# How Injuries Affect Fitness via VO2Max

In April 2017, I tore the meniscus in my right knee and in July 2017 I finally had surgery to repair it. It took me about a week to walk again, but due to atrophy in my right quad, it was months before I could run again. Now more than a year later, I'm curious how this injury affected my fitness. How does it compare to my peak months climbing North America's highest mountains?

## VO2Max: A Better Measure of Fitness

Back in the 1990s, baseball fans and teams alike used two primary metrics to measure player performance: batting average (BA) and earned run average (ERA). By the late 1990s and early 2000s, "sabermetricians" (i.e., baseball nerds) developed better metrics to measure player performance and value: first came on-base percentage (OBP) and walks/hits per inning pitched (WHIP), then a bunch of intermediate "sabermetrics," and today we have Wins Above Replacement (WAR) and weighted on-based average (wOBA). The beginning of this transition was the subject of the book and film "Moneyball." WAR is such a good measure of player value that even old-school broadcasters on ESPN are using it.

When we think about personal aerobic fitness, we are often stuck using a basic metric akin to batting average: pace (min/miles). Pace has a lot of problems: we go slower uphill and faster downhill. Our pace varies with altitude. Sometimes we deliberately train at a faster pace or a slower pace. In fact, low-intensity endurance training is frequently recommended to be the base of an aerobic athlete's training regiment. While Strava now calculates Grade-Adjusted Pace, this does not give us a measure of fitness when we aren't trying to maximize our pace. Wouldn't it be great if we had a barometer of fitness for any activity? Enter $$VO_{2}Max$$.

$$VO_{2}Max$$ is defined as the maximal rate of oxygen uptake and consumption during exercise. It is measured in mL/(kg·min). In some sense, it's a measure of the horsepower of the engine that is our aerobic system. The more oxygen we are able to use per min, the faster we are able to go. While elite athletes may hit a ceiling trying to over-optimize $$VO_{2}Max$$, the rest of us will likely experience fitness gains when increasing our $$VO_{2}Max$$.

Fortunately, most fitness and smart watches that track heart rate (including the Apple Watch) now provide an estimate of $$VO_{2}Max$$. How good are these estimates? It depends on the equipment and manufacturer, but using a heart rate strap, the estimates may be as close as 2%. The methodology, as far as I can tell, has been developed by a single company: Firstbeat. My best guess is that estimate depends on the relationship between heart rate and pace. I would love to reverse-engineer the calculation, so stayed tuned for that!

## The Data

I have a Suunto Ambit2 fitness watch with a heart rate strap. I try to use the heart rate strap on runs and occasionally on hikes, climbs, and bike rides. Here's a plot of my activities using the Ambit2. Larger circles are more mileage.

For the purposes of this analysis, I chose to only look at the running data, since the estimates of $$VO_{2}Max$$ seem to be quite different for other activities. For example, while "trekking," I frequently carry a heavy pack.

Suunto has an online platform called "MovesCount," which provides an estimate of $$VO_{2}Max$$. Unfortunately, there is no export function for these estimates! To download these data, I first found a list of my MoveIDs. I then used Selenium in Python to access each "move" (necessary because MovesCount is Javascript-heavy) and then fed the resulting XML into BeautifulSoup and scraped the data. This was a massive pain, but I guess Suunto is trying to protect customer data.

## VO2Max Over Time

Here is the plot of my $$VO_{2}Max$$ from 2015 to 2018. I've annotated it with some climbs and the red line is the date of my surgery. Somewhat surprisingly, there is not an immediate dip—a short October run had an estimated $$VO_{2}Max$$ of 48—but there is a dip after a winter of neither bike commuting nor running.

My fitness is highest right before major climbs and often crashes immediately after, perhaps because of fatigue and recovery. It seems to generally increase after those climbs. And the good news is it seems to be increasing again!

So in conclusion: it appears the the surgery itself did not impact my fitness, but a winter of minimal aerobic exercise did. Ohio winters…

## Possible Issues with the Estimated VO2Max

Anecdotally, I have noticed that the estimated $$VO_{2}Max$$ is higher for more intense runs. Are there other "external" factors that affect these estimates? Short answer: yes.

The above scatterplot matrix shows correlation between variables. We can see estimated $$VO_{2}Max$$ is correlated with average heart rate (r = 0.47), temperature (r=-0.34), and % of the run in the "hard" heart rate zone (r=0.42). So just working harder means a higher estimate of $$VO_{2}Max$$ . And higher temperature means a lower estimate of $$VO_{2}Max$$. We can also see a strong relationship between % hard and average heart rate.

So the methodology appears to have some issues—ideally, we would see a consistent estimate of $$VO_{2}Max$$ between a low-intensity and high-intensity workout for an equal level of fitness. And we're getting docked in hot weather.

On the flip side, the correlation between average heart rate and estimated $$VO_{2}Max$$ is not that strong, which is encouraging. Additionally, the estimated $$VO_{2}Max$$ over time don't appear to vary too wildly.

How should we view these estimates? I think they do capture trends of my true $$VO_{2}Max$$, but there are some problems with the method that should be addressed. There is room for improvement and hopefully we will see it as fitness and smart watches gain additional sensors. Perhaps I'll give it a shot!