In the Gaps Between Models

In my Anatomy of a Shot I hinted that we might measure different component parts of xG and compare them. That’s exactly what I’m going to do in this post – take what I call chance quality, a form of xG that includes positional data but excludes the shot itself, and compare it to my expected save value for that shot. Because think about what happens between those two measurements – the first model says, “in general, teams have such-and-such a chance of scoring from some sort of shot over here”, the second says “shit, did you see that? He must have a foot like a traction engine.

What comes between those two models? Well, something resembling finishing quality, or at least good decision making. Even if a player isn’t converting a ton of chances, if they’re reliable making shots more difficult to save, they’re shooting well. If they’re taking prime quality chances but making them easy to save, well, maybe that’s rubbish shooting. That’s the theory at least, what do the numbers look like? Here’s everyone with 20+ shots in the Premier League this year:

Player Shots On Target Goals SoTR Conv% Chance Quality Save Difficulty SD/CQ SD-CQ
Olivier Giroud 23 12 4 52.17% 17.39% 14.43% 20.57% 142.57% 6.14%
Juan Mata 20 7 3 35.00% 15.00% 9.86% 15.08% 153.01% 5.23%
Sergio Agüero 33 14 6 42.42% 18.18% 12.44% 17.64% 141.77% 5.20%
Bafétimbi Gomis 23 11 4 47.83% 17.39% 14.17% 17.06% 120.40% 2.89%
Harry Kane 33 12 2 36.36% 6.06% 9.43% 12.28% 130.20% 2.85%
Ross Barkley 28 9 2 32.14% 7.14% 5.30% 7.92% 149.30% 2.61%
Jamie Vardy 38 17 9 44.74% 23.68% 15.73% 17.96% 114.18% 2.23%
Sadio Mané 26 10 2 38.46% 7.69% 9.42% 11.65% 123.63% 2.23%
Yohan Cabaye 21 8 4 38.10% 19.05% 16.11% 17.99% 111.70% 1.88%
Romelu Lukaku 28 12 5 42.86% 17.86% 12.59% 13.46% 106.91% 0.87%
Riyad Mahrez 25 11 5 44.00% 20.00% 13.27% 13.70% 103.22% 0.43%
Theo Walcott 26 12 2 46.15% 7.69% 14.68% 15.09% 102.83% 0.42%
Odion Ighalo 26 9 5 34.62% 19.23% 9.56% 9.61% 100.49% 0.05%
Graziano Pellè 38 11 5 28.95% 13.16% 12.60% 12.33% 97.88% -0.27%
Alexis Sánchez 45 15 6 33.33% 13.33% 12.17% 11.39% 93.53% -0.79%
Memphis Depay 25 8 1 32.00% 4.00% 8.09% 7.13% 88.15% -0.96%
Diafra Sakho 29 10 3 34.48% 10.34% 13.32% 11.82% 88.76% -1.50%
Philippe Coutinho 39 11 1 28.21% 2.56% 7.23% 5.68% 78.63% -1.54%
Santiago Cazorla 20 7 0 35.00% 0.00% 6.92% 5.28% 76.24% -1.64%
Jonjo Shelvey 21 7 0 33.33% 0.00% 4.83% 2.92% 60.54% -1.90%
Gnegneri Yaya Touré 26 8 1 30.77% 3.85% 9.23% 6.49% 70.28% -2.74%
Rudy Gestede 22 7 3 31.82% 13.64% 10.96% 8.10% 73.97% -2.85%
Aaron Ramsey 27 8 1 29.63% 3.70% 10.09% 6.94% 68.81% -3.15%
Jason Puncheon 20 3 0 15.00% 0.00% 7.08% 1.74% 24.65% -5.33%
Troy Deeney 23 4 0 17.39% 0.00% 8.43% 1.62% 19.28% -6.80%

I should note that the save difficulty number here, because I want an aggregate over all their shots, counts off-target shots as a save difficulty on zero. The raw number obviously averages out roughly to the global conversion rate of on-target shots (around 30%). So, we can see some players increase the average difficulty of their shots for keepers, others make them easier. I’ve calculated both the ratio (i.e. Juan Mata increases his shots’ difficulty by 1.5x), and the difference, (i.e. Juan Mata increased his shot quality of around 10% to a save difficulty of around 15%).

cq-vs-sd

To the right are better chances, top the top are better shots. You can see examples like Olivier Giroud and Sergio Agüero, who are making already quite good chances even scarier, Ross Barkley’s making bad chances look very slightly more exciting, and Jason Puncheon and Troy Deeney just need to stop.

