Time-To-Shot

Expected goals, in all its forms, lets us measure the danger of a shot. There are increasingly many non-shots expected goals models that go beyond this, measuring the danger of the attacks that build up to shots, or beyond, to cover all the different situations that can occur in a game. In fact here’s Sarah Rudd, now of StatDNA, talking about a model using Markov Chains all the way back in 2011. In the ideal world what we want is to be able to show a computer a game state – as if we’d been watching the game on TV and hit the pause button – and ask, how good or bad is this situation for each team?

Today I’m going to introduce an extremely simple (really, overly simple) approach to answering that question, called Time to Shot, or TTS. TTS looks at a particular game state and simply calculates the time – in seconds – until the team in possession makes a shot (Time To Shot For, or TTSF) and the time until their opponents make a shot (Time To Shot Against, or TTSA). The lower this time, the more dangerous the situation for one team or the other, the higher the time, the safer. Obviously this isn’t taking into account the quality of the shot, and that’s a pity, but it has the advantage that it’s enormously simple to implement.

In this post, we’ll use raw, real-world values for TTS, looking at team averages for a bunch of interesting situations. Then, over the next few days and weeks we’ll also see if we can build a predictive model that’s any better than just taking the average, so that we can ask more complicated questions. For example, which players reduce expected TTSF or increase expected TTSA the most? Which teams *cough* Leicester *cough* seem to be able to pull shots out of nowhere in contrast to their expected TTSF?

My hope is that ‘time to shot’ outputs are much easier to communicate, especially in neutral situations, than tiny probabilities. An xG from some possession far from the goal of about 1 in 1000 for and 1 in 3000 against is pretty hard to visualise. But if I tell you a specific game state is on average 120 seconds away from a shot for and 360 seconds away from a shot against, it’s a bit more grounded in reality.

It’s also easy to wrap your head around for particular short-term strategies:

  • Most of the time you’re looking to decrease your TTSF (to zero, hopefully) without drastically decreasing your TTSA.
  • If you are a counter-attacking team, you might allow a team to decrease their TTSF, as long as your TTSF is also coming down.
  • If you’re trailing towards the end of the game, you might risk reducing your TTSA for a decrease in your TTSF.
  • If you’re ahead in the dying minutes of a game, you’re probably more concerned with increasing you TTSA at the expense of everything else.

Okay, I said it was easier to communicate and then used a bunch of abbreviations to make it sound complicated, but seriously, I just think it’s easier to visualise as a concept. And just so you know – if you have the ball, then on average you’re 4 minutes 3 seconds away from having a shot, and 4 minutes 57 seconds away from conceding one. This dearth of action presumably explains much of the defending we see in the MLS.

League Table

Here’s the TTS league table – TTS (F)or, (A)gainst and (D)ifference, the latter calculated as TTSA minus TTSF:

Team TTSF TTSA TTSD
Manchester City 185 395 210
Tottenham Hotspur 187 386 199
Liverpool 187 365 178
Arsenal 204 312 108
Manchester United 253 354 101
Chelsea 217 301 84
Bournemouth 255 334 79
Southampton 232 305 73
Leicester City 238 280 42
Everton 244 280 36
Stoke City 267 288 21
Aston Villa 282 287 5
West Ham United 245 249 4
Norwich City 284 280 -4
Swansea City 281 275 -6
Watford 278 266 -12
Newcastle United 269 256 -13
Crystal Palace 291 248 -43
Sunderland 289 236 -53
West Bromwich Albion 305 251 -54

On average, you’re 185 seconds away from a Man City shot, whereas millions of mayflies hatch into their adult form, only to die never having seen West Brom shoot. City are making history with their shots conceded numbers, and they win the TTSA battle here as you’d expect. Now, remember that TTSF and TTSA are values for the team in possession, so the average TTSA will be higher, as the opponent would need to first win the ball back before they can eventually make a shot.

Overall these numbers aren’t very interesting, nor are they news – we already have shot totals and per 90s, so what’s the point?

