If you’d read our site at all, you know that part of the process we go through is to try and calculate various statistics that help describe how a team or player operates. Sometimes they are helpful, and sometimes they aren’t.

Take offensive efficiency for example. If we want to know how a team does on offense, knowing the percentage of their possessions that result in goals is a pretty good place to start. Once we have that, we have more or less determined who has a good offense, and who doesn’t. Simple.

Then there is something like shooting percentage. The story here is a bit more nuanced. In theory, the more of your shots that find the net, the better. But you could imagine a team missing the net a lot, backing up those shots, and scoring after a long possession of probing the defense.

This team could have a low shooting percentage, but a high offensive efficiency. You’d rather have the latter of course, but that does not mean that a lower shooting percentage is better. It just means that the shooting percentage statistic doesn’t give you the whole story. All things equal, you’d still rather have a higher shooting percentage.

Then there is shots per possession, which is in a class of its own: I have no idea whether a high number of shots per possession is better than a low number.

It’s an interesting stat though. On an average possession, how many shots does the team get off? If you scored a goal on your first shot every time down the field, you’d have a shots/possession value of 1.0. If you were to launch a shot over the net, back it up, and score the next time you’d have a value of 2.0. If you turn the ball over before getting a shot off half the time, you’d be around .5 shots/possession.

Coming into this analysis/post, I had not figured out what sort of signal, if any, exists in this statistic, but it seems like there is something interesting there. A team that is always putting shots on net is probably going to have a fairly low number; their shots are either getting saved or resulting in goals. A team that is launching a bunch of shots that are getting backed up is going to have a high number, but probably a low shooting percentage.

The point is that there is a trade-off between shooting percentage, time-of-possession, shots/possession, and probably turnover rate. As an analyst, these are the interesting things to look at. How do teams balance those trade-offs?

Let’s start with the basics

Shots/Poss Off Efficiency Shooting % Turnover % Win Rate .66 – .76 21.6% 30.5% 42.2% 34.9% .76 – .85 24.9 31.1 37.3 48.6 .85 – .95 26.5 29.4 36.4 50.4 .95 – 1.05 28.1 28.2 34.3 53.8 1.05 – 1.15 29.8 27.2 31.9 57.5 1.15 – 1.25 29.4 24.7 28.6 60.8

Each row represents the bucket of games where a team’s shots/possession number falls into the range in the first column.

As of this writing, there have been 302 games played this year, which means that there are 604 shots/possession stats (2 per game, one for each team) to look at. From the table above, it’s clear that we have answered our overarching question: having a higher number of shots per possession is definitely good.

Now that said, good teams win more games. It also appears that good teams take more shots / possession. (Very important that you not interpret this as: “shoot more shots per possession and you’ll win more”.)

I had not expected the relationship between shots/possession and win rate to be as strong as it seems to be. Shots/possession is a fairly complicated metric that is going to be influenced by many different factors (shooting percentages, back-up rates, time-of-possession). To see that it correlates so cleanly with the ultimate stat (winning percentage) is surprising.

I was also surprised that the relationship with turnover rate was so strong (in the negative direction). One hypothesis was that teams that take a lot of shots per possession have more chances to turn the ball over. We’ve seen that longer average possessions sometimes lead to higher turnover rates; I thought the same might be true here. It clearly is not.

Apples to apples

Now you might be saying: wait a second, if shots/possession is so well correlated with all these other positive metrics, why wouldn’t we assume that it’s just a side effect of being a good offense or team?

Well, let’s look at the gap between two teams instead of the raw number. Anecdotally, it is interesting that when you have more shots/possession than your opponent, you win more often than not. And when you have way more shots/possession, you win way more.

Shots/Poss Gap Off Efficiency Shooting % Turnover % Win Rate -.44 to -.34 21.5% 29.9% 44.1% 29.4% -.34 to -.24 23.3 29.2 38.6 32.7 -.24 to -.14 25.6 30.4 38.3 43.8% -.04 to .05 26.6 29.9 37.9 48% .05 to .15 26.6 28.1 35.0 55.1% .15 to .25 27.6 26.6 30.3 56.5% .25 to .35 28.0 25.8 31.1 64.7% .35 to .45 28.7 26.0 29.7 75.0%

The left-hand column now describes the how many more shots/possession a team had than their opponent.

Now, it is clear that this gap metric is still pretty cleanly correlated with offensive efficiency (although less so with shooting percentage). Again, it’s important to say that more efficient teams win more often AND they seem to tend to have a higher shots/possession metric relative to their opponent.

But remember, we are looking at the gap now. So let’s imagine 2 strong offenses, with high efficiencies and high shots/possession stats, do battle. Even if they came in with the exact same profile, we would expect the one with more shots/possession to win the game.

An important feature of a useful stat is that it is consistent. Shots/possession is clearly consistent (i.e. not random). The question is now whether it is just a more-complicated version of offensive efficiency? Or is there some additional nugget of insight here?

Putting on our Data-Detective hat

There is one thing that makes me think that shots-per-possession is more fundamental than efficiencies, which are obviously very influenced by the opponent. And the clue comes from some basic statistical concepts: standard deviation and variation.

