The Impact of Temperature on Relative Power Output

In my recent posts I’ve introduced the concept of relative power output where a rider’s weighted average power in a particular race is compared to the average of all of their races to create a rider specific relative measure. Given sufficient sample size both of races for individual riders and riders in the data-set we can show what factors contribute to higher or lower power output on stages. So far, it looks like races with a lot of climbing, time trials, shorter races in general, high finishing position on the stage, and being in the breakaway leads to higher relative power output.

Another significant factor is the temperature the race is ridden at. I have temperature data for >95% of race-days in my data-set. The average temperature is about 20.5 C and 11% of race-days have an average temperature over 30 C.

To find the impact of temperature, we can leverage to relative power output model built in a recent post. That considers factors like the length and climbing difficulty of a stage, as well as the finishing position of the riders. That model produces predictions and we can train the temperature model on the residuals of that model and the actual power output on the stage. For example, stage 5 of the UAE Tour in 2019 is predicted to have a relative power output of 93% of a rider’s average weighted average power (eg, 256 watts if their average weighted average power is 275 watts). We can train the temperature impact model on the residual of that prediction (93%) and the actual (73%).

The ideal temperature is about 13 degrees Celsius (57 degrees Fahrenheit); this is where relative power output has peaked for the pro peloton. Higher temperatures have shown extreme impacts on the relative power output with a race at 30 C coming in about 3% lower than average and the hottest days like 2020 Strade Bianche impacting relative power output by -10%!

Incorporating temperature into the model shows that for every 1 degree Celsius away from 13 C relative power output drops by 0.4 percentage points such that the 2020 Strade Bianche race would be expected to have -10.6% lower relative power output than the average race. Adding temperature also increases the R^2 of the model from 0.25 to 0.29; it also improves the model fit out-of-sample with R^2 increasing and SE dropping from 0.10 to 0.09.