Pressing & Counterpressing

The point is, we can do things like this, splitting team’s values up by different event types:

Team Ball Recovery Dispossessed Interception Tackle
Tottenham Hotspur 184 211 211 212
Manchester City 186 196 206 222
Liverpool 196 253 199 222
Chelsea 206 215 250 247
Arsenal 212 221 242 237
Leicester City 246 227 283 280
Everton 247 224 302 310
Southampton 252 258 276 276
West Ham United 256 230 306 331
Manchester United 257 285 291 287
Bournemouth 259 309 272 308
Newcastle United 273 264 276 325
Stoke City 273 292 275 319
Norwich City 285 265 356 355
Watford 286 325 310 311
Aston Villa 289 316 336 345
Sunderland 290 323 315 333
West Bromwich Albion 294 329 367 345
Swansea City 301 329 298 291
Crystal Palace 306 322 348 300

These are the median TTSF values for a variety of actions related to pressing – note that Pochettino’s Tottenham are the quickest team on average to take a shot after a ball recovery. Liverpool aren’t far behind – under Rodgers this numbers was 217 seconds, with Klopp it’s been 191 on average, and indeed they lead the league on TTSF from interceptions. Look at Liverpool’s TTSF off dispossessions though – it seems low, implying that they’re not generating many shots from counterpressing opportunities.

These absolute numbers don’t necessarily tell us anything about team style – better teams get shots off more quickly no matter the situation. Let’s make sure we’re actually measuring a real pattern here, and look at the TTSF values as a percentage of the team’s average.

Team Ball Recovery Dispossessed Interception Tackle
West Bromwich Albion 83% 93% 103% 97%
Manchester City 83% 87% 92% 99%
Tottenham Hotspur 83% 95% 95% 96%
West Ham United 84% 76% 101% 109%
Bournemouth 85% 101% 89% 101%
Chelsea 85% 89% 103% 102%
Norwich City 86% 80% 107% 107%
Liverpool 86% 112% 88% 98%
Manchester United 87% 96% 98% 97%
Everton 88% 80% 108% 110%
Watford 88% 100% 96% 96%
Aston Villa 88% 97% 103% 106%
Leicester City 88% 82% 102% 101%
Arsenal 89% 92% 101% 99%
Newcastle United 90% 87% 91% 107%
Sunderland 90% 100% 98% 104%
Stoke City 95% 102% 96% 111%
Southampton 96% 98% 105% 105%
Crystal Palace 100% 105% 113% 98%
Swansea City 100% 109% 99% 97%

That dispossession number really sticks out now – as a percentage of their average, Liverpool’s TTSF off dispossessions is the worst in the league. Their pressing is certainly affording them some control, as detailed by Dustin Ward in his recent excellent piece on Liverpool, but they’re either unable or unwilling to create scoring opportunities from counterpressing.

Forget the minutiae of pressing for a moment, what I’m trying to show you is this: we have a metric we can employ for every team, anywhere on the pitch, for any type of event.

Defensive Areas

Part of the motivation for a metric like this is experimenting with replacements for ball progression in PATCH. Different teams allow ball progression in different areas, because they’re set up to deal with it. A famous example this year is Leicester, who often allow opponents to penetrate down the wings, because their low block is often able to mop up afterwards. These tables represent a football pitch split into a 10×10 grid, with the defending goal in the middle on the left. The percentages are the ratio of the opponent’s TTSF in that grid square, compared to the global average. So, high, green values are safer spaces – areas where the opponent is usually further away from a shot. Low, red values are areas in which opponents are closer to a shot on average. Here’s Leicester:

Area 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
0-10 95% 143% 108% 142% 97% 137% 87% 135% 82% 74%
10-20 178% 59% 71% 86% 77% 96% 121% 62% 13% 75%
20-30 56% 18% 93% 79% 110% 88% 99% 115% 172% 93%
30-40 66% 24% 60% 123% 144% 92% 121% 89% 111% 105%
40-50 1% 34% 86% 146% 53% 115% 75% 196% 164% 80%
50-60 196% 120% 44% 93% 104% 42% 90% 124% 108% 113%
60-70 67% 63% 76% 50% 85% 101% 154% 129% 50%
70-80 149% 6% 108% 115% 170% 104% 104% 132% 164% 144%
80-90 86% 20% 98% 89% 118% 49% 233% 130% 99% 86%
90-100 93% 102% 116% 107% 75% 115% 93% 109% 81% 51%

