Are heat-adjusted pace calculations accurate for the marathon?

Last week I published my heat-adjusted pace calculator, which estimates how much you’ll have to slow down in hot, humid conditions during a long workout or long race in the heat.

The timing of the release provided a very nice opportunity for a validation test: the marathon at the 2025 World Athletics Championships, which was held this past weekend in brutally hot conditions in Tokyo.

The women’s race on Sunday was held in 86° F (30° C) and 70% humidity; the men’s race on Monday was held in 82° F (28° C) and 72% humidity. These, clearly, are far from ideal marathon conditions, and the finish times reflect the difficult conditions.

By looking at how slow the top athletes actually ran, compared with how slow they were predicted to run by my calculator, we can check how accurate these “heat-adjusted paces” really are.

Validating my heat-adjusted pace predictions

We’ll look at the top 10 results for both the men and the women. For each finisher, we’re interested in four things:

• Their ideal-condition fitness – we don’t know this, but we can estimate it by looking at the athlete’s best performance in the last two years (a more appropriate “season best” since marathoners race so infrequently)
• Their actual performance in Tokyo – which we can just get from the results
• Their predicted performance in Tokyo – we can calculate this by inputting the athlete’s ideal marathon pace, plus the actual conditions of the race, into the heat-adjusted pace calculator
• The discrepancy between the predicted and actual performance – which is self-explanatory

Here’s what the performances and slowdowns look like for the men and women:

It’s a little easier if we convert these to pace per kilometer to get better intuitions about the practical accuracy (since you’d be checking splits during the race; knowing the overall slowdown is less helpful for pacing).

Here’s the data we need, converted to pace per kilometer:

Just eyeballing the tables, the results look pretty good! But let’s put some graphs and numbers on it.

In terms of the model’s accuracy across runners, the mean absolute error was 2.6 seconds. Not bad! Although 20 runners is a little small for looking at percentiles, in 90% of cases, the heat-adjusted pace  was within six seconds per kilometer of the runner’s actual pace.

Here’s the same data visualized:

Are elite runners getting better at handling heat?

When looking at the model’s average error, I was surprised to see that the model tended to predict times that were a little too slow: across all 20 athletes, predictions were 2.2 sec/km slow on average.

Much of this tendency for slow predictions came from three runners (Julia Paternain, Alisa Vainio and Abel Chelangat) whose season best was very close to their actual performance at the World Championships—we’ll examine these outliers in a moment.

Even so, the model still skewed about a second per kilometer slower for the other athletes. I was expecting the opposite! I had figured that championship-style racing could lead to a very sluggish early pace, like it did in the men’s 10,000m a few days before. But there might be a few factors that made the athletes in Tokyo run better than the calculator predicted:

• The athletes knew that Tokyo was going to be hot, and presumably they prepared for it
• Athletes who run well in the heat might have self-selected into competing in the race (and vice versa for athletes who know they do not handle the heat well)
• Heat training methods have advanced significantly in the last 10 years
• Heat management strategies (misting stations, ice packs, cold sponges, headbands) have also advanced significantly, and the race course was set up to have frequent opportunities for cooling
• If you are confident in your ability to handle the heat, the best strategy is to run at a pace that is too fast for a less thermally tolerant runner

This finding makes me wonder if elite athletes are actually running better in hot conditions than they used to in decades past.

The outliers: who ran especially well in the heat?

As noted above, three runners stand out for running very close to their season best: Julia Paternain, Alisa Vainio and Abel Chelangat.

Paternain was running only her second marathon ever—her first race was a controlled 2:27:09 at a small race north of New York City in March. Chelangat was also relatively new to the marathon, with only two races ever on the international stage before Tokyo (a 2:10 and a 2:08). Alisa Vainio is more experienced, having run between 2:25 and 2:28 three times before Tokyo.

My best guess is that these three athletes were in better ideal-weather shape than their season best indicated. Still, it’s clear that all three ran exceptionally well in the heat. It will be interesting to see how they do the next time they race in cool conditions on a fast course.

Some caveats about using elite performances as a benchmark for heat adjustments

While I’m very happy to see how well the predictive model performed, there are a few caveats to keep in mind regarding these results.

Elite championships races are “in-distribution”

In predictive modeling, there’s a concept of “in-distribution” versus “out-of-distribution” predictions. When you build your model, you need a dataset.

In the case of my HAP calculator, that dataset was the collection of race-day weather conditions and marathon finish times in this 2022 scientific paper. In that 2022 dataset, a significant chunk of the performances were from Olympic and World Championship events.

So, even though this year’s competition was new data that had not been used to build the predictive model, these new observations were arguably still “from the same distribution” of data used to build the model.^[1] So, we should expect the model to perform pretty well for this year’s World Championships marathon races.

One shortcoming of that 2022 paper is that the marathon performances for recreational runners only go back to about 3:30 (so, about 8:00/mi or 5:00/km pace). An out-of-distribution prediction would be a 4:15 marathoner using my calculator to predict their heat-adjusted pace.

This prediction would be out-of-distribution because this runner is pretty importantly different from the runners whose performances were used to build the calculator. That doesn’t guarantee that the prediction would be wrong—it just means that our 4:15 marathoner would need to be more careful with the result. Sometimes out-of-distribution predictions work just fine! Other times not.

Looking at top performances doesn’t deal with drop-outs or massive slowdowns

If you watched the World Championships marathon, you likely noticed many of the favorites either faded badly or did not finish at all. That obviously creates some bias in the data we used to validate the heat-adjusted pace model: runners who fade badly in the heat are very unlikely to make it into the top ten!^[2] 

This blind spot is actually shared with the original data used to build the heat-adjusted pace model. Indeed, I discuss exactly this limitation in the write-up for it.

So, the right way to think about this model’s predictions might be “for the kind of runner who tends to run well in the heat, here is how much to slow down” – which is a different prediction than “for a typical runner, here’s how much to slow down,” to say nothing of runners with very poor heat acclimation.

I’ll reiterate what I wrote in my heat-adjusted pace calculator write-up: the real solution to this problem is using longitudinal data, looking at how the same runners do in different levels of heat (and ideally, accounting for heat acclimation as well). When I figure out a good way to do this, I’ll update the calculator accordingly.

Recap: Heat-adjusted paces are reasonably accurate (for well-prepared runners)

For high-level runners, my heat-adjusted pace calculator can predict heat adjustments for the marathon within about six seconds per kilometer or ten seconds per mile in the vast majority (~90%) of cases. On average, the predictions are only off by 2.6 seconds per kilometer (4 seconds per mile).

Keep in mind that these predictions are for well-prepared high-level runners, who presumably used heat acclimation in training and definitely had liberal access to fluids, ice, cold sponges, and other heat management strategies.

Predictions on “out of distribution” performances, like recreational runners, runners poorly prepared for the heat, and conditions that are much hotter than the weather seen in the dataset may not be as accurate.

If you haven't already, try out my heat-adjusted pace calculator here:

☀️ Check out my new heat-adjusted pace calculator here! 🌡️

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Footnotes

^[1] In fact, one of the races in the dataset is from the 2007 Osaka World Championships, which was also in Japan and also very hot and humid!

^[2] At championship races, top athletes often drop out of the marathon when it becomes clear they will not get a medal—financially speaking it’s better for them to save their body for a fall or winter marathon that will pay an appearance fee and have a bigger prize purse.

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