Editor's note: John has been a long time community member, and I've invited him to jump up from fanposts to actual posts. Please welcome him!
Author's Disclaimer: I'll only be talking about even strength stats here, and I've gotten all of my numbers from stats.hockeyanalysis.com.
Last year, Matt Beleskey was easily a better goal scorer than Milan Lucic was. He ended the season with 18 even strength goals to Lucic's 13. How did he do it? Well the consensus seems to be that his goal totals are nothing more than the result of a flukey shooting percentage. His shots went into the net at a 14.57% rate. That's nearly 50% more than the 10.93% rate that Lucic scored at. Lucic's career shooting percentage is 13.42%, while Beleskey's is 9.83%. Last year was clearly an outlier for both players. Therefore, you'd be forgiven for thinking that Beleskey won't score more than Lucic next year.
Well, the numbers would say that he probably can. Hold on with the "unsustainable shooting percentage" stuff. Both Beleskey and Lucic have the exact same career goals/60, .82. And Beleskey's goals/60 actually seems more sustainable! The kicker is that Beleskey's career shooting percentage is lower than Lucic's, by quite a lot. His career shots/60, therefore, are quite a lot higher than Lucic's.
Lucic's career shooting percentage is 13.42%, while his shots/60 are 6.13. Meanwhile, Beleskey's career shooting percentage is 9.63%, while his shots/60 are 8.48. That works out to a .82 goals/60 for both players, but Beleskey has done it in a much more sustainable way. Criticisms of Beleskey's shooting percentage, then, seem a bit misplaced.
How did they both do last year? Well, in 2014-15 the mean shots/60 among all forwards was 6.904, while the standard deviation was 1.797. Lucic had 6.47 shots/60, so he was about a quarter of a standard deviation below the mean. Matt Beleskey, however, had 9.45 shots/60. That's 1.4 standard deviations above the mean. That's pretty darn good. To give you a comparison, there's this guy you may have heard of named Patrice Bergeron. He quite a lotta shots. Last year he had 9.73 shots/60, or 1.5 standard deviations above the mean. That's pretty good.
I'm going to do some more comparisons, but first, an aside. Last year, the average shooting percentage among forwards with 200 or more minutes spent on the ice was 8.77%, with a standard deviation of 3.71%. That's some pretty high variance. It's over 40% of the mean. Therefore, take this whole comparison with a grain of salt. A player's shooting percentage will rarely regress to the mean. It's much better to think of player's as having a hidden shooting percentage that's probably somewhere within two standard deviations of the mean, and we just don't know where it is. You can think of a player's shooting percentage as an unknown P in a binomial distribution. Hockey Prospectus has a very good explanation of this here. Check it out if you're interested. For now, we won't be using a binomial distribution to estimate the shooting percentages of Matt Beleskey or Milan Lucic. Because both of them are coming off years where their shooting percentages were heavy outliers, and we're trying to predict how they'll do next year, it seems like it could easily be misleading. Instead, we'll just look at what would happen if both of them shot at an average rate for a forward with 200 or more minutes on ice in 2014-15.
So, now I'm going to find the probability that either player could have ended up with x number of goals at the end of the year. To do this, I'm going to assume both players had an average shooting percentage of 8.77% and that both players played the same amount of minutes as Milan Lucic did. So, the only thing that will differentiate their curves will be their shots/60. I'll model each of their year long performances using a binomial distribution. This model is used to estimate the probability of having a certain number of succeses in an an experiment consisting of a number of trails that will yield one of two binary results. Our experiment is a season, our trials are shots, our successes are goals, and our percentage of trials that will yield a success is a shooting percentage. There are four conditions this model needs to meet. Here they are:
1. The experiment consists of a number of repeated trials.
Easily met. A season consists of a number of shots.
2. Each trial can have only 2 outcomes, a success or a failure.
Also easily. A success is a goal and a fail is a save.
3. Every trial has the same chance of success.
We're taking this as an assumption. Of course, we know that breakaways will have a higher shooting percentage than center ice shots. We also know that two different players will both have different "true" shooting percentages. We're allowing this to slide simply because we're trying to see how each player does when their shooting percentage isn't really a factor.
4. Every trial is independent.
Kind of an assumption. Goalies can get inside of a shooter's head and possibly make later shots harder. It's possible that a shooter can be given a crap load of tough minutes, and fatigue can impair his abilities. But, for all practical, quantifiable reasons, we can meet this assumption.
And, now that that's done, here's both players probability curves.
Lucic's curve is to the left, Beleskey's to the right. The bottom axis shows the number of goals each could have ended up with at the end of year, while the left axis shows the probability of ending the year with each amount of goals. Again, this is assuming he shot at an average rate for a forward. Shots/60 tend not to vary all that much from year to year among forwards of Lucic and Beleskey's age, so these curves will probably be pretty accurate for next season as well. Again, this is assuming they both shoot at an average rate, which they very likely won't. If Beleskey's played next to Krejci, it's very, very easy to imagine his shooting percentage increasing, and therefore moving his curve more towards the right. This is also showing only even strength season totals. No powerplay goals included. If you laughed off the idea of Beleskey scoring 20 goals next year, you may end up pleasantly surprised.
The big thing Beleskey needs next year is ice time. Last year, he scored 18 goals at even strength, but he only played 787 minutes. Lucic played 1103 minutes and only has 13 even strength goals. That means Beleskey scored 38% more goals than Lucic did with only 70% the ice time. Extrapolating that, he would have scored 25 goals only at even strength if given the ice time Lucic was given. That's more than 2010-11 Lucic scored at ES, and he had both comparable ice time AND a higher shooting percentage than 2014-15 Beleskey. And that was the season that made Lucic the 6 million dollar man.
So, we seem to have a pretty clear conclusion. Beleskey, even without having a crazy high shooting percentage, just as good of a goal scorer as Milan Lucic. If not, better. Both have the same career goals/60, .82. But Lucic scored the vast majority of his goals playing next to David Krejci, while Beleskey scored at the same rate next to fourthline centers, and Ryan Kesler for a year. Their goals/60 are equal now, but with Beleskey likely to get played next to a true play maker like David Krejci next year, and with Lucic's play generally on the down swing, it's hard to imagine that still being true by this time next year.
Don't count out 39 just yet.