I say fundamental in the sense of it being a defining characteristic of a team’s approach or skill-level. Offensive efficiency isn’t really fundamental to a team because it depends equally on the opponent as well as the team you are looking at. Conversely, pace is something that I would consider to be more fundamental. A team can play fast regardless of what their opponent does. It is more fundamental to who they are.

From a statistical point of view, fundamental stats should vary less from game to game. And that is where the coefficient of variation comes in. It is also where shots/possession starts to stand out.

Statistic Avg. Value Standard Dev. Coeff of Variation Turnover Rate 33.8% 11.2% .330 Shooting Pct 29.4% 8.5% .290 Efficiency 28.0% 7.7% .276 Shots/Possession .974 .183 .188

I looked at 2018 data (no shot clock, I know), to see how the 4 metrics above varied for each team over the course of the season. (I used 2018 data because it represents more games for each team; the same pattern holds so far in 2019 too.) As I discussed above, the more volatile metrics have the higher coefficients of variation.

I interpret the table above to mean that shots/possession is a more fundamental descriptor for an offense than the others. Conversely, seeing the high variation figure for turnover rate indicates that turnovers are highly influenced by the opposing defense (seems likely) or just fluky (less plausible).

So what does that mean? Well, for starters, it means that shots/possession is not just a dressed up version of efficiency, which is interesting.

Let’s get weird

Ok, so this has already been a fairly wonky post. If you are still with me, then I hope you will follow me a little bit farther.

Thus far, we’ve focused mostly on comparing shots/possession to other offensive metrics. We’ve determined that it is closely related to efficiency, but that it’s a more fundamental metric to a team’s offensive persona.

So the next logical place to go is to look at what happens when a team does stray from its normal approach. And we can do that using the same statistical approaches we used before.

First step is to classify each team-game in terms of how a team’s shots/possession differed from their season average. We can then compare the outcomes of the various degrees of difference. For example:

Relative Shots/Poss # of Games Pct of Games Efficiency Delta Win Pct -.17 to -.13 46 7.6% -2.2% 43.5% -.13 to -.09 47 7.8 -1.8 42.6 -.09 to -.03 58 9.6 +0.2 62.1 -.03 to .03 131 21.7 — 45.0 .03 to .07 58 9.6 +1.5 56.9 .07 to .11 50 8.3 2.4 54.0 .11 to .15 34 5.6 2.4 64.7

The far left column indicates how much a team’s shot/possession metric differs from their season average (this is 2019 data). So the top rows indicate the games where a team had fewer shots/possession than normal. Note that this doesn’t include all games as we excluded the extremely small number of games that fall outside of 1 standard deviation in either direction.

And we can see that increases in shots/possession broadly track with an improvement in the team’s efficiency (again, relative to their average). Which is consistent with the sections above. Where it gets a little funky is with the win percentages.

Since this covers all games, the average win percentage overall is 50%. Taking the top row as our example, when a team has between .13 and .17 fewer shots per possession (relative to their season average), they win 43.5% of their games. That is a net 6.5% reduction in win percentage associated with that type of game.

And at the margins, you see commensurate reductions or increases in both winning percentage and efficiency (i.e. the first two and bottom two rows). But in the middle rows, something strange happens.

Take a look at the 4th row, which represents games when teams are right at their season average. In those games, the average win percentage is 45%, 5 percentage points worse than average.

On either side of that, you see higher win percentages (62% in row 3 and 57% in row 5). What?!?! That means that this season, when a team is slightly above or below their long-term average in terms of shots/possession, they do better than when they are right at the average.

This does make a degree of sense. Remember that we found that turnover rate is largely a metric that is driven by the opposition. So across all games, we would not expect turnovers to influence a team’s shots/possession number. So if you exclude turnovers, shots/possession only changes if a) more shots go in (and therefore future shots in the possession aren’t needed or b) more shots miss the net and are backed up (since most shots are backed up by the offense).

In either case, you see a bump in efficiency, which is also what we see in the table. It gets interesting though, because in 2019 so far, the higher winning percentage comes when the efficiency bump was smaller and the shots/possession metric was slightly below the team’s average. (The same pattern holds up across the larger sample of all 2018 games as well.)

This goes back to the idea of shots/possession being something different than efficiency. Since the win rates are higher when shots/possession is lower and efficiency is slightly higher (than when efficiency is much higher), it follows that there is something beneficial about a lower shots/possession number in and of itself.

So if we are looking for a way to incorporate shots/possession into our understanding or coverage of the game, that seems like a good place to start.

If a team is generating far fewer shots/possession than their season average, look out; that is not good. If they are well above pace, then rejoice. If they are doing their normal thing and hovering around their season average, not much changes.

But…if you are watching a team that is slightly above or slightly below their long-term pace, that bodes well for their chances. It may be a small increase, but every bit counts. What is interesting is that this is across all teams, not teams with a certain shots/possession profile.

So there you have it. Shots/possession is a thing. More of it is better, except for some situations when maybe a little bit less is a harbinger of good things.