You can see that in their own half, down the flanks, Leicester keep their opponents to an above average TTSF. Compare and contrast to Everton:

Area 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
0-10 74% 63% 68% 76% 93% 105% 55% 135% 113% 82%
10-20 23% 89% 98% 74% 76% 137% 132% 76% 110% 42%
20-30 16% 29% 112% 115% 95% 55% 61% 94% 189%
30-40 1% 137% 67% 71% 120% 77% 58% 42% 106% 102%
40-50 86% 10% 105% 52% 99% 62% 80% 93% 101% 125%
50-60 122% 35% 116% 52% 125% 85% 87% 129% 62% 124%
60-70 149% 73% 36% 53% 119% 98% 88% 81% 95% 102%
70-80 15% 12% 74% 97% 83% 127% 125% 122% 92% 37%
80-90 35% 35% 61% 28% 61% 120% 93% 103% 51% 333%
90-100 31% 37% 59% 97% 111% 175% 91% 120% 89% 94%

Everton seem pretty weak down the flanks in comparison. You can imagine plugging this into PATCH – look at each opponent’s attacking moves, observe the average opponent’s TTSF values, and instead of judging a defender by the ball progression, judge them by how much closer we think the opponent is to a shot having been allowed to move through that defender’s territory.

Again, there’s no magic here, I’m just hoping to convince you that this is a flexible little metric that we can apply to all sorts of situations.

Time Wasting

Another simple application is time wasting. Which teams are best at keeping their TTSA up when they’re leading? This table shows TTSA at +1 goal difference as a ratio of the team’s TTSA when tied, all limited to 80 mins plus, when we’re reasonably sure a team ought to be protecting their lead:

Team Ratio Games
Liverpool 291% 12
Sunderland 196% 7
Norwich City 188% 6
Watford 139% 8
Aston Villa 127% 3
Crystal Palace 104% 9
Newcastle United 101% 6
West Bromwich Albion 97% 11
West Ham United 97% 10
Bournemouth 96% 8
Stoke City 87% 9
Chelsea 86% 8
Manchester City 85% 6
Southampton 77% 7
Swansea City 66% 9
Manchester United 65% 13
Arsenal 62% 9
Tottenham Hotspur 57% 10
Everton 56% 6
Leicester City 45% 13

We can probably ignore Villa as it’s such a small sample size, but Liverpool are the kings of sitting on a 1 goal lead with safe possession. This is slightly odd as their collapse against Southampton is fairly fresh in the mind, but it’s true – one goal up after 80+ minutes their shot suppression numbers are good in absolute terms, but even better compared to tied game states. Also riding high are Sunderland, helmed by Sam Allardyce, who rates well in an analysis by Daniel Altman about teams camping out in the corner when ahead at the end of the game.

At the other end, Leicester, who have recently extended their run to five 1-0 victories in six matches… what’s up with that? Well, obviously they’re up 1-0 a lot, but that doesn’t explain why this relative value is so bad – but it’s real. They really are losing the ball and conceding shots more than twice as quickly when defending a lead than when tied. I suppose this is their “bend, don’t break” defence in action, i.e. do all the things a bad defence would do, short of losing. ¯\_(ツ)_/¯

Substitute Effects

Let’s have a look at how substitutes affect teams’ TTS numbers. There are certainly some interesting outliers:

Team TTSF TTSA
Tottenham Hotspur 100% 81%
Southampton 87% 91%
West Ham United 80% 96%
Everton 112% 101%
Chelsea 115% 102%
Newcastle United 114% 111%
Manchester City 114% 114%
Watford 113% 118%
West Bromwich Albion 61% 125%
Sunderland 105% 127%
Swansea City 87% 127%
Stoke City 97% 128%
Leicester City 109% 128%
Norwich City 127% 130%
Liverpool 81% 131%
Aston Villa 88% 133%
Bournemouth 98% 136%
Crystal Palace 115% 138%
Arsenal 97% 139%
Manchester United 97% 149%

When Pulis sends a man on, a shot will surely follow. Now that’s probably not a huge surprise, if perhaps he only makes substitutions before corners – for my sins I didn’t check, because look at that other number sticking out like a sore thumb: when Tottenham make a substitution, their TTSA falls to 81% of its usual value! I asked a few people about this possible pattern on Twitter, and a few pointed the finger at the looming presence of Ryan Mason. More generally, it seems possible that either Pochettino’s system requires a degree of concentration that can be disrupted by substitutions, or perhaps Tottenham’s squad depth is lacking and the subs are just plain bad. Or maybe he just sends people on before defending corners. Either way, an interesting one to follow up later.

