Observed Distribution of Shooting Talent
by Hawerchuk on Jul 29, 2010 9:00 AM EDT
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Don't ask me why, but I was thinking about how unlikely it was that Jody Shelley scored two goals in the final two games of the regular season, and I got to wondering about the spread of shooting talent in the NHL. I think this chart pretty clearly shows the range of talent we're trying to pick out:
So to explain this chart: I calculated the expected shooting percentage (aka shot quality or shot location) for every initial non-rebound shot taken on the road by every player at 5v5 over the last five seasons. Then, for the players shown above, I randomly selected 100 of their shots and looked at how much they exceeded the expected shooting for the league as a whole. I repeated this process 1000 times to arrive at a distribution for their mean talent.
Note that there is not one player in the entire NHL who - by this method - we can say is an above-average or below-average shooter with 95% confidence. Kovalchuk is very close, and we can be extremely confident that he's a better shooter at 5v5 than Jody Shelley, but we can't even be sure of that after five years of watching Kovalchuk's slick offensive play and Shelley's brutal hands. (I'm willing to bet on Kovalchuk, btw...I'm just saying we don't know for sure...)
Now keep in mind that this doesn't capture a player's ability to get in position to take a shot. Andrew Brunette led the league in shooting percentage last season because he has the ability to frequently get an open shot right around the net. But once he has the puck, he is no more likely to pick the top corner from those same spots as any other player.
Edit:
Another way to see what's going on here is through histograms (the PDF as opposed to the CDF) of shooting performance. It's possible that Jody Shelley will outshoot Kovalchuk over their next hundred shots. It's just very unlikely.
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What are your parameters for “Goons”?
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by Bettman's Nightmare on Jul 29, 2010 1:42 PM EDT reply actions
So counterintuitive.
Its hard to accept that snipers known for their shot aren’t better able to pick corners from similar spots. It sure seems like they are. I know that players have a feel for their own shot and tend not to take it when they don’t believe they have a chance to score. But that wouldn’t explain shooting % on equal shots.
What if you took every single shot of Kovalchuk’s career and computed the expected scoring % to get the expected career goals and then compared that to his actual goal total, instead of randomly selecting 1000 100 shot samples. Can’t you compute the probability that Kovalchuk would have scored the # of goals that he scored if he was an exactly average shooter? Then we could say that that’s the chance that he’s really an average shooter. My intuition tells me that it would be much less than 5% (that is much greater than 95% that he’s better than average). I don’t know how to do that though.
consider this, though:
A: it’s only counting 5 on 5
B: this isn’t measuring ‘true accuracy’ – true accuracy would, IMO, be using missed shots and shots on goal. i’d be real curious if anyone’s done any work with that, because that’s where i would suspect we’d see some of the shooting skill show up.
Cool idea, and terrific execution.
For my eyes and brain, that graph would have been easier to digest if you’d plotted each of the players out as histograms. So Kovalchuk would be a bell shaped curve centred at about +5 with tails petering out well before -5 and +15.
And I’m sure that would represent a probabalistic forecast of the “Gabe’s Shooting Talent” for Kovy’s next 100 5v5 shots on goal. NOT his talent level at shooting. His talent level likelihood distribution would be much narrower, because the dude has taken a tonne of shots over the last five years, so we know more about him.
It might be just me getting confused by the wording in your post.
Would you agree, though, Gabe?
yeah, I was thinking histograms and I changed my mind. I kind of like the idea of being able to see where the 90th %ile lies. I’ll generate a new plot with histograms when i get a chance.
I think you’re right about the talent vs next 100 shots. But with better information (giveaway, one-timer, odd-man rush) they should converge more closely, right?
No, not at all, Gabe. Don’t get me wrong, I think your reasoning as expressed by your math here is terrific. I just am struggling to match your words to your math.
It’s a bit like PECOTA, it’s a forecast that manages to skip the step of building an ability likelihood distribution for the player or league. So that’s cool, I mean this what we’re really after. It’s an end run around a lot of work.
Without doing the math, let’s say that your stuff shows that, over the next 100 5v5 non-rebound, non-empy-net shots … Shelley has a 3% chance of being a better shooter over that stretch than Kovalchuk, as measured by your system. It looks like it would be in tha range, by eye.
I don’t doubt that. Hell, you could use this for wagering.
This does NOT mean that there is a 3% chance (33 to 1) that Shelley possesses more shooting talent than Kovy. The odds of that are more likely in the million to 1 range, probably more. Might be less if Shelley has taken a super low level of shots in his NHL career, and if we ignore his history outside the NHL. I don’t have the data. And it would be a tonne of work to figure that out.
The point is … talent level and forecast results are very different things. You’ve given us the latter, which is really what we’re after. So that’s cool.
Gotcha. Kovalchuk’s performance over the say 1 million shots necessary to determine true talent to within sufficiently tight bounds is almost certainly better than Shelley’s performance over same.
How would you construct an ability distribution for shooting? Look at regression to the mean for randomly-selected 100 shot samples?
I don’t know, Gabe. It would be a tough thing to model.
by Vic Ferrari on Jul 29, 2010 10:34 PM EDT up reply actions
Hey Gabe! Welcome back.
FWIW I like the second graph a lot better, too. Personally, I handle numbers better. Kovalchuk is +5 with a 90% CI of [0,10] or whatever.
I would model it as a logistic regression (like the goalie stuff I did) I plan to head that direction. I suspect there is going to be a signal to noise problem (big confidence intervals), but I also expect a wider range of talents (more like baseball hitters).
by DoctorMyBrainHurts on Jul 29, 2010 10:55 PM EDT up reply actions
This guy, for one, is shocked at this chart.
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