Road Race Stats - Marathons & Other Running Races

Friday, May 13, 2005

Temperature Effects on Half-Marathon Times

How do you modify your pace with changing temperatures? If you can run a half-marathon in 2:00 when it's 60°F, what should your pace be if it's 70°F? That's the question I'm investigating.

Indianapolis 500 Festival Mini-Marathons

I've started with the half-marathon since I've been working on the stats of last Saturday's Indianapolis Half-Marathon. This seemed to be a good starting point for this kind of analysis. It's the largest half-marathon in the country, and there are several years of race results. I'll keep refining this analysis with additional data from additional half-marathon races. Also, in the future, I'll repeat this analysis for marathons and races of other distances.

I've collected race results from the Indianapolis Half-Marathon since 2001. Also, I recorded the temperature at each race about an hour after its start. This seemed to make for a good average temperature for the race. I then tried to see if I could identify an average slowdown for each additional degree in temperature.

Comparing Times Between Races

Next, I had to determine how to compare times between the races. I needed to remove other variables that could mask the temperature relationship. For example, let's say in 2001 it was 65°F at the race and the race consisted of all males. Then in 2002, the temperature was 55°F but the race consisted of all females. The finish times in 2002 would likely be slower than 2001 even though the temperature was 10° cooler. The gender variable masked the temperature variable.

So I decided to categorized the runners according to the two variables that clearly affect finish times: gender and age.

Then I had to determine a type of average time to use for each category. Both mean and median times can be affected by the field of runners at a race. Let's say in 2002 there was a ton of pre-race advertising. Consequently, a lot of recreational runners entered. However, in 2001, there wasn't much pre-race advertising, and most of the participants were serious runners. One would expect the mean or median times to be slower in 2002 than 2001. In the previous post, I had quoted this statistic from the Philadelphia Inquirer which shows how finish times have slowed down as marathons have become more popular: "average marathon finishing times for men have jumped from 3 hours, 32 minutes in 1980 to 4 hours, 19 minutes last year".

So to minimize this "quality-of-runner" variable, I included several additional times in addition to median times. These included the times of the 10th, 100th, and 500th place runner in the particular age and gender group. My idea is that if a race gets many more casual runners, there will still be a large group of serious runners. So by picking specific places, this should reduce the effect of this "quality-of-runner" variable. I also included 3 different places since I anticipated differences between elite runners and average runners. One would think elite runners would be less affected by temperature.

Displaying the Results

The results are shown below in the table. The last column in the table provides the average slowdown for each group. For example, a slowdown number of 9 represents that the group on average slowed down 9 seconds for each rise of 1°F in temperature.

To determine the average slowdown, I assumed a linear relationship and used the method of ordinary least squares. This basically tries to find the slope that best fits the temperatures and finish times. You can think of this data on an X-Y graph in which temperature is on the X-axis and finish time is on the Y-axis. One would expect as temperatures increase, finish times should also increase. For simplicity, I assumed a linear relationship. I'm sure this linearity doesn't hold as temperatures get real cold or real hot. But for a reasonable temperature range, this seemed like a reasonable assumption.

An Example

On top of the table I included an ideal case as an example. This ideal running group had an average time of 1:32:21. This is the mean time for this group for all of the races (from 2001 through 2005). The time at each race could be any type of time (median, 10th place, etc.)

I ordered the years by increasing temperature. This is the temperature about an hour after the start of the race as provided by

One would expect that the finish times should slow down for rising temperature. I may try to include graphs in the future. For the ideal case, you would see a rising slope from left to right. For the table below, I represent this by minus and plus signs. The minus sign represents a finish time below the average. The plus sign represents a finish time above the average. Bold represents times more than 60 seconds below or above the average.

So in the ideal case, note how the year with the coolest temperature (2003) has a bold minus sign. The next coolest year then has a unbold minus sign. The next two then have a unbold plus sign. Finally the warmest year (2001) has a bold plus sign representing a slow finish time above the average.

To see the exact finish time, move your mouse over the cells with the minus/plus signs.

All these minus/plus signs are essentially summarized by the slowdown number. For the ideal case, this number was 9 sec/°F. At 53°F the finish time was 1:31:17. At 54°F, it was 9 seconds slower (1:31:26). Then finally, at 67°F the finish time was (67-53)*9 seconds slower or 1:33:23. As can be seen, this ideal case would generate a straight line with a slope of 9 (increasing 9 seconds for each increase of 1°F).

In the non-ideal case, other variables come into play. The 5 finish times won't create a straight line. So to try to find the best straight line fit, I used the ordinary least squares method.

The Results

Although it wasn't an exact fit, a slowdown was seen for each group as temperatures increased. But it wasn't as much as I expected. I didn't have a large temperature range. Perhaps the slowdown is minimal below 70°F. Maybe over 70°F, the slowdown increases at a higher rate.

There wasn't much slowdown difference between the 10th place finish times and the 100th place finish times. There was actually less slowdown for the 100th place than the 10th place.

The slowdowns for the 500th place time and median time did tend to be larger than the 10th and 100th place times. There is one exception to this. The women median times had a smaller slowdown than the other times. In fact, the forties and fifties age groups had a large speedup with temperature. So other variables must have had a bigger effect.

But excluding the median times, in the other times (10th, 100th, and 500th place times) the women tended to have a larger slowdown than the men. So similar to observations in other posts, it seems that temperature has more effect on women.

How to Use This

So let's say you are a female 33 years-old who finished with a time of about 2 hours in a half-marathon last year. At that race the average temperature was around 55°F.

If you feel you are at about the same fitness level as last year and if the average temperature at race day is going to be 65°F, you can estimate that your finish time will be 150 seconds slower. This is based on the slowdown factor of 15 for a female in her thirties who had around a 500th place finish (or about 2 hours). Multiplying 15 by 10 (the temperature difference) gives 150 seconds or 2.5 minutes.

