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Module 1, Part 1: Height (by Overall Distribution)

Western Bulldogs Overall

Yay for histograms that do my work for me.

As you can see, our peak frequency occurs in the 181-185cm range, with 14 of 44 players (31.82%) fitting within this range.  Given that the AFL average height is 188.30cm, this is perhaps indicative of a list with relatively more players under 189cm than expected.  This is supported by the club's mean height of 186.82cm - just under two centimetres below the AFL average.

The histogram appears to indicate that this skew is caused by an above-expected proportion of players within the 181-185cm range and a below-expected proportion of players within the 196-200cm range.  Not exactly surprising.

Some other tidbits:

• Our most frequent height is 182cm, with six players (Clay Smith, Daniel Pearce, Josh Prudden, Bailey Dale, Declan Hamilton and Roarke Smith) coming in at this height.
• Our median height is 186cm - approximately equal to our mean height.
• Despite our list being 2cm lower than the league average, Caleb Daniel still shows up as a statistical outlier in our list.
• Our list's height profile is approximately normally distributed (Kolmogorov-Smirnov statistic = .123, p = .095, for those who care [probably not many - myself included]).
• Our standard deviation is 7.67cm.

Layman's conclusion: We are shorter than the AFL average by about 2cm, likely due mostly to an abundance of players within the 181-185cm range.

Hawthorn Overall

As shown in the above histogram, the Hawthorn list's height profile is congregated quite heavily within the 176-195 range, with only seven of 47 players (14.89%) falling outside this range.  Their most frequent height range is 191-195cm, with 27.66% of their list falling within this range.  It paints a picture of a list that would appear to be above the AFL average - but this is not the case.  The Hawks' average height is 188.28cm, falling 0.02 centimetres below the AFL player average.

Some other tidbits:

• Hawthorn's most frequent height is 193cm, with six players - Jarryd Roughead, Grant Birchall, Jack Gunston, Tim O'Brien, Kurt Heatherley and James Frawley - coming in at this height.
• Their median height is 188.5cm - approximately equal to their mean height.
• Their list profile is approximately normally distributed (KS = .105, p > .200).
• Their standard deviation is 7.40.

Layman's conclusion: Hawthorn's list is very slightly smaller than the AFL average, but features an abundance of players in the 186-195cm range.

Brisbane Overall

The distribution of player height in Brisbane's list is interesting - 24 (51.06%) players are either between 181-185cm or 191-195cm, with only 17.02% fitting in between the 186-190cm range.  They also have a total of 17.02% of players in the upper key position player range of 196-200cm.  This all combines to give a mean height of 189.23cm - just under 1cm above the AFL player average height.

Some other tidbits:

• Brisbane's most frequent height is 192cm, with five players - Luke McGuane, Nick Robertson, Tom Cutler, Matt Maguire and Jackson Paine - fitting within this range.
• Their median height is 190cm - significantly larger than their mean height (most likely due to having so many more players above 196cm than below 181cm).
• Their list profile is approximately normally distributed (KS = .099, p > .200).
• Their standard deviation is 7.05cm.

Layman's conclusion: Brisbane's list is, on average, taller than the AFL average player height, due primarily to possessing a large number of 196-200cm players.

St Kilda Overall

St Kilda's list is, on average, approximately 0.41cm below the AFL average player height, with a mean height of 187.89cm.  This is illustrated by a relatively even frequency plot.  11 players (24.44%) are between 191cm and 195cm, with 10 (22.22%) between 181-185cm, 8 (17.78%) between 186-190cm, and 6 (13.33%) between 176-180cm.  It's also worth noting that 8.89% of their list is above 200cm, which is larger than expected.

Some other tidbits:

• St Kilda's most frequent height is 194cm, with five players - Tom Lee, Dylan Roberton, Sam Gilbert, Luke Delaney and Patrick McCartin - coming in at this height.
• Their median height is 188cm - approximately equal to their mean height.
• Their list profile is approximately normally distributed (KS = .074, p > .200).
• Their standard deviation is 7.42cm.