John Stones

One final one, just because I thought it was too cute not to share. John Stones, as we know, likes to bring the ball forward at his feet. We’ve seen his Cruyff turns, but what do they contribute? Well, the time-to-shot-for from a John Stones take on is 258 seconds. The time-to-shot-against? 258 seconds. That’s right, every time you see him dribble, you will know that we stand delicately positioned at the nexus of possibilities, a cosmic coin-flip deciding whether Stones is to be the hero or the villain.

Conclusions

So, there you have it, Time-to-Shot, a dead simple metric for measuring all sorts of stuff. Given that some of the results above are a little surprising, we ought to poke deeper and make sure we’re not missing anything important. There are certainly some caveats:

  • Events occurring when there is no shot for the rest of the half don’t get a TTS value, so this generally skews the values lower than they should be. One way around this is giving missing values a static, high value for TTSF and TTSA, but that’s a bit arbitrary.
  • Sample sizes for calculating averages drop the more criteria you add, increasing the uncertainty.
  • We don’t include any measure of shot quality. This is another model that reflects Liverpool’s good work at reducing the number of shots they concede, but ignores the quality of chances they conceded, which has at various points undone all that work.

Next stop is the almost impossible task of creating a predictive model to estimate TTS values for events. It’s unlikely we’ll get close to the average (still pretty bad) accuracy of an xG model, but being able to compare player’s actual TTS values to even a vaguely sensible estimate will hopefully give us some interesting results in the aggregate.

I hope you don’t think this metric is just complete junk, though I’ll admit I’ve been back and forth about it for a long while. It is certainly not as powerful as a decent non-shots xG model, but the fact that it can be applied to so many different situations with such ease is hugely attractive to me. If a predictive model is at all possible I think it’ll yield some useful results. Either way, happy to take the abuse here or on Twitter if you think it’s not worth pursuing. Alternatively, if there are any interesting teams or situations you’d like to see measured with this approach, get in touch.

I’m also looking for feedback on these new slightly garish colour-scale tables. I’ve gone with a design that I think is clearest at a glance, but it might be too much for people. Other designs are available.

Time-To-Shot

11 thoughts on “Time-To-Shot

  1. Daniel Ambrus says:

    Hi Thom, my first time reading one of your posts. I’m a doc in the US with epidemiology training and a big Arsenal fan. My first thoughts when I see descriptive statistics: a) what constitutes a “normal” value? What is the range and mean/median for the PL as a whole? b) are the data points normally distributed, or skewed? and c) how precise this measurement? do you have a standard deviation for the mean values? This information would give these numbers some context.

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  2. Person from the Internet says:

    “if you have the ball, then on average you’re 5 minutes 53 seconds away from having a shot, and 6 minutes 49 seconds away from conceding one”

    Not sure I understand these numbers in light of the table below it. 5 minutes and 53 seconds would be 353 seconds, yet not a single team in the table has a TTSF of 553 seconds. How can that be the average?

    Also, if you can give more information without giving anything away, how did you calculate TTS for given events? For example, I might have a ball recovery, but then I give the ball away, then recover it again, and give it away again. But then I have a successful tackle and eventually I get a shot off before I give the ball away again. From which of those events are you starting your time clock? Lots of possession changes and all kinds of non-unique occurrences of the events you separate by happen between shots.

    For a simple metric I seem unnecessarily confused by some of this.

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    1. Thom Lawrence says:

      The answer to your first question is that I apparently set out to deliberately confuse people by calculating the mean for that 5 mins 53 seconds stat, only to use the median elsewhere. Apologies, I’ll recalculate it to avoid further confusion – well spotted.

      Second, TTS is literally as simple as looking at every event, and calculating the time until the next shot, whatever happens in between. We don’t really care about the complexity of a series of events, because we hope that in the aggregate TTSF and TTSA give us information about whether things went well or badly.

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