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.