Layman's conclusion: The Saints are slightly below the AFL average height despite possessing 11 players between 191-195cm, and four above 200cm - likely due to an abundance of players below 186cm, and few between 196-200cm.

Western Bulldogs vs. Hawthorn vs. Brisbane vs. St Kilda - General

I've used a box plot to best illustrate the comparisons here:

For the record, that open circle drifting somewhere in the middle of nowhere on our column is Caleb Daniel being his statistical-outlying self.

Simply, this diagram shows that our median height (the thick, black, horizontal line) is lower than all three other sides.  Brisbane's median in particular is significantly larger than ours, meaning that if you order all players from shortest to tallest, Brisbane's middle player is taller than ours (for the record, it's looking at Lukas Webb/Easton Wood vs. Hugh Beasley - a difference of four centimetres).

It also shows that our 75th percentile (the line on top of the yellow box) player is quite a bit shorter than those of the other clubs.  More explicitly, similar to the median, if we line up all of the players from shortest to tallest, the player in the 75th percentile for height on our list (mid-way between Jake Stringer and Jarrad Grant - so 191.5cm) is shorter than those of the other clubs (Jack Gunston/Grant Birchall, Justin Clarke and Patrick McCartin).

With a median and 75th percentile lower than all three comparison teams', it is reasonable to expect that our 25th percentile (the line on the bottom of the yellow box) would be lower than the other teams'; that is, the player in the 25th percentile for height on our list (Bailey Dale) would be shorter than those in the 25th percentile for height on the other three teams' lists (Alex Woodward, James Aish/Jed Adcock and David Armitage).  In the case of Brisbane and St Kilda, this is true - however, Dale is the same height as Woodward.  The difference between Dale and the others is also quite a bit less than the difference was for our median/75th percentile players.  This makes the difference between our 25th and 75th percentiles much smaller than those of the other sides.

So what does this actually mean?  Basically, that if you order our players from shortest to tallest, and locate our middle 50% of players in terms of height, they are clustered within a relatively small height range compared to other sides.  Visually, our list's height distribution is fat and short rather than narrow and long; we have more players that are very similar height-wise to the median than the other three sides do.  This is supported by simply eyeballing our list's height.  29 players on our list - 65.91% - slot in between 180cm and 192cm.  Compare this to 52.17% for Hawthorn, 55.31% for Brisbane and 54.35% for St Kilda and you'll see that our list is overly concentrated within these ranges.  This is also illustrated by the histograms presented in the opening sections.  Not only do we have the most players within the 181-185cm height range (14), we also have the most players within a single height range of any of the teams (second-most is Hawthorn with 13 players coming in at heights between 191cm and 195cm).  In simple terms, we've got a lot of eggs in one basket of heights.

Looking at the histograms again, there is more to learn.  Despite being significantly shorter than the other sides, we have fewer players under 176cm than St Kilda, the same amount as Brisbane, and only one more than Hawthorn (although, granted, one of our two is the only statistical outlier in the dataset).  In the 176-180cm range we are again middle-of-the-road, possessing less than both Hawthorn (8) and St Kilda (6), but more than Brisbane (3) with five players in this range.  It is the 181-185cm range, however, that illustrates the points made above.  Fourteen players come in at heights within this range, compared to twelve for Brisbane, ten for St Kilda, and only seven for the successful Hawks.  Due to this concentration of players with below-average height (and the resulting constraint of list spots), we have significantly less players above the AFL's average height.  We possess only 14 players above 190cm, compared to 19 for Hawthorn, 22 for Brisbane, and 18 for St Kilda.  To put it in perspective, we have 14 players above 190cm - Hawthorn have 13 in the narrow range of 191-195cm.

Layman's conclusion: A lot of our players are bunched between 180cm and 192cm, leading to a lack of players within the crucial key position height ranges due to restricted list spots, and an overall mix that lines up at a height disadvantage against other clubs.