So for the ideal run, adjust your pace for a 2:02:30 finish rather than a 2:00:00 finish.

Future Work

In the future, I'll keep collecting more data (more races with more temperature ranges.) Plus, I'll keep looking at how to factor in or out the effects from other variables. Some things that might need to be considered are humidity, altitude and elevation changes.

I thought about combing the humidity with the temperature like what's done with the heat index. However, the heat index calculation seems to require temperatures above 80°F. This may be appropriate when you're not active. But for high intensity workouts, humidity seems like it has a big impact even with temperatures under 70°F. I'll have to keep investigating this.

Finally, I'll look into graphical representations of the data. I've tried to make the tables easy to view, but I have to admit that sometimes a picture is worth a thousand words.

As I mentioned, I'll also look into other distances like marathons. One would expect the longer the race, the more effect there will be from temperatures.

If you have any suggestions, please leave a comment. Thanks!

Half-Marathon Finish Times vs Temperature (Move mouse over plus/minus cells to see exact finish times for the specific year)

Compared to AverageAvg
Ideal runner
Male 10th place runner
Male 100th place runner
Male 500th place runner
Male median runner
Female 10th place runner
Female 100th place runner
Female 500th place runner
Female median runner

The above stats are based on results from the Indianapolis 500 Festival Mini-Marathons for 2005, 2004, 2003, 2002, and 2001. The temperatures are based on data from history for Indianapolis, Indiana for 05/07/2005, 05/08/2004, 05/03/2003, 05/04/2002, and 05/05/2001.

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  • Very intriguing...

    Knowing the athlete's physical status each year would be so helpful, but it unattainable.

    I am wondering if you did any diagnostics on your regression? Only curious on how well the model did.

    The table is a great and practicle way to estimate.

    The marathon will have some harder assumptions to make on temperature. With runners being out on the course for 2,4,6 and maybe 7 hours, the weather can change drastically. And if it does get hot, you would have to include some fatigue factor - temperature interaction. That is, fatigue should be affected by the temperature. The hotter it is, the greater the fatigue... the slower the time.

    By Anonymous Anonymous, at 8:28 AM  

  • Thanks for the inputs.

    I didn't do any diagnostics on the regression. Sounds like a good idea as I collect more data. I'm sure the linear model is too simple especially with higher temperatures.

    Yea, I think temperature modeling for a marathon has some complications. A race where the temp goes from 50 to 80 degrees will be much different than one that stays at 65. But both have the same averages.

    Not quite sure I understand the concern over the fatigue factor. In hot weather would this be an additional factor to slow down a runner?

    By Blogger Ken, at 3:34 PM  

  • Ken,

    To better understand the effects of heat at the Mini, you should add 2000 to your analysis. It was so hot that year that the race officials put black flags out on the course and turned the race into a nonscored event.

    The Top 500 finishers receive special medals. Usually the 500th finisher comes in between 1:30 and 1:31. This becomes the time goal for all self-respecting runners! In 2000, the 500th time was 1:37:03.

    Another thing to keep in mind is that the race start time has varied over the years. To the best of my recollection, the race started at 9:00 am in 2000, at 8:00 am in 2001-2004 and at 7:30 am (7:33 actually) in 2005. (I have not bothered to audit your temperature readings to see if you picked the correct start time for each year.)

    Other variables to think about when comparing races: amount of shade (or lack thereof) on the course and the availability of fluids. For the Mini, there is little shade on the course. The 2.5 miles on the Speedway are hot no matter...radiant heat from running in a smooth asphalt bowl maybe? The Mini does have plenty of fluids available to runners. Something like 17 aid stations.

    Fun stuff...

    By Anonymous Anonymous, at 5:34 PM  

  • Jeff, Thanks for your inputs. I think I will add in 2000 and perhaps some previous years. The reason why I decided to stop at 2001 was due to them changing the results format. I'll just put in some extra work and add those results.

    I did take into account the changing start time. However, my temperature data may not be the best. I'm getting it from and they only usually list temps at every hour. Also, I believe these temps are at the airport so this could be somewhat different than at the race.

    And that's a good point about shade and fluid availability. Official temperatures are taken in the shade which can be much cooler than in the sun. So at the very least, I probably also need to track sky conditions. If it's cloudy, the official temps should be close to the temps at the race. However, in sunny conditions, it'll get more complicated.

    By Blogger Ken, at 9:47 AM  

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    By Blogger alena, at 4:39 PM  

  • Is there and source that contains data on 'average' finish times or some sort of comparative data for various marathons in the US? I hoping this data can be used in determining (to a limited extent) which marathons are 'fast/easy' and which are 'slow/hard'. If you can send your response to megabyzus at hot mail dot com. Thanks!

    By Anonymous Anonymous, at 8:06 PM  

  • Have you looked at shorter races like 5k,10k and 5 miles? I was wondering how to make adjustments for really hot days (80+) with high humidity?

    By Anonymous Anonymous, at 10:32 AM  

  • You are very gracious to humor what seems like a lot of backseat driving amid the commentary. I have to say, having only dabbled in statistics, I am bowled over by the degree of care and attention you devoted not only to the planning of your matrix but also to the mapping of your results.

    I would agree with your initial assessment that a humidity factor would further refine your analysis. I have only been running for about two years and have finally broken into sub-30 digits but have found that wind and wet air (not actual rain or snow) present the most formidable challenges, regardless of other weather conditions.

    Keep up the awesome work!

    By Anonymous Anonymous, at 8:10 PM  

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    By Blogger Carol William, at 11:32 PM  

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