Fringe in Practice: How Does Sleep Affect Performance?

Does Sleep Affect Performance?

This is a great question! Conventional wisdom in the running world has taught me that it is not the night before which affects performance - the sleep two nights prior is key.

I decided to test this.

As of today, I have been recording a number of data points daily for 1 year exactly. It is apropos to investigate these numbers, then. The recoreded data points contain features such as:

• Hours of sleep
• Training volume (hours)
• Calories in
• Calories out
• Fatigue (1-10, 1 being the least fatigued)
• Freshness (1-10, 1 being the least fresh)
• RPE (rating of perceived effort, 1-10, 1 being the least taxing level)
• RPP (rating of perceived performance, 1-10, 1 being the most taxing level)

I also keep track of a number of other features (such as ATL, CTL, TSB, etc.), but these are not relevant for this discussion, as you will see briefly.

It is worth noting that I am not a fanatic about recording data - there are plenty of holes in the data which reflect times when it was not feasible to record data. For instance, ATL and CTL rely on heart rate or power data to be accurate - but I do not always use a heart rate monitor or power meter for my workouts. If I am travelling, I may not have access to the measurement tools (such as a scale).

It is also worth noting that I use specialized software to track workouts and caloric intake (in the form of macronutrients). While not a perfect representation of reality, the tool does model things reasonably well. I recently compared my actual weight differential over the past year with the estimated weight differential from the software and the difference between the two values was somewhere about 1%. I probably got lucky because hydration levels could easily account for a few pounds differential - but the point is that tracking does provide some degree of accuracy.

With that out of the way, let's get to the fringe. Using R, I quickly created a correlation plot of some of the features I suspected might affect RPP (my perception of performance):

Correlation Plot of Features Thought to Affect Performance

This plot does not really tell a whole lot. The red dots indicate that TSB is strongly and inversely related to ATL, which is basically the definition of TSB. Consequently, we should remove ATL and TSB for our next attempt. Same for ATL and RPE, also CTL and RPE. These are all expected, this correlation plot just validates that thought.

Sleep seems to be somewhat related to TSS and TSS is strongly related to RPE, calories consumed, IF and ATL. Again, these are all expected - the longer you work out per day, the harder the effort and the more food you need.

Let's try again, this time removing the strong (but obvious) correlations in order to show any correlations which may have been shaddowed by strong correlations.

Take 2: Remove obvious correlations

Now we are getting somewhere! Despite the direct correlation between calories in (KCal.in) and RPE, we see that sleep is correlated to RPE.

Time to investigate this further. I am performing these next calculations in Google Sheets (a very capable online spreadsheet). Armed with what I just learned from the correlation plots, I will look at the the covariance and correlation between some of these interesting features.

The covariance value tells us how much two values are related to each other, but that number is not scaled for comparison. The correlation is sort of like the normalized covariance and is represented in a number between -1 and 1. For both covariance and correlation, a negative value indicates an inverse relationship and a positive value indicates a direct relationship.

For example, consider that a and b have a covariance of 0.29, while c and d have a covariance of 0.98. We cannot make any claims that a and b are less related than c and d because the relationships between the two pairs may be vastly different. However, after we calculate the correlation of the two covariances, we can compare the correlation values. Continuing the example, let's say that a and b have a correlation of 0.62 and c and d have a correlation value of 0.22. We can now have more confidence when we assert that the correlation between a and b is stronger than that of c and d.

My end-game is to figure out what contributes to optimal performance, so I need to start defining what "optimal performance" is. For now, let's start with "low RPE and high RPP". The actual optimization will be a topic for another day, but for now, I am using a combing function which examines both RPE and RPP in order to derive a value, QWS (quality workout score). The higher QWS is, the better.

Considering the amount of sleep the night before, these are my findings:

Sleep The Night Prior

	RPE	RPP	QWS
Covariance	0.29	0.24	0.02
Correlation	0.13	0.11	0.12

The most important number is the bottom-right number: the "correlation" of sleep vs. QWS. The correlation is somewhat low, but perhaps still significant. 

For the next two charts, keep in mind that the slope indicates the correlation - the steeper the slope, the stronger the correlation. Plotting the values of sleep the night prior vs. QWS , we get this chart:

Sleep Two Nights Prior

	RPE	RPP	QWS
Covariance	0.20	0.18	0.00
Correlation	0.10	0.08	0.02

In this case, the sleep vs. QWS correlation is extremely low and probably not significant at all. Plotting this data we end up with a chart that looks like this:

My data and analysis shows that the sleep 2 nights prior is far less important than the sleep the night prior. However, the sleep the night prior is not a terribly good indicator of QWS. Perhaps we would have to look at multiple days of sleep leading up to a workout in order to get a better idea of how sleep plays into performance. Or consider more than one feature at a time (i.e. CTL, ATL and sleep). Also, using data for higher volume only days might yield better results. This is because most shorter workouts tend to be easy, steady state efforts and I suspect that I am not as likely to consider the workouts as tough.

This is certainly a fascinating topic and I would love to explore this further.

Takeaway

The sleep the night before does not appear to have a big affect on the QWS of a workout, and the sleep two days prior is essentially a non-player. Your mileage may vary.

One Last Point

NOTE: I looked at the covariance and correlation between weight and QWS as well as carry over balance (basically eating a lot of "extra" food the day before a long workout) and QWS, and these are my findings:

• The heavier I am (within my normal range), the fresher I feel; QWS is slightly negatively correlated. I think the physiological advantage gained by being a few pounds heavier outweighs the negative affect on performance. It might be useful to figure out the optimal weight, as well.
• Carrying extra calories into a workout has an extremely small affect QWS. Consequently, there is little need to consume extra calories the day before a big workout or event.

I also looked at how training volume correlates to QWS and found a significant inverse correlation. Simply put, the more time I work out in any one day, the less fatigued I feel. As well, more sleep leads to less fatigue.