Let’s look at a bigger sample, here’s 2014, 50+ shots:

Player Shots On Target Goals SoTR Conv% Chance Quality Save Difficulty SD/CQ SD-CQ
Nacer Chadli 54 22 11 40.74% 20.37% 9.69% 16.00% 165.11% 6.31%
Steven Gerrard 55 22 10 40.00% 18.18% 13.18% 18.66% 141.62% 5.48%
Olivier Giroud 70 29 14 41.43% 20.00% 11.49% 15.67% 136.36% 4.18%
Diego Da Silva Costa 76 37 20 48.68% 26.32% 15.22% 19.36% 127.25% 4.15%
Harry Kane 113 48 22 42.48% 19.47% 11.65% 15.71% 134.87% 4.06%
David Silva 66 27 12 40.91% 18.18% 11.51% 15.26% 132.61% 3.75%
Eden Hazard 78 33 14 42.31% 17.95% 13.94% 16.87% 121.04% 2.93%
Aaron Ramsey 63 17 6 26.98% 9.52% 8.56% 10.81% 126.27% 2.25%
Wayne Rooney 79 27 12 34.18% 15.19% 10.89% 12.66% 116.25% 1.77%
Mame Biram Diouf 55 22 11 40.00% 20.00% 17.00% 18.71% 110.01% 1.70%
Robin van Persie 76 37 10 48.68% 13.16% 13.27% 14.92% 112.41% 1.65%
Ayoze Pérez Gutiérrez 61 24 7 39.34% 11.48% 10.37% 12.02% 115.85% 1.64%
Bafétimbi Gomis 69 24 7 34.78% 10.14% 9.50% 11.10% 116.76% 1.59%
Raheem Sterling 84 33 7 39.29% 8.33% 8.96% 10.52% 117.51% 1.57%
Jonjo Shelvey 63 20 4 31.75% 6.35% 7.44% 8.92% 119.87% 1.48%
Charlie Austin 130 53 18 40.77% 13.85% 12.41% 13.86% 111.67% 1.45%
Gylfi Sigurdsson 67 24 7 35.82% 10.45% 7.50% 8.91% 118.77% 1.41%
Kevin Mirallas 52 16 7 30.77% 13.46% 7.63% 8.76% 114.92% 1.14%
Sergio Agüero 148 62 26 41.89% 17.57% 14.82% 15.75% 106.32% 0.94%
Saido Berahino 86 37 14 43.02% 16.28% 13.67% 14.59% 106.71% 0.92%
Alexis Sánchez 121 49 16 40.50% 13.22% 9.97% 10.85% 108.90% 0.89%
Charlie Adam 62 17 7 27.42% 11.29% 7.53% 8.34% 110.69% 0.80%
Sadio Mané 60 25 10 41.67% 16.67% 11.93% 12.68% 106.30% 0.75%
Christian Eriksen 97 26 10 26.80% 10.31% 7.22% 7.94% 109.90% 0.71%
Christian Benteke 80 29 13 36.25% 16.25% 12.29% 12.96% 105.43% 0.67%
Leroy Fer 54 14 6 25.93% 11.11% 8.47% 9.02% 106.47% 0.55%
Stewart Downing 70 19 6 27.14% 8.57% 6.73% 7.14% 106.10% 0.41%
Riyad Mahrez 63 24 4 38.10% 6.35% 7.65% 7.97% 104.15% 0.32%
Gnegneri Yaya Touré 89 27 10 30.34% 11.24% 8.66% 8.98% 103.61% 0.31%
Romelu Lukaku 106 43 11 40.57% 10.38% 11.56% 11.65% 100.81% 0.09%
Nikica Jelavic 57 15 8 26.32% 14.04% 10.53% 10.55% 100.23% 0.02%
Diafra Sakho 66 22 10 33.33% 15.15% 13.53% 13.52% 99.97% -0.00%
Craig Gardner 56 18 3 32.14% 5.36% 7.57% 7.49% 99.01% -0.07%
Wilfried Bony 89 35 11 39.33% 12.36% 11.33% 11.15% 98.43% -0.18%
Danny Ings 97 33 11 34.02% 11.34% 11.41% 10.65% 93.35% -0.76%
Jordan Henderson 50 14 6 28.00% 12.00% 9.95% 9.17% 92.16% -0.78%
Dusan Tadic 53 21 4 39.62% 7.55% 11.21% 10.32% 92.10% -0.89%
Danny Welbeck 58 23 4 39.66% 6.90% 12.18% 11.24% 92.33% -0.93%
Philippe Coutinho 103 34 5 33.01% 4.85% 6.13% 5.11% 83.40% -1.02%
Willian Borges Da Silva 55 17 2 30.91% 3.64% 6.90% 5.70% 82.65% -1.20%
Jason Puncheon 65 20 6 30.77% 9.23% 6.28% 5.06% 80.63% -1.22%
Oscar dos Santos Emboaba Junior 72 23 6 31.94% 8.33% 8.43% 7.17% 85.05% -1.26%
Santiago Cazorla 93 33 7 35.48% 7.53% 12.00% 10.44% 87.04% -1.55%
Ángel Di María 61 18 3 29.51% 4.92% 6.06% 4.38% 72.26% -1.68%
Yannick Bolasie 69 19 4 27.54% 5.80% 7.49% 5.80% 77.43% -1.69%
Abel Hernández 52 19 4 36.54% 7.69% 11.66% 9.95% 85.33% -1.71%
Gabriel Agbonlahor 53 17 6 32.08% 11.32% 11.33% 9.34% 82.39% -2.00%
Ross Barkley 51 14 2 27.45% 3.92% 7.31% 5.27% 72.01% -2.05%
Connor Wickham 83 24 5 28.92% 6.02% 9.04% 6.88% 76.11% -2.16%
Enner Valencia 72 21 4 29.17% 5.56% 10.62% 8.05% 75.77% -2.57%
Ashley Barnes 66 21 5 31.82% 7.58% 11.15% 8.33% 74.71% -2.82%
Graziano Pellè 123 38 12 30.89% 9.76% 14.29% 10.80% 75.61% -3.49%
Mario Balotelli 56 20 1 35.71% 1.79% 10.08% 6.51% 64.60% -3.57%
Peter Crouch 59 17 8 28.81% 13.56% 13.07% 8.63% 65.99% -4.45%

