During Friday’s podcast, I wondered something aloud (the best way to wonder something during a recorded-voice program, incidentally):

Steven Stamkos had scored 50 goals while no other NHLer had touched 40. Rob and I were trying to do the old “compare generations” thing that always gets messy. We were asking ”A 50-goal season today is worth a __ goal season during Gretzky’s era.”

I wondered how many standard deviations from the mean Stamkos’ numbers are this year, compared to how many Gretzky’s were in his day when he was filling the net.

Well, friend of the blog ”Nick the Bruins fan from Montreal” actually took the time to help us out by putting together some numbers, because he’s an awesome guy and curious like us.

One minor problem: Nick is really good at this stuff. While I took a stats course in college (and did miserably in it), trying to sift my way through the MOUNTAIN of excellent data he compiled hasn’t gone as swimmingly as I’d hoped.

So for now, let’s keep it simple and take a look at some of the more basic stats he put together so we can gain some context as to just how good a season Stamkos is having. I’ll try to parse more information from the data in the meantime.

For starters: here’s a graph that plots the NHL’s forwards in terms of games played and goals scored. He’s kinda running away with things:

(If you click it a couple times, you can see it full-sized.)

Obviously, each dot represents an NHL player.

Now, here’s how his season stacks up against the best offensive seasons in the history of the NHL (hand-selected on personal opinion), in terms of standard deviations. For those of you unfamiliar with that term, I’ll simplify – the more standard deviations you are from the mean (or the “average”), the more exceptional the number.

(Note: Orr’s numbers are compared strictly to other defensemen.)

As Nick pointed out, look how insanely similar Gretzky and Lemieux’s two best seasons are (6.20, 6.19, 6.18, 6.17). It seems unlikely that anybody could ever extend themselves beyond that level of greatness (6.2 standard deviations range) when comparing a player to his present-day peers.

Some more takeaways from our Montreal-based B’s fan friend:

* “As far as mega-superstar seasons go, Stamkos isn’t quite up there. His 5.34 standard dev’s from the mean is quite a bit lower than the 6-ish range that Lemieux/Gretzky have reached. It is, however, better than Jagr’s best year ever, when he scored 65 times.”

* “If you suspended disbelief and imagine for a second that Bobby Orr would’ve been as far ahead of everyone else if he’d played forward instead of defense, his 7.62 standard deviations above the mean in goals would’ve put him at 111 goals the year Gretzky scored 92. But yeah, that’s way out in left field and isn’t really the point, it’s just fun to imagine.”

* “Ovechkin’s 65 goals (6.12 standard devs from the mean) puts him in the same ballpark as the best goal scoring seasons I’ve measured – he’s only two goals way from Gretzky’s 92-goal year (6.19) and Lemieux’s best ever (6.20).”

I’m going to do a lot more digging through these numbers in the days to come, it’s fun to have some basis for comparison here.

It’s not my forte, but Nick broke it down for those of you interested enough to try this at home – “If you want to play the game of “this guy’s this many goals in year X are like that many goals in year Y”, this is the formula to use: [Average goals in year Y]+[Player's # of standard deviations from the mean in year X]*[Standard deviation in year Y] = number of goals he “would’ve” scored to be that exceptional in year Y.”

Er…..got it. I’ll get to work on some more of these ASAP.

Comments (7)

  1. Sounds cool but it was way to confusing too understand- both those graphs. But I do agree with your conclusion.

    • The first graph (the cloud of points) goes like this: the further up the graph you are, the more games you’ve played, and the further right you are, the more goals you’ve scored. Guys who stand out from the cloud anywhere were on a really high goals-per-game pace. You can sort of project what injured guys like Andy McDonald would have ended up at if they played the entire season at the pace they were at – draw a straight line from 0 (bottom left corner) through Andy MacDonald and he ends up somewhere in the 30s.

      The second one is a lot harder to describe, but one standard deviation is basically a way of quantifying how spread out guys are. It’s a way of quantifying things like how much more impressive a 50 goal season is if nobody else has more than 20 than if there are a bunch of guys in the 30s and 40s. It still isn’t perfect, but it’s a general way of measuring how exceptional it is to be way ahead of the pack in scoring. In past years there was more scoring overall AND more spread between guys (look at all the guys who scored 50 goals in the 80s – they aren’t all Stamkos/Ovechkin caliber players), so while you have to be careful about making blanket statements like “Ovechkin would’ve scored 89-ish goals in 1980-1981,” you certainly CAN say “Ovechkin was almost as exceptionally better at scoring than everyone else when he got 65 goals as Gretzky was in his prime”.

      • Hi Niq the Bruins fan from Montreal!

        You are a legend where I come from… I heard about the time when you ate 6 boston cream donuts in one day! Anyways, I just wanted to compliment you on your fantastic math skillz and deductive reasoning. Could you explain how a standard deviation works, I don’t quite understand.

        I see you have been working quite diligently on your deep beams the last few weeks!

  2. “The Wayne Gretzky analysis” – http://sciencewitness.com/news/37.html

  3. Just some advice for next time, I think it would make more sense to have games played on the x axis as opposed to goals. It will probably make it easier to understand, because y (goals) usually depends on x (the number of games played).

  4. Can we have the M, SD and kurtosis (if you have it) spread sheet?

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