AFL Overall

As can be seen in the above histogram, the AFL's peak frequency occurs in the 186-190cm range, with 206 of 817 players (25.21%) fitting within this range.  This comes at no great surprise given that the average height in the AFL is 188.30cm - right in the middle of these parameters.  Perhaps more interestingly, the next most prevalent height range is 181-185cm - a range that was shown to be less popular amongst back-to-back premiers Hawthorn.  196 players - 23.99% - are between these heights.  This is considerably higher than the third-most prevalent height range of 191-195cm, with only 150 players (18.36%) being within these heights.  Only 25 of 817 individuals in the AFL player population are under 176cm - a percentage of only 3.06%.

Some other tidbits:

• The AFL's most frequently occurring height is 188cm.  48 players - or 5.88% of the AFL player population - are 188cm.
• The AFL's median height is also 188cm.
• The AFL's standard deviation is 7.39cm.

Western Bulldogs vs. the AFL

Again, a box plot is probably the most fitting here:

Before we get into it, I'll define the outliers present in both plots.  Caleb Daniel is the outlier on our column (#44).  He's also presented in the AFL column as #226.  Brent Harvey (North Melbourne; 167cm), Mason Cox (Collingwood; 211cm) and Aaron Sandilands (Fremantle; 211cm) are the three other outliers.

The box plots indicate that our median is significantly lower than the AFL median - 186cm compared to 188cm.  It also indicates a 75th percentile (191.5cm) lower than the AFL's 75th percentile of 193cm, and a 25th percentile (182cm) lower than the AFL's 25th percentile (183cm).  This indicates a distribution of heights that centre around a lower midpoint than the AFL's overall distribution.  This is also backed up by a difference of approximately 1.5cm between our mean height - 186.83cm - and the AFL's - 188.30cm.

It is interesting to note that our inter-quartile range (that is, the height of the yellow box, or the difference between the 75th and 25th percentiles) is only 0.5cm shorter than the AFL's.  In simpler terms, the yellow boxes presented above are approximately equal in size.  This means that the middle 50% of our distribution is spread across an approximately expected total number of heights; we don't have too many players bunched within too few heights when you look at the middle 50% in isolation.  This does appear, however, to contradict what is shown in the histogram comparisons: that we have a larger-than-expected concentration of players within the narrow limits of 181-185cm. 

So what does this mean?  My conclusion is essentially that, while we have an acceptable number of players spread in these broader ranges, when you begin to narrow the parameters that you're looking at, it becomes clearer that we're disproportionate to what is expected - both compared to other sides, and to the AFL overall.  While our middle 50% of heights cover an appropriate range, the distribution within this range is heavily skewed towards shorter heights.  Essentially, our distribution is somewhat similar to the AFL's - just shifted towards shorter heights.

Layman's conclusion: Our overall distribution isn't too dissimilar from the AFL's overall distribution, however, it is more biased towards shorter heights than is expected.

In Summary

There is no groundbreaking or shocking facts put forth in this post - simply statistics that back up what many have suspected: compared to other sides we have more players clustered at the short end of the spectrum, resulting in a significantly smaller proportion of taller players.  Overall we are quite a bit shorter than the average height for an AFL player due mostly to a massive collection of players between 181 and 185 centimetres.  In addition, our most frequent height of 182cm is an enormous ten centimetres lower than that of the next-lowest (Brisbane with 192cm being their most frequent), meaning that we are heavily concentrated at different sizes than the three other sides presented here.

Putting quality, age, experience, position (for now) and all other factors aside, the height profile of our list appears unbalanced and a fair way behind that of the other three clubs - Hawthorn, Brisbane and St Kilda - presented here.  In essence, while we have a greater chance than these clubs at finding a competent small, we are spreading our chances way too thin at the opposite end of the spectrum.

*Disclaimer: player heights courtesy of https://www.draftguru.com.au - some may be slightly inaccurate.