## Shooting Percentage vs. Shot Rate: Sidney Crosby Edition

Why is Sidney Crosby so bad between Saturday and Tuesday?

To the best of my knowledge, I’m the first person to ask that question. Yet Crosby’s statistics for last season show that he was a substantially better scorer between Wednesday and Friday than on other days of the week. Here are his numbers, by weekday, pro-rated to 10 games each:

• Sunday: 12 points, minus-5
• Monday: 10 points, minus-5
• Tuesday: 14 points, minus-2
• Wednesday: 19 points, plus-5
• Thursday: 22 points, plus-2
• Friday: 22 points, plus-10
• Saturday: 14 points, even

Looking back over Crosby’s career, we see a lot of variation. In 2007-08, this pattern is essentially reversed, with Saturday through Tuesday all being very strong days, but Wednesday through Friday being bad days. In 2006-07, Crosby’s play dropped off on weekends. In 2005-06, he could do no wrong on Fridays.

Maybe there’s a cause. Maybe Crosby studies Spanish one day a week, and it exhausts him mentally (or fuels his creativity?), but it’s a different day each year. More likely though is the notion that this is all completely random. The amateur psychologist in all of us could undoubtedly rationalize some sort of explanation. However, as I looked through his weekly data over his NHL career, I could find no pattern in his scoring results. I did notice some interesting things, though.

Let’s start with variance. Shot rate fluctuated very little over different days of the week; Crosby averaged 3.19 shots per game with a standard deviation of 0.61. Points were slightly less stable, and shooting percentage was off the map. Here are the relative variances (square of the standard deviation divided by the square of the mean multiplied by 100) for each measurement:

• Shot Rate: 3.66%
• Total Points: 4.67%
• Shooting Percentage: 30.2%

What does that mean? Basically, it means that while shot rate (and to a lesser extent total points) are highly repeatable, shooting percentage is almost completely random. That’s a very important thing to know, because point scoring (and more specifically goal scoring) are highly dependent on shooting percentage, more so than on any other factor.

### Application

Let’s move away from the math and consider what this means in the real world. Basically, what it means is that Sidney Crosby will shoot the puck at a consistent rate. He’ll hover close to three shots per game every game, with very little change. However, the number of pucks that go in on a given day, or in a given week, or over a 10-game span will vary wildly, because his shooting percentage varies wildly. In other words, we would expect a lot of variation in how many goals Crosby scores simply as a result of chance (or if you prefer, luck).

Other factors come into play as well over the course of a season, including injury, emotional state and all sorts of external factors both tangible and intangible (linemates, ice-time, power-play opportunities, chemistry, etc.). I would never argue that these aren’t there, or that they have no impact.

However, I do think that most people around the game make too much of intangible factors when they analyze a player on a streak. We hear about confidence, improved conditioning, chemistry with linemates, different mental approaches to the game, new custom-designed sticks, clutchness, and all sorts of things causing the streak. But the fact of the matter is that we expect these streaks anyways. They happen for other reasons besides chance, but many of them would happen simply due to chance alone. Certainly streaks caused by improved shooting percentages should be viewed in this light; there’s so much noise there that it’s impossible to tell what’s due to improved effort and what’s simply the result of luck.

Shot data, on the other hand, is highly repeatable, with very little variation. Thus, while Crosby’s (or by extension, any other player’s) shooting percentage might drop or spike for no reason, a drop or spike in shot rates is highly unlikely, even over a short sample. Generally, there’s a cause for it. If a player’s shot rate drops off, there’s probably a concrete reason for it. If it spikes, there’s probably a concrete reason for that too.

One example of this is the contrast between Vincent Lecavalier and Steven Stamkos, a contrast I’ve mentioned previously. Lecavalier is firing pucks at the net at a rate of 3.5 per game, up from his career average of 3.0. However, his shooting percentage is clocking in at 6.3%; half of his career average of 12.6%. That’s probably chance. Meanwhile, Stamkos has improved his shot rate, from 2.3 shots per game to 3.2 That’s a definite jump, but his shooting percentage spike (12.4% to 22.4%) is probably luck. Notably, Lecavalier’s shot rate is still higher than Stamkos’. More significantly, Lecavalier’s on-ice shot rate is quite a bit better than Stamkos’, strongly suggesting to me that Lecavalier is the superior player at this point in their respective careers.

That’s not to say that players don’t have different odds of scoring; I strongly believe that shooting percentage varies from player to player. What I am saying is that it also varies wildly from day to day for the same player.

1. Great article Jonathan. As Usual.

Using Crosby as an example makes a lot of sense, because of how universally he is regarded as an elite player in the league, and the comparison between Stamkos and Vinny is also quite good, especially considering the comments about the two on the interweb this season.

Based on the shooting data you have for Sid, and the variance of his “good days” and “bad days” throughout his seasons in the NHL, it would suggest that there would be a very qeak correlation between players actually having days of the week when they are better/play better hockey. Have you ever run across data on a player that suggests the opposite?

2. Jordan:

Thanks.

To answer your question, no. I’ve never seen anything to indicate that players would be better on Wednesdays or Saturdays or whatever. I’ve heard commentators bring it up before (generally in reference to Sunday afternoon games) but I believe it should be completely random.

3. Your intro had me ready to lay into you, sir.

I thought this was going to be a Kevin Quinn-like piece.

Awesome work here, this should be part of Hockey 101.

4. love your articles, really interesting how you put his goal scoring as “luck”, guess you gotta be good to be lucky and lucky to be good.