85
10FlanaganLIV1226141140.960.351.930.46
11ZabaletaMCI218024150.950.011.830.28
12CoutinhoLIV183119660.950.341.740.26
13ToureMCI232427030.940.001.690.13
14NasriMCI162919560.91-0.041.840.29
15MikelCHE903813100.840.210.71-0.57
16DzekoMCI1253111090.82-0.141.20-0.39
17HartMCI189021090.78-0.181.34-0.24
18NastasicMCI1029103170.77-0.181.25-0.34
19KolarovMCI150015870.74-0.221.21-0.38
20Eto'oCHE118014590.730.101.640.43
21SuarezLIV224325060.730.111.570.08
22SterlingLIV159616960.720.101.730.25
23SchürrleCHE94081580.720.081.900.71
24MilnerMCI92381480.71-0.240.39-1.25
25CissokhoLIV1044113160.710.081.630.13
26CahillCHE216024070.690.061.470.25
27ColeCHE1103130180.690.050.84-0.42
28AggerLIV1141124150.680.061.710.22
29JohnsonLIV1796201100.680.051.46-0.04
30TerryCHE261029020.660.021.19-0.05
31TorresCHE126113990.650.021.19-0.05
32IvanovicCHE254928120.650.021.12-0.13
33HazardCHE263530100.640.011.23-0.01
34CechCHE279031000.640.001.23-0.01
35SkrtelLIV250128030.630.001.44-0.06
36AzpilicuetaCHE178520380.62-0.021.560.35
37MignoletLIV270030010.62-0.011.40-0.11
38HendersonLIV267830010.62-0.011.40-0.11
39RamiresCHE247227130.61-0.030.90-0.36
40OscarCHE189820920.61-0.031.23-0.01
41SakhoLIV1028121150.60-0.030.99-0.55
42WelbeckMAN1197119110.550.250.20-0.21
43Da SilvaMAN1278134140.550.250.580.19
44WalcottARS86094180.530.230.41-0.28
45VidicMAN1655182110.520.220.12-0.30
46FlaminiARS122312980.510.220.66-0.01
47SturridgeLIV175720290.51-0.131.45-0.05
48GerrardLIV219624250.50-0.141.35-0.16
49Luiz RosaCHE1249142150.50-0.141.480.26
50LucasLIV1556173110.49-0.150.89-0.65
51RamseyARS1492162130.490.200.920.27
52LampardCHE144414890.49-0.160.96-0.29
53PienaarEVE161018490.430.200.570.01
54ValenciaMAN162017680.430.130.570.18
55WillianCHE129914680.43-0.211.13-0.12
56ToureLIV1437154120.42-0.220.99-0.54
57GibbsARS178619660.410.121.160.52
58OsmanEVE1676161320.400.170.740.20
59YoungMAN82988150.400.090.28-0.13
60SigurdssonTOT999109120.390.25-0.15-0.27
61MataMAN1509100210.380.070.460.07
62RosickyARS1133128110.360.070.32-0.37
63CarrickMAN187321190.360.060.36-0.04
64TownsendTOT1171128110.360.210.190.10
65SoldadoTOT180320560.360.220.210.12
66ShawSOU237125330.350.110.370.18
67GiroudARS241827130.340.040.700.03
68ClyneSOU1478146110.340.090.710.54
69RodriguezSOU245027400.330.090.11-0.10
70OzilARS182821160.310.020.940.29
71De GeaMAN270030010.310.000.410.01
72CisseNEW1022109120.310.23-0.67-0.80
73RoseTOT1296141160.300.160.540.47
74BorucSOU212723170.300.060.330.13
75EvraMAN245727130.30-0.010.490.10
76SzczesnyARS270030010.29-0.010.62-0.05
77CazorlaARS198122270.29-0.010.66-0.01
78JagielkaEVE216024070.280.040.48-0.09
79FonteSOU255228120.270.030.220.02
80MyhillWBA1260140160.260.17-0.59-0.13
81FellainiMAN1060114160.26-0.05-0.07-0.49
82MertesackerARS252028030.26-0.040.64-0.03
83JanuzajMAN133014890.26-0.060.450.06
84BainesEVE202922180.260.010.25-0.33
