This post is part of a series of analyses looking at how the morphology of elite professional MMA fighters affect outcomes.

The fundamental premise of this series is that MMA is not an attribute based sport. Due to the permissive rule set it offers an infinite number of ways to win & as such realtime problem solving skills are paramount (assuming a sufficient toolbox of strategy, tactic & technique). Attributes may confer advantages in particular ranges & situations e.g. reach in striking, however these can be overcome due to the flexible nature of the sport e.g. taking the rangier fighter down to eliminate the reach advantage. As always we are promoting MMA 3.0 (MMA as sport /art not a collection of...).

Our hypothesis is therefore: morphology will not play a significant role in success (at least not among the elite).

Other than weight (over which there is broad consensus & therefore weightclasses), height & reach (covered in our next post) are the most fundamental morphological features of an athlete. Height is largely ignored in favour of reach which has obvious advantages in the distance striking component. The ratio between the 2, while studied, is often overlooked entirely (we will address this in detail in an upcoming post).

Here we look at height for the sake of completeness & to provide the basis for the work on the reach-to-height ratio. We also assume that since height & reach are so closely related that height could act as a proxy for reach & hence we should see heights clustered at the upper end of weightclasses. You could think of this as the null hypothesis.

### Average Height by Weightclass

The 1st step is to group the fighters by weightclass & calculate some descriptive statistics.

#### table 01: UFC Heights by Weightclass

class count mean std min 25% 50% 75% max
F - 115 51 63.52 1.95 60.00 62.00 64.00 65.00 68.00
F - 125 52 65.65 1.46 63.00 64.75 66.00 67.00 69.00
F - 135 35 66.51 1.77 64.00 65.00 66.00 67.00 71.00
F - 145 7 67.85 2.03 66.00 66.50 68.00 68.00 72.00
M - 125 68 65.66 1.66 62.00 65.00 65.50 66.00 70.00
M - 135 141 67.20 1.87 63.00 66.00 67.00 68.00 73.00
M - 145 168 68.85 1.93 64.00 67.75 69.00 70.00 74.00
M - 155 238 69.89 1.90 66.00 69.00 70.00 71.00 76.00
M - 170 246 71.39 1.72 66.00 70.00 71.00 73.00 76.00
M - 185 165 72.64 1.86 66.00 72.00 73.00 74.00 78.00
M - 205 127 73.80 1.79 68.00 73.00 74.00 75.00 78.00
M - 265 109 74.80 2.15 69.00 74.00 75.00 76.00 83.00

#### fig 02: Height by Weightclass (Female)

The average difference between weightclasses is just over an inch & making the difference between weightclasses virtually imperceptible. From Fly to Heavy though there is an accumulated 10 - 11 inches, almost a foot. Add to that the volume & the difference is quite clear.

### Do Taller Fighters Win More?

In order to answer that question we calculate the excess height as:

$\mathit{excess height}=\mathit{athlete height}-\mathit{weightclass mean height}$

& the excess win ratio as:

$\mathit{excess wins}=\mathit{athlete wins}-\mathit{weightclass mean wins}$

where:

$\mathit{athlete wins}=\left(\frac{\mathit{fights won}}{\mathit{total fights}}\right)•100$

We then run a linear regression model to determine the extent to which excess wins can be explained by excess height.

#### fig 03: Excess Height vs Excess Wins

slope: 1.75e-3; intercept: -2.98e-17; R2: 9.18e-4; std err: 1.54e-3

The regression line crosses incredibly close to zero & has imperceptible slope. A flat line, as with an E.C.G., implies the idea is dead. Even without the regression line it should be clear that there is no correlation between excess height & excess wins. In fact a trained eye will spot that the distribution appears roughly Gaussian (normally distributed) along both axes. Which in itself is a confirmation that being taller is not an advantage in MMA. If it where an advantage we would see a left skewed distribution with the bulk of the fighters clustered around the high end of the weightclass.

#### fig 03: Distribution of Excess Height

mean: -1.70e-15; median: 1.05e-1; skew: 1.53e-1

A skew that small could simply be sampling or more likely rounding error. The skew for our G.O.A.T. list (-1.08e-1) is also insignificant. Note too that the mean is extremely close to zero (-6.23e-1 for our G.O.A.T. list). For all intents & purposes heights are normally distributed across the weightclass confirming that there is no advantage to just being tall in MMA. You have to be able to implement a strategy that allows you to take advantage of your excess height.

#### Notes:

• Athletes used in these analyses must:
• have had a minimum of 5 professional fights,
• have fought in the UFC.
For a total of ~2,000 athletes with an average win ratio of ~70%. Truly Elite!
• Own calculations based on data from:

- mec