A statistical formula that correlates strongly to league position

Back in January, I wrote a post for uMAXit in which I derived a formula from looking at and thinking about shots on target, shots conceded on target, and shot conversion rate. You can read the original piece here. After this, I got a message from someone in the stats community, asking why I hadn’t checked back to see if the correlation I showed in the uMAXit piece held true. This was a very reasonable point – I had showed a strong correlation (positive in this instance, as I had inverted league position to run the Pearson test), but not followed it up.

This was sloppy writing on my part – making a pronouncement without following it up in any meaningful way. So, I have now done that. If you recall (or read above in the link), Q is a value I derived from dividing shots on target achieved by shots on target given up, then multiplying the resulting number by shot conversion rate (including blocks). The intention was to factor that some teams are productive in terms of shots on target but give up a lot, some are weak going forwards but miserly at the back, and some are lethal in front of goal while not necessarily standing out in other ways: the formula seemed a good way of incorporating those factors.

Below I have arranged tables for this season and the five preceding seasons. The main takeaways: there is a strong correlation in all six seasons looked at between Q and league position. The teams finishing first and second in four seasons have the top two Q values as well, and the teams in last place have the lowest Q value five of six seasons too. 2014/15 shows an especially strong correlation. The teams with the best Q values in the last six seasons are Manchester City 2013/14 and this season’s Chelsea – despite that article in The Telegraph this week, shots on target conceded and shot conversion rate are pretty important.

Whether this has a predictive quality is something I am looking at, but for the time being, it’s pretty clear that Q has some value, now I’ve actually run it more than once!

Anyway, here are the tables.

2016/17 – up to 23 matches played:

Team Shots, on Target Shots on Target Faced Shot Conversion Rate (inc. Blocks) Q League position
Chelsea 119 59 14.55 29.35 1
Liverpool 143 71 13.4 26.99 4
Tottenham Hotspur 140 65 11.14 23.99 2
Manchester City 125 67 12.77 23.82 5
Arsenal 121 90 14.05 18.89 3
Manchester United 137 69 8.44 16.76 6
Everton 113 85 11.37 15.12 7
Bournemouth 95 105 11.94 10.80 14
Southampton 108 69 6.73 10.53 12
Watford 86 101 11.02 9.38 13
Crystal Palace 89 112 11.76 9.35 18
Swansea City 96 115 10.73 8.96 17
West Bromwich Albion 74 109 13.19 8.95 8
Stoke City 88 113 10.94 8.52 9
Leicester City 79 107 9.52 7.03 16
West Ham United 78 115 9.29 6.30 11
Burnley 74 137 10.59 5.72 10
‘Boro 56 95 9.09 5.36 15
Hull City 80 138 8.4 4.87 19
Sunderland 65 144 9.01 4.07 20

Value of R = -0.8417, a strong negative correlation (negative, because a high Q value correlates strongly to a low league position value, which is in turn a high league position).

2015/16

Team Shots, on Target Shots on Target Faced Shot Conversion Rate (inc. Blocks) Q League position
Tottenham Hotspur 252 122 10.47 21.63 3
Manchester City 210 128 11.54 18.93 4
Leicester City 179 142 13.03 16.43 1
Arsenal 211 152 11.38 15.80 2
Liverpool 202 132 10.02 15.33 8
Southampton 166 139 11.37 13.58 6
Manchester United 144 125 11.4 13.13 5
West Ham United 185 167 11.65 12.91 7
Everton 175 184 12.02 11.43 11
Chelsea 173 176 11.22 11.03 10
Newcastle United 151 179 11.08 9.35 18
Bournemouth 143 156 9.7 8.89 16
Swansea City 136 168 9.52 7.71 12
Watford 140 169 8.99 7.45 13
Crystal Palace 153 173 8.32 7.36 15
Norwich City 129 172 9.35 7.01 19
Stoke City 128 179 9.79 7.00 9
Sunderland 141 223 10.93 6.91 17
West Bromwich Albion 107 158 8.76 5.93 14
Aston Villa 110 191 7.11 4.09 20

Value of R = -0.8554, a strong negative correlation (negative, because a high Q value correlates strongly to a low league position value, which is in turn a high league position)

2014/15

Team Shots, on Target Shots on Target Faced Shot Conversion Rate (inc. Blocks) Q League position
Chelsea 210 123 12.94 22.09 1
Manchester City 229 129 12.39 21.99 2
Arsenal 227 130 11.64 20.33 3
Southampton 169 114 10.61 15.73 7
Manchester United 180 140 12.11 15.57 4
Everton 166 130 9.94 12.69 11
Liverpool 192 142 8.81 11.91 6
Tottenham Hotspur 171 171 11.01 11.01 5
Crystal Palace 139 151 10.66 9.81 10
Stoke City 136 142 9.6 9.19 9
Swansea City 147 192 10.8 8.27 8
Leicester City 137 175 10.09 7.90 14
West Ham United 152 179 9.02 7.66 12
Newcastle United 143 163 8.55 7.50 15
West Bromwich Albion 132 186 9.22 6.54 13
Hull City 131 159 7.71 6.35 18
Aston Villa 125 170 7.42 5.46 17
Queens Park Rangers 150 217 7.87 5.44 20
Sunderland 130 193 7.6 5.12 16
Burnley 125 185 6.51 4.40 19

Value of R = -0.8893, a strong negative correlation (negative, because a high Q value correlates strongly to a low league position value, which is in turn a high league position).