85SessegnonWBA1407164100.260.16-0.300.17
86van PersieMAN1461171130.25-0.060.670.29
87ColemanEVE241827040.250.010.660.10
88DavisSOU189820740.250.010.330.13
89VertonghenTOT198022090.250.10-0.04-0.15
90DistinEVE234026050.250.010.640.09
91HowardEVE245227130.250.000.55-0.02
92BonySWA175219750.240.30-0.230.13
93SagnaARS234126140.24-0.070.58-0.09
94RooneyMAN210123260.24-0.080.38-0.02
95AnelkaWBA850102180.240.14-0.260.22
96SchneiderlinSOU229725240.24-0.010.280.08
97SmallingMAN1579174100.24-0.080.37-0.03
98AnitaNEW174818850.230.16-0.42-0.53
99KoscielnyARS228925240.23-0.070.940.29
100PaulinhoTOT187922270.230.080.01-0.10
101WilshereARS169118580.23-0.080.63-0.04
102EriksenTOT1352153100.220.070.330.25
103LovrenSOU215724070.22-0.030.19-0.02
104LallanaSOU251328300.22-0.030.17-0.04
105Ward-ProwseSOU1346121630.22-0.030.10-0.12
106RatWHM1134114160.210.63-0.45-0.26
107McCarthyEVE210523230.20-0.050.49-0.07
108IrelandSTO939811120.200.370.110.17
109LambertSOU225325510.20-0.060.18-0.03
110JonesMAN1610172120.19-0.120.820.45
111NaughtonTOT1116114160.190.040.05-0.05
112ArtetaARS171519490.18-0.120.62-0.06
113CorkSOU1239138100.18-0.07-0.06-0.29
114AmalfitanoWBA156718360.180.08-0.280.20
115WanyamaSOU1296135130.18-0.070.350.15
116ChadliTOT1066118120.170.02-0.24-0.36
117BarkleyEVE175417950.17-0.070.48-0.09
118YacobWBA176120460.170.08-0.64-0.19
119CleverleyMAN1463155110.17-0.150.36-0.04
120ColocciniNEW1684190120.170.090.130.05
121WalkerTOT229725150.160.01-0.22-0.34
122LukakuEVE179419570.16-0.090.920.39
123JonesWBA1558163110.160.06-0.58-0.12
124CanasSWA166719480.150.21-0.44-0.09
125ChambersSOU1384144130.14-0.11-0.33-0.58
126MirallasEVE203423530.14-0.110.33-0.25
127BarryEVE216024070.14-0.110.630.08
128MorrisonWHM1154124150.140.56-0.66-0.49
129OlssonWBA229025140.130.03-0.420.05
130GouffranNEW193220740.120.040.490.45
131McAuleyWBA240827030.120.03-0.50-0.04
132DawsonTOT250128030.11-0.05-0.21-0.33
133WilliamsonNEW219224160.110.020.170.10
134SissokoNEW259428210.100.020.01-0.08
135VormSWA1710190120.100.15-0.070.30
136RidgewellWBA250827210.08-0.02-0.320.15
137KrulNEW270030010.08-0.01-0.01-0.09
138BruntWBA170319380.07-0.03-0.66-0.21
139LlorisTOT270030010.07-0.10-0.01-0.12
140Ben ArfaNEW1186111280.07-0.02-0.59-0.72
141MulumbuWBA241926310.06-0.04-0.63-0.17
142ReidWBA944101190.06-0.04-0.65-0.19
143DembeleTOT176317950.06-0.100.430.35
144DaviesSWA230025150.050.10-0.320.04
145RoutledgeSWA198322540.050.10-0.190.17
146AnichebeWBA10511010100.04-0.06-1.38-0.97
147HernándezSWA11081010110.040.09-0.290.06
148DebuchyNEW215724160.04-0.050.03-0.05
149MonrealARS835811120.04-0.260.23-0.47
150RemyNEW186622180.02-0.070.630.60
151BerahinoWBA99991560.02-0.080.420.94
152ReidWHM1048114160.010.42-0.120.09
153EvansMAN1315142150.01-0.320.30-0.10
154RangelSWA210623170.000.05-0.220.14
155DyerSWA147315610-0.010.04-0.220.13
156TioteNEW20522236-0.01-0.10-0.03-0.11
