Boston Marathon times, 2021–2024
Motivation
The Boston Marathon is the oldest and among the most famous annual marathon races. It is also one of the most competitive: to be allowed to run in the Boston Marathon, you must show you have already completed another marathon with a time that exceeds a strict standard, limiting the Boston Marathon to only the fastest runners. These standards are used to limit the marathon to about 30,000 runners so the course is not too crowded, though about half a million spectators also crowd along the route.
In modern marathons, runners wear a race bib with an identifying number and an RFID tag that allows electronic monitors around the course to track each runner. This is used to calculate each runner’s time and determine the winner, but also allows spectators to follow a runner’s progress—helpful if you’re attending to support a particular runner and want to know when they’ll pass you or when they’ll arrive at the finish line.
Onyejekwe and Gerber (2026) considered whether a runner’s pace at certain milestones throughout the marathon can be used to accurately when the runner will pass the finish line. They obtained data from all runners in the Boston Marathon between 2021 and 2024: their pace at various points throughout the race and their ultimate total time to complete the marathon. Can this data be used to predict finish times?
Data
Each row is one runner in a particular year, 2021–2024.
boston-marathon-2021-2024.csv.gz
Variable descriptions
| Variable | Description |
|---|---|
| Name | Runner name |
| Age | Runner age (years) |
| M/F | Runner gender (qualifying time standards vary by gender) |
| 5K | Time the runner took to run the first 5,000 meters (seconds) |
| 10K | Time the runner took to run the first 10,000 meters (seconds) |
| 15K | (as above) |
| 20K | (as above) |
| HALF | Time the runner took to run the first half (about 21,000 meters; seconds) |
| 25K | (as above) |
| 30K | (as above) |
| 35K | (as above) |
| 40K | (as above) |
| Finish Net | Time the runner took to run the full marathon, 42,195 meters (seconds) |
| Year | Year of the marathon, 2021–2024 |
Questions
- Runners probably slow down throughout the race as they grow fatigued. Calculate the runner’s speed every 5K as the amount of time it took the runner to run that 5K (so the speed at 10K is the difference in time between the 5K and 10K points). Build a visualization showing the speed of runners every 5K. Do they indeed slow down throughout the race?
- Build a model to predict finish time (
Finish Net) using the time taken to complete the half marathon (HALF). Interpret the coefficients. If runners were consistent and maintained the same pace,Finish Net = 2 * HALF; is that the case? - Each year may be slightly different, as the temperature and wind vary and may speed up or slow down the runners. (On a very hot day, perhaps runners fatigue much more quickly.) Consider adding a term to your model for year. What should you add to allow the model to change by year? Add the term and conduct an appropriate hypothesis test to determine whether the relationship varies by year.
- The relationship may also depend on runner gender and age, so