2013/14

Team Shots, on Target Shots on Target Faced Shot Conversion Rate (inc. Blocks) Q League position
Manchester City 238 122 15.16 29.57 1
Liverpool 258 152 15.51 26.33 2
Chelsea 229 122 10.26 19.26 3
Arsenal 213 157 13 17.64 4
Manchester United 183 144 12.17 15.47 7
Everton 196 153 10.87 13.92 5
Southampton 179 130 10.11 13.92 8
Tottenham Hotspur 192 157 9.35 11.43 6
Swansea City 161 155 10.91 11.33 12
Stoke City 137 180 10.51 8.00 9
Newcastle United 182 170 7.43 7.95 10
West Bromwich Albion 147 171 8.85 7.61 17
Hull City 132 163 8.9 7.21 16
Aston Villa 135 170 9.05 7.19 15
Crystal Palace 143 169 7.97 6.74 11
Fulham 149 245 9.28 5.64 19
West Ham United 122 207 9.48 5.59 13
Sunderland 138 214 8.35 5.38 14
Norwich City 148 193 6 4.60 18
Cardiff City 124 232 7.66 4.09 20

Value of R = -0.8678, a strong negative correlation (negative, because a high Q value correlates strongly to a low league position value, which is in turn a high league position).

2012/13

Team Shots, on Target Shots on Target Faced Shot Conversion Rate (inc. Blocks) Q League position
Manchester United 213 149 15.33 21.91 1
Manchester City 231 116 10 19.91 2
Tottenham Hotspur 241 128 9.69 18.24 5
Arsenal 205 143 12.06 17.29 4
Liverpool 232 141 9.61 15.81 7
Chelsea 212 161 11.98 15.77 3
Everton 207 147 8.69 12.24 6
Southampton 167 155 9.5 10.24 14
West Bromwich Albion 170 189 10.47 9.42 8
Wigan Athletic 170 182 9.4 8.78 18
Fulham 160 211 10.87 8.24 12
Aston Villa 141 189 10.73 8.00 15
Newcastle United 174 187 8.44 7.85 16
Swansea City 167 206 9.33 7.56 9
Norwich City 134 180 9.93 7.39 11
Sunderland 139 207 9.83 6.60 17
West Ham United 158 220 9.15 6.57 10
Stoke City 114 154 8.72 6.46 13
Reading 128 240 10.91 5.82 19
Queens Park Rangers 146 204 6 4.29 20

Value of R = -0.8615, a strong negative correlation (negative, because a high Q value correlates strongly to a low league position value, which is in turn a high league position).

2011/12

Team Shots, on Target Shots on Target Faced Shot Conversion Rate (inc. Blocks) Q League position
Manchester City 250 131 12.6 24.05 1
Manchester United 243 156 13.78 21.47 2
Arsenal 236 131 11.62 20.93 3
Chelsea 224 153 9.69 14.19 6
Tottenham Hotspur 230 160 9.42 13.54 4
Everton 164 133 9.62 11.86 7
Liverpool 207 129 7.05 11.31 8
Newcastle United 154 175 11.45 10.08 5
Fulham 195 198 8.87 8.74 9
Blackburn Rovers 143 186 10.6 8.15 19
Sunderland 141 171 9.83 8.11 13
West Bromwich Albion 167 173 8.27 7.98 10
Norwich City 164 216 10.12 7.68 12
Swansea City 145 188 9.32 7.19 11
Wigan Athletic 162 184 8.09 7.12 15
Bolton Wanderers 163 222 9.29 6.82 18
Aston Villa 138 176 8.45 6.63 16
Queens Park Rangers 150 198 7.98 6.05 17
Stoke City 94 178 9.57 5.05 14
Wolverhampton Wanderers 152 264 8.46 4.87 20

Value of R = -0.8471, a strong negative correlation (negative, because a high Q value correlates strongly to a low league position value, which is in turn a high league position).

 

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One comment

  1. […] having just posted something backing up a uMAXit piece I wrote, Simon Gleave made a suggestion about incorporating shot conversion rate against. So, I have done […]

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