157SantonNEW20832326-0.02-0.110.310.25
158HuthSTO106612019-0.020.15-0.12-0.08
159AmatSWA8169319-0.020.03-0.94-0.62
160AmeobiNEW92291012-0.02-0.110.00-0.08
161ArnautovicSTO16381675-0.020.150.330.40
162Yanga-MbiwaNEW134313612-0.03-0.120.420.36
163TetteyNOR114813315-0.030.36-0.77-0.19
164AdebayorTOT126514116-0.04-0.200.310.22
165MorrisonWBA17111785-0.04-0.15-0.230.25
166FosterWBA142816014-0.04-0.15-0.430.04
167LennonTOT168820110-0.05-0.21-0.11-0.22
168ChicoSWA24042704-0.06-0.01-0.270.08
169ChirichesTOT112512115-0.07-0.230.530.46
170BegovicSTO23402605-0.070.100.060.12
171JaaskelainenWHM162018013-0.080.34-0.36-0.17
172VlaarAST20832316-0.080.190.090.30
173WaltersSTO21172164-0.090.08-0.25-0.21
174ChesterHUL137515313-0.100.180.200.15
175WilliamsSWA24092704-0.11-0.07-0.340.02
176BrittonSWA138315214-0.11-0.07-0.120.24
177CabayeNEW150417212-0.12-0.220.700.67
178BentalebTOT9961032-0.12-0.280.09-0.01
179ChamakhCRY19052155-0.120.15-0.59-0.07
180WilsonSTO20622156-0.130.040.280.35
181MichuSWA108712217-0.15-0.11-0.180.19
182SagboHUL14061579-0.150.12-0.24-0.31
183PuncheonCRY18912245-0.160.12-0.500.04
184van WolfswinkelNOR119213810-0.160.23-0.050.57
185WeimannAST20512271-0.170.09-0.20-0.01
186ShelveySWA17631957-0.17-0.13-0.44-0.10
187N'ZonziSTO24102632-0.17-0.01-0.23-0.20
188CameronSTO27003001-0.18-0.02-0.21-0.17
189OdemwingieSTO14851498-0.18-0.020.360.43
190LivermoreHUL24142713-0.190.090.05-0.01
191ShawcrossSTO27903100-0.19-0.03-0.19-0.15
192El AhmadiAST17932055-0.190.060.280.51
193DelphAST23742613-0.200.06-0.29-0.11
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197HuddlestoneHUL26112911-0.200.080.02-0.04
198BacunaAST21602442-0.210.05-0.170.02
199GabbidonCRY19702209-0.210.06-0.54-0.01
200WhelanSTO17341876-0.21-0.050.260.33
201DaviesHUL26052902-0.220.060.060.01
202BentekeAST20362235-0.220.04-0.180.02
203CrouchSTO22252443-0.23-0.060.040.09
204WestwoodAST23582703-0.230.03-0.32-0.14
205KorenHUL100881013-0.230.040.430.40
206KacaniklicFUL1186101110-0.240.49-0.620.49
207DelaneyCRY25642812-0.240.02-0.500.03
208MartinNOR19872227-0.240.15-0.68-0.09
209DikgacoiCRY154516411-0.240.02-0.420.12
210LunaAST138115213-0.250.01-0.160.03
211ElmohamadyHUL26142911-0.250.020.100.05
212De GuzmanSWA18651975-0.25-0.22-0.250.11
213DowningWHM18372047-0.250.160.000.22
214GuzanAST27003000-0.260.00-0.24-0.05
215BassongNOR21972416-0.260.13-0.70-0.11
216LowtonAST115612414-0.26-0.01-0.090.11
217SperoniCRY27003001-0.270.00-0.60-0.07
218JedinakCRY27003001-0.270.00-0.60-0.07
219BradyHUL8919715-0.270.000.160.11
220BannanCRY99710517-0.27-0.01-0.340.20
221GiaccheriniSUN119213512-0.270.19-0.50-0.20
222TomkinsWHM19352128-0.270.13-0.060.15
223RoseniorHUL144115610-0.28-0.010.210.17
224NolanWHM21122425-0.280.130.000.22
225PietersSTO24762731-0.28-0.12-0.33-0.30
226DiaeWHM18081894-0.280.12-0.41-0.22
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