I’m an Arsenal fan. It’s often not fun. That’s not a complaint about results. Most teams in the English league pyramid would love to have success like 18-straight Champions Leagues appearances (or whatever the number is). It’s just that the actual games themselves often make for stressful viewing because the Gunners rarely put teams away, even when they are destroying them in every way but the scoreline.

Of the four or five candidates for ‘Most Arsenal Thing’ of last season, all certainly involved Arsenal conceding. At least once. (I’d go with either leaving Skrtel unmarked at the back post in the 17th minute of stoppage time at Anfield; or Arsenaling away a 3-0 lead. At home. In the Champions League. To a team that didn’t even win its crummy domestic league.)

Anyway, Arsenal can’t hold a lead. At least it feels that way to me and probably Jacob Steinberg. And it particularly feels that way when they are up 2-0. It’s almost like, this past seasons, Arsenal caused opponents to score by going up two goals on them.

Here’s what that looks like:

Before:





After:







Okay, here’s what we’re looking at. This is R giving us a list of odds-multipliers (technically log odds-multipliers). We’re just looking at two of them. The first line—for ‘game.state1:shotTakentrailing’—is where a team has a 1-goal lead (game.state1) and the other team, the trailing team (‘shotTakentrailing’), takes a shot. It’s pretty literal, even if it’s all smushed together. The second line is the same but for a 2-goal lead.

To get anything intelligible we have to exponentiate that number; that tells us how much the odds a shot goes in change relative to nothing (in this case ‘nothing’ is the game being tied).

Or: e ^ -2.020992e-01 = 0.817

So the odds go down about 18.3% (1-.817 = .183)

If you’re still confused, just understand we took that number and did some math. The result of that math is it turns out it’s a little harder to score when you’re already down a goal. Specifically, the odds a shot goes in at 1-0 decrease by about 18% compared to the same shot if the score were 0-0 (or 1-1 or 2-2, etc.¹).

The period by itself (the ‘.’) across from ‘game.state2:shotTakentrailing’ means that, when down two goals, the odds don’t change². So, from a mathematic shot-probability standpoint, being down 2-0 is no different than being down 0-0³.

That’s the ‘Before’. Oh, here ‘Before’ is every shot from the EPL in the 2014-15 season. ‘After’ is after removing every shot taken against Arsenal for the entire season, then doing the same calculations. The idea here is that if teams really had a such an easy time scoring on Arsenal when down two goals, then once we remove those shots from the dataset, we should see that number move.

Turns out it doesn’t. Even without Arsenal in the data, a two goal lead is effectively no different than a tie game (the same as it was with our ‘Before’ set; there is a period across from “game.state2:shotTakentrailing’).

So we lied. Arsenal aren’t exceedingly easy to score on when they are up 2-0. More accurately, any effect of ‘just Arsenal’ isn’t large enough to impact the overall league probability that a team down 2 goals has a better or worse chance of scoring.

It’s not a trivial distinction. Arsenal might still be giving up goals pretty easily at 2-0—think of it as them maybe allowing counters or tap-ins with that lead—they just aren’t doing anything so terribly bad that it fundamentally alters the expectation any given shot goes in at 2-0 league wide. So whatever is happening isn’t enough to have any impact on the calculations. It still has an impact on the emotional stability of my soul, as well as what’s actually going on in the games. I counted 16 times last season that Arsenal established a 2-goal lead (if they went up two, conceded, then re-established the lead, I didn’t count the re-establishing). In those games they gave up the next goal six times. Is that a lot? I honestly don’t know. I haven’t (and probably won’t) compared that to the league as the whole. It’s still enough to make me uncannily nervous watching the Gunners.

And maybe that’s warranted because if you go back and look at the difference in the coefficients on the 1-goal leads, you’ll notice that, once you remove Arsenal, the odds-multiplier drops from 18.3 to 19.2. In other words, after we take Arsenal out of the data, it’s even harder to score when down a goal. So teams are finding it easier (relatively) enough to score against Arsenal when down a single goal that it is effecting the entire dataset. That’s bad.

We probably shouldn’t read a ton into that though as, fortunately (from an Arsenal fan standpoint), the change in the effect is so small that it’s not really making a major impact⁴. If we feed a couple of random shot values back in, it’s like the difference between a shot having a probability .0719 versus .0711 of going in. It’s less than a tenth of a percent.

Still, if the enduring league narrative—all hail the narrative—over the past few seasons is that Arsenal lack the mental strength (and defensive skill) to see games out, then numerically we’re not exactly destroying that myth. But we’re also not confirming our own confirmation bias. Win some, lose some.

¹ This is not true always and everywhere. We removed effects for home vs. away. And it’s using data for just the 2014-15 season in England. In fact ~20% might not even be a good rule of thumb (although it might be). It’s just what we get for this specific dataset with these specific variables. Heck, I’d bet it’s different for EPL seasons when Mourinho was managing elsewhere.

² Probably. Given the selection criterion used here this coefficient doesn’t have any effect.

³ This in itself is a bit interesting. The whole notion that a 2-goal lead is ‘dangerous’ has been fairly debunked. However, here we’re seeing a possible numeric indication that defenses aren’t as ‘switched-on’ up two, as when they have only a one goal lead (we’ve got a lot of non-psychological effects, too; so this is more theoretical). And yes, ‘being down 0-0’ was intentional.

⁴ There are all kinds of variables here. And most of the information in whether a shot goes in isn’t in the score differential. So for grins we re-ran everything using ONLY the score difference and whether the leading or trailing team shot as variables. The results were pretty much identical. Removing Arsenal has no impact on a 2-goal lead. And they made it slightly easier to score league-wide at 1-0. Gotta admit, I’m more than a little surprised by the results at 1-0, particularly when considering that Arsenal allowed the second-fewest number of goals over the course of the season. Arsenal gave up tying goals six times when up one. Now they might have been on bad shots or on fewer shots (and bad ones) such that it’s having a small effect. Also we pulled out own goals and penalties, that might be influencing things. On the plus side I have a theory as to what is actually happening and it might not be the ‘fault’ of Arsenal at all. But that’s for another post.