Which in turn looks like this:

cq-vs-sd-2014

Steven Gerrard’s numbers here are padded a bit by penalties, but he took good penalties, so you can see the boost he gets. Costa was a monster, Nacer Chadli was incredibly sharp (though seems to have crashed hard this season, basically halving the xG on every shot). Ross Barkley’s chances were just as bad, but unlike this year, they didn’t go in. Jason Puncheon just needs to stop.

So this is fun, but is it really any more interesting than conversion rate et al? Let’s look at how predictive each season is of the next. I’ll limit it to full seasons, players with 50+ shots. Here’s how various metrics perform:

Metric R2
2011-2012 2012-2013 2013-2014
SoTR 0.1967 0.041 0.0215
Conversion 0.4299 0.1271 0.2224
Scoring % 0.1844 0.0228 0.0584
SD/SQ 0.2122 0.2436 0.1161
SD-SQ 0.3498 0.2729 0.0929

While it’s clear we haven’t found the holy gail of a strongly repeatable shooting metric, I still like our composite model. It has the benefit that as my chance quality and save difficulty models get better, these numbers may also improve, and I’ll be sure to look into that.

At the very least, I think the idea of having small, granular models, and looking at the gaps between them is an interesting way to find some new metrics and insights, and I’ll see what else I can find with a similar approach.

In the Gaps Between Models

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