Pittsburgh Penguins v Toronto Maple Leafs

Last year Backhand Shelf reader/listener Nick put a chart together comparing Steven Stamkos’ goal output to the greatest seasons of all time here. The smart thing is, he didn’t use the raw stat of “goals” to make the comparison – he used standard deviations from the mean. It’s the most logical way to compare stats across generations.

This year he’s back with more, evaluating just how good Sidney Crosby’s numbers are. His assist total, specifically, is impressive.


- Commentary by Nick

First, a look at Crosby’s total goals (against some of the best seasons ever), which aren’t about to blow anyone out of the water.

crosby chart 1

Conclusion: Crosby definitely isn’t hanging with the greats as far as goals go (not surprising, since his season is impressive due to assists).

His points however (5.19 standard deviations from the mean) put him right in the middle of the greatness pack. The only people ahead of him are four dudes named Lemieux, Lemieux, Gretzky, and Gretzky. It’s safe to say his points totals are about as impressive as any season not had by Lemieux or Gretzky, and even then it’s right near Lemieux’s 1995-1996 season.

Because we’re dazzled by Crosby’s assists and not his goals, here’s the same graph with assists and points (instead of goals and points). Crosby’s point is the red diamond.

crosby chart 2

  • Here’s where it gets interesting. Crosby’s assists (5.94 standard deviations from the mean) and points (5.19) place him right in the middle of some of the best seasons ever. He’s higher in both stats than Jagr’s best season.
  • At the risk of setting the internet on fire… Crosby is outpacing the rest of the league in assists more than Lemieux did in his best seasons. I guess this is where I should be a buzz kill and provide the disclaimer: don’t forget that this season’s numbers really only amount to what would’ve been a third of a year in any other season, and I’m sure that Lemieux’s best 26-game stretch over that period was even more insane. But still, for the sake of headlines, how does “CROSBY: BETTER PLAYMAKER THAN LEMIEUX” sound? (Editor’s Note: love the idea, but chose to opt out.)
  • All jokes aside, though, Crosby’s definitely on pace for a legitimately great season. He’s currently performing better as a set-up man than Lemieux or Jagr did during their best seasons and is only slightly below Gretzky during his 92-goal year.
  • This wasn’t the point of the exercise, but Gretzky’s assists in 1985-1986 (the year he got 215 points) are almost two standard deviations ahead of anybody else. That’s ridiculous, and it’s probably evidence that Gretzky sold his soul to Satan. It’s probably as good a sign as any that this record will never be broken. For his assists to be as impressive as Gretzky’s that year (calculated using of standard deviations from the mean, which should correct for there being less goals in this era than in Gretzky’s), Crosby would need another 10 assists, for 43 assists in 28 games.
  • Round 2 of the disclaimer: the seasons on the graph were selected last year for their goals or points totals (to compare to Stamkos), not for their assists. So it’s possible that Adam Oates or someone has an equally impressive season, and it wouldn’t be wise to conclude that Crosby is having the 3rd-best playmaking season of all time. But still, we can say that he’s having an unbelievable first half, and that if he keeps it up his assists and points totals are certainly in the ballpark of with Lemieux’s and Gretzky’s best seasons.
  • Setting the internet on fire, part 2: how good could Crosby be if he was a better scorer than, say, Jakub Voracek (also with 12 goals in 27 games)? Maybe he’s sacrificing a few goals to get a ridiculous number of assists, since he’s had some respectable goals totals in the past, or maybe he’s more of an Adam Oates than Mario Lemieux. There’s plenty of ammunition to troll Pens fans with here: maybe Kunitz and Dupuis are carrying Crosby to the Hall of Fame. 20 of his 33 assists are at even strength, so Malkin and Neal aren’t the only guys deserving some of the credit.
  • Here’s the raw data from the second graph:
Player (year)

Std. Devs from mean

  Goals Points Assists
Jagr (1995-1996)




Lemieux (1995-1996)




Lemieux (1988-1989)




Gretzky (1985-1986)




Gretzky (1981-1982)




Crosby (2012-2013)




Last but not least, here’s a graph showing everyone’s games played (x-axis) and point totals (y-axis). Every dot on the graph is at least one player (guys with the same GP and PTS have their dots on top of each other, so you only see one). Not to start this whole process all over again, but Letang is comfortably in 3rd place despite having played less games AND being a defenseman. And St. Louis is having himself quite a playmaking season too, even though he’s in Crosby’s shadow.

