In previous installments in this series I’ve broken down the history of team PDO and team save percentages — today I will concentrate on team shooting percentages. We’ve seen evidence suggesting that PDO is not just a random walk through peaks and valleys, it can be sustained in a fashion more than probability would allow. We’ve also seen that team save percentages are a large culprit for this behaviour — employing a good goalie is not something that should be attributed to luck. But what about team shooting percentages? I’ll treat this topic to the exact investigation I explored with the others.
To begin, I translated each team’s team 5 on 5 shooting percentage for each season since 2007-2008 into normal cumulative distribution scores between 0 and 1. 0.5 represents the mean, while one standard deviation below and above the mean would occur between 0.16 and 0.84, etc. Above 0.5 means you’re above league average, and below 0.5 means you’re below league average.
I’ve sorted the teams based on their 6-season average, with the top shooting team at the top, the Pittsburgh Penguins, and the offensively challenged San Jose Sharks at the bottom (wait, what?). Right away, you can see that a fair amount of teams are tending towards our long-run expectation of 0.50. To see this phenomenon in more detail, have a look at the 6-season averages in a chart:
You can see that many teams are now within the arbitrary yellow band within +/- 10% of 0.50 — in all, 16 out of 30 teams are inside the yellow band, while 7 more are just outside of it. This suggests that compared to PDO or team save percentage, team shooting percentage does exhibit a much stronger gravitational pull towards the expected long-run mean of 0.50. Here’s a table of the top and bottom 5 teams:
Here we see that the top and bottom teams in shooting percentage are closer to 0.50 than the similarly-placed teams in save percentage. There are some teams that likely could have been predicted on the best list — Pittsburgh has the benefit of the top two players of their generation playing on the same team, Chicago has elite offensive talent at all positions, Tampa Bay has Stamkos — but there is also a team like Dallas that’s somehow maintained a high degree of accuracy over the last 6 years. It is telling that the 5th best team here is only 2.2% away from being in the yellow band in the graph above. Tampa is only one down year away from their average being very close to 0.5.
The bottom 5 teams have teams I would have bet on being there beforehand, such as the Islanders and the Panthers, but also includes teams like San Jose and the Rangers, who’ve consistently employed some of the best offensive players in the league over this 6-year timeframe. This fact should start to raise questions of how a team which has employed Jaromir Jagr, Marian Gaborik, Brad Richards, and Brian Boyle could be considered a poor shooting percentage team over the long term. At least to me, it feels like there’s some randomness here.
But how much randomness? In my first post I created a probability tree that estimated what the expected probabilities were for a team to have 1 above average season and 5 below average seasons out of 6, or 2 above average and 4 below average, etc. The rationale is that if this was truly random, you have a 50% chance being either above or below average — it’s a true coin flip. The next step is to compare reality to theory — what percentage of teams performed as expected?
The behaviour seen in previous installments in this series are totally absent — this data definitely shows adherence to our expected probabilities, and even a bit of a central tendency:
If this data were random, we’d expect 31.3% of teams to have 3 above and 3 below average shooting percentage seasons. In reality, 36.7% of teams displayed such a strong central tendency. In terms of the far extremes of this graph that were so well populated in save percentages, we see that the actual % of teams tracks very well to the expected % of teams. To me, this suggests that team shooting percentages are randomized over the long-term.
Let’s test this using frequentist methods: I set up a regression model where I used one year’s shooting percentage for a team to predict that team’s following year’s shooting percentage. If this was not random, we’d see a statistically significant correlation between the two (a high shooting team tending to shoot high the next year, suggesting one year could be predictive of the other). In fact, I found the opposite. The two have a r-squared correlation of 0.003, meaning very little influence. The p-value for the prior year’s shooting percentage coefficient was 0.51, well above the <0.05 I’d need to reject the null hypothesis. Therefore, this is not a statistically significant relationship, and we can say that one year’s shooting percentage has no predictive power in determining next year’s for any given team.
Now I know some people will point to the team that has 6 straight years of above average shooting percentage (Dallas) and say: “if it’s random, then how is this possible?”. The answer is that chance allows for such a team to maintain such results over such a long period of time. Only 1 out of 30 teams has managed to maintain 6 straight years of above or below average results. It’s a rare event for sure, but it is expected.
This has implications for how we view luck and PDO in general. Team shooting percentages are seemingly random, and we should expect those to regress to league average over the long term. But we’ve also seen that team save percentages are not random, and can be sustained at high or low levels. Expecting PDO (a combination of the two) to regress to league average, therefore, is misguided. A new method needs to be fashioned to properly gauge how ‘lucky’ a team is. I’ll take a crack at that in the next part of my series.