How big is the big bad Western Conference?

I can forgive you for wanting to forget about it, but on Tuesday, the Leafs got their teeth kicked in by the Los Angeles Kings. The narratives from this game were aplenty. The young Leafs were shown how to win by the experienced Kings. A speedy Toronto team was neutralized by the brawn of LA. The former champions showed the (hopeful) future champions how far they had to go. And so on and so on.

Don’t believe me? Check out these passages from Sportsnet’s game recap:

One of the younger teams in the league, the Leafs were ultimately schooled by a more veteran opponent, one that's captured the Stanley Cups twice in the past five seasons.

[...]

Often, the Kings size and strength was just too much for Toronto to handle at both ends of the rink. They floated easily into the Toronto end, scoring off the rush and through a punishing cycle game.

The size element is something interesting to me. On a larger scale, it’s often said that the Western Conference is where the big, tough, and physical teams come to play. To compete, it’s said that your team needs to be similarly brawny. My initial reaction whenever I hear this (which is often) is one of skepticism. To start, it’s not clear to me that the West is unilaterally bigger or more physical than the East. And even if it is, small teams like the Blackhawks have dominated the conference at times. This skepticism motivated me to see if there was any relationship between the conferences and the size of their teams. Is this common saying fact, fiction, or something in between?

Methods and Preamble

For the sake of this study, I’m concerning myself with the average weight of a team, as a proxy for how ‘big’ or ‘physical’ they are. There are some issues with this. In a perfect world, I would adjust weight for playing time (adding John Scott would increase your average weight by a lot, but if he’s playing 5 minutes a game, he’s probably not affecting your on-ice play too significantly). And while weight is a decent proxy for physicality, we can all think of players who play bigger or smaller than they are.

Nonetheless, we’ll make do with what we have, which is weight data by team at the start of the 2016/2017 season. This is courtesy of James Mirtle, who compiles this information yearly on his personal blog.

The Information

To start, lets take a look at some of the key metrics in this dataset, summarized in the table below, across conferences and divisions.

So what can we glean from the table? Immediately, it’s clear that there’s no real difference in the mean average weight between conferences. Two pounds is not particularly notable. The median is slightly further apart between the conferences, but again, we’re talking about 1.5% increase. Nothing notable there. I conducted a regression analysis to see if this difference was significant, and that is not the case (you can find all R code at the end of this article). In plain English, there’s no evidence of a relationship between the conference a team plays in, and its average weight.

Lets go a little further. If we look at divisions, we see that the Central division is notably a little heavier than everyone else, at least by its mean and median. This is a more notable distinction than before, but if we perform a Tukey Test on the means, we note that there’s no evidence of a relationship between the division a team plays in and its average weight.

The lack of statistically significant result here has a lot to do with the fact that we’re dealing with a small sample size. With that in mind, lets look at these figures on a more granular level.

Pretty Graphs

Below are two box plots which look at how average weight is distributed across conferences and divisions.

Here, we can start to see a little more about this narrative. While there’s no significant difference in the means between the average weights by division or conference, we can see that the Western Conference, and in particular, the Central Division, has some of the more extreme average weights in the NHL, both on the high and low end. This results in there being no real difference in the averages across divisions and conferences, but it doesn’t mean that the individual teams in each division or conference are entirely similar to one another in this respect. If I had to guess, I’d say that this narrative arose as teams like LA (third in average weight), St. Louis (sixth) and San Jose (11th) became year over year contenders. To beat the West, you have to beat those teams (among others)... but it doesn’t mean the West is unilaterally a bigger or more physical conference than the East.

So when you hear people say that you need a tough, physical player (or team) to succeed in the West... well, they’re not totally wrong. A Western Conference team will have to face (and presumably succeed against) the heaviest the league has to offer more often than and Eastern Conference team. But you have to succeed against the skinny teams too, and as Chicago has shown, they’re no picnic. Best bet is to get you some players who can do both.

R Code:

library(ggplot2)

data = read.table("data.csv", sep = ",", header = TRUE)

data = data[1:30,] # annoying data artifact

attach(data)

Conferences = factor(Conference)

Divisions = factor(Division, levels = c("A","M","C","P"))

model_conf = lm(Wt ~ factor(Conference))

model_div = lm(Wt ~ factor(Division, levels = c("A","M","C","P")))

summary(model_conf)

summary(model_div)

# means, medians, sds

mean(Wt[Conference=="WC"])

mean(Wt)

mean(Wt[Conference=="EC"])

# can replicate for other divisions and statistics easily - omitted as it is trivial

# average weight by conference (box plot)

p <- ggplot(data, aes(Conferences, Wt))

p1 <- p + geom_boxplot(outlier.shape = NA, aes(fill = Conferences))

p1 + geom_point(position = position_jitter(width = 0.2)) + ggtitle("Average Weight by Conference") + labs(x="Conference",y="Weight")

# average weight by division (box plot)

p <- ggplot(data, aes(Divisions, Wt))

p1 <- p + geom_boxplot(outlier.shape = NA, aes(fill = Divisions))

p1 + geom_point(position = position_jitter(width = 0.2))+ ggtitle("Average Weight by Division") + labs(x="Divis",y="Weight")

# Tukey Comparison

aov2 = aov(Wt ~ Divisions); summary(aov2)

TukeyHSD(aov2)