And just in case anybody needed another wacky stat based on an even smaller sample size, Tobias Enstrom (a defenceman) has 11 assists in 13 games. If he had played every game and maintained his pace, he’d be in the St. Louis and Letang neighbourhood. Maybe he got lucky, or maybe he’s secretly the 3rd-best playmaker in the game.

crosby chart 3 fix

Comments (29)

  1. I really like the concept of standard deviations to compare across eras statistically. Nice work.

    • The baseball guys have been using this concept for ERA+ and OPS+ for a while. It’s a really good way to compare players across eras.

    • It really is the best way to look at it. Though I’d feel like it was more meaningful if we weren’t comparing 26 games to 82.

      • Agreed. This is just a fun exercise, and like I pointed out you could certainly find some better 26-game stretches in the historical seasons that Lemieux put up. It doesn’t mean “Crosby is better than Lemieux,” it means “Crosby is on pace for a better season than Lemieux”. The bigger your sample size the less chance that you’re looking at an anomaly.

        It’s too bad that this isn’t an 82-game season though, because then you’d really be able to compare. Even if Crosby has 48 great games he’ll lose some credit simply because the season was cut in half. But that’s the nature of stats – take them for what they’re worth, and understand their limitations.

        • There was a trivia question (a trivium?) on the Rangers game last Tuesday, about the longest scoring streak in Rangers history. Turns out it was Brian Leetch, 17 games, and IIRC he had 24 assists in that stretch, which is a better run (in terms of APG) than the 33 in 28 so far for Crosby.

          I’m not sure what that would be in standard deviations. That was the year Leetch had 80 assists in an 80-game schedule (third in the league), and the Rangers had FIVE 30-goal scorers, which is somewhat ridiculous. But the point remains, there are some ridiculous hot stretches in history. Some have even been lost to us because we don’t have complete game logs before 1985 or so, the way that Retrosheet (and hordes of boxscore clippers) created for major league baseball.

  2. That last chart really confuses me – are the x and y axis labels flipped? Also, I get that it demonstrates that of the group of players that have played a certain number of games, St Louis / Crosby / Enstrom have gotten the most assists, but wouldn’t it be easier to just map out assists/GP?

    I’m enjoying Crosby beasting this season, though I’m curious how his numbers for the part of the season before his concussion compare.

    • Dammit, you’re right. I used to do the graphs the other way around and forgot to switch the axes. Good call.

      And “per game” stats tend to always be skewed towards some guy who played 3 games and got lucky, so there’s an issue of trying to figure out a threshold for games played and all kinds of other issues to figure out. The Enstrom example fits here – he would be somewhere around St Louis/Letang’s assists per game, and a model which puts him in 3rd place or so is probably not the best given he only played 11 games.

  3. This just made the engineering nerd in me sooo happy on Pi Day (3/14)

  4. The Score should hire Nick.

  5. I’m no math wiz and happy to be corrected, but for goals, am I wrong to think that Rocket Richard should be on the list for his 44-45 season? (50 goals in 50 games and the league average was below 10)

    • Sorry, I keep getting screwed up by the reply button being above the post and not below. Look 2 posts down.

      Sorry Justin, I’m making a mess out of your comments section.

  6. I love standard deviation -I think its a fair way to determine how well/dominant a player is agaisnt his peer.s Using raw numbers doesn’t tell the whole story.

    I know this wa a basis for some self-selected seasons, but does the standard deviation account for all players or just forwards? (are we comparing apples to apples).

    Essentially what I am trying to ascertain is just how ridiculous some of the seasons Bobby Orr put up are. If you compare them to Gretzky, Lemieux they would still be impressive, but if his standard deviation was measured agaisnt just defenseman how insane would his numbers be?

    • Good idea. The seasons we used for comparison were decided in a completely unscientific way – Justin wondered out loud on the podcast, I checked out a few of the seasons he was wondering about and added a few of my own, and that was it. The choke point is actually the tediousness of copy pasting an entire season’s worth of data into the spreadsheet each time. The more players, the more pages I have to scroll through copy pasting. So there’s no real logic or diss in excluding Richard or any other great year, we just picked some historical greats and threw some recent seasons in for comparison..

      I was fortunate enough to find the entire season’s stats on one page (rather than having to copy-paste the data from 17 pages like on NHL.com) and it was pretty simple to plug into my spreadsheet. Here’s the data:

      Total players in 1944-1945: 117
      Average goals scored: 9.42
      (Standard deviation: 9.46)
      Average points: 20.71
      (Standard deviation: 18.46)

      Maurice Richard got 50 goals, putting him 4.29 standard deviations above the mean in goals. That’s actually quite a bit less than I would have thought too.

      Keep in mind that this might be where the shortcomings of this methodology start to show – you can compare years in the 80s to recent years, but in 1944-1945 less than 20 different players suited up per team (6 teams, 117 players total!). I don’t think there was a 4th line in those days, and there were certainly less players being called up for a few games. If there were no 4th line in today’s NHL, Crosby wouldn’t have so many guys getting 4 minutes of ice time a night dragging down the average and standard deviation either.

      Here are the 1944-1945 stats I used:


      • Good point on the different nature of the game then. It’s easiest to tell with the goalkeepers. Basically, nobody had a real backup, and if your guy was healthy it was a given that he’d play every minute of every game. Starting with your link, switching to goalie stats, and clicking through the years, you usually only see ten keepers for the entire league.

        1952 is an extreme example: five of the six teams had the same goalie start all 70 games, and three of them went wire-to-wire. The two guys who didn’t gave up a grand total of 50 minutes to their backups.

        (Cool trivium about one of them: Moe Roberts, who’d been retired for six years, was pressed into service when Harry Lumley got hurt in a Blackhawks game. He tossed a shutout period for the Blackhawks at age 46, 18 years after last appearing in an NHL game, for a team [the Americans] that no longer existed.)

  7. This is good stuff, thanks. Agree with the conclusion that It’s safe to say his points totals are about as impressive as any season not had by Lemieux or Gretzky.

    Too bad no mention of Lemiuex’s 1993 season when he was on pace for 92 goals and 213 points while recovering from cancer treatment. If you made one based on points-per-game (minimum of 50 or 60 games played) that would be awesome.

    • Edit: I apparently suck at clicking the “reply button”. All of this was intended for the post above you. Sorry.

      • EDIT2: aaagh not again. Sorry. The Reply button being above the text and not below it is screwing me up. Ignore this, I suck at the internet.

  8. Thanks for giving me a stats boner…

    • Hey man, whatever floats your boat. I know a cute trinomial distribution looking for a date tonight, I’ll give it your number and we’ll see what happens.

  9. Excellent stuff.
    I would love to see a career statistical analysis (Std. Dev perhaps) of Lemieux vs Gretzky. Make it so!

  10. oh come on why people do this seems silly u cant comare players who played ears ago to now and he is playing in a short season and funny he is not tht far ahead of the next guy on the scoring list when 99 played he was 100 points better then the next guy >what is Sid like 10 points ahead of the next guy . he is so overrated bye the sports guys

    • I have to agree. Not only is math stupid and dumb, but so are grammar, spelling, and punctuation!

    • “when 99 played he was 100 points better then the next guy”

      See the above on Richard. Standard Deviations make it fairly simple to accurately control for era-based differences (although I think you kinda have to treat pre-expansion stats as markedly different from post-expansion, personally)

  11. gretzky has 163 assists in one season.. noone else besides super mario even got 163 points.. nuff said

    • “gretzky has 163 assists in one season.. noone else besides super mario even got 163 points.. nuff said”
      True, it was a great season, but you’re completely missing the point of the standard deviations method. There’s no way a young Gretzky puts up 163 assists in today’s NHL, so we try to compare how well each player performed compared to his peers in his own era.

  12. You actually left out Gretzky’s best season: 1983 – 1984.

    51-game scoring streak (AKA he’d have scored a point in every single game of this shortened season).

    87 goals
    205 points

    … only 74 games played (he basically took a week off after the streak ended).

    2.77 PPG average is the highest in NHL history.

  13. Why do people like to overate active players?
    Crosby will never be better then Gretzky,Lemieux or Jagr.

    Take a Jagr for example.The lesser legend from the last three names.
    He won Stanley Cup twice, Art Ross Trophy 5 times,Lester B. Paerson 3 times,Olympic gold medal,world championship gold medal.
    He scored more then 120 points in three seasons and have a record of 9 consecutieve seasons in NHL over 70 points.
    This guy is in his 40′s and still playing in NHL.
    How can Crosby ever achieve something like that?
    The stats are rubbish.
    So far I know Crosby never scored anywhere near 90 points in a season.
    He will never even touch the legends of Gretzky and Lemieux and have a 90% chance (my estimate) to fail to get as far as Jagr.

    But that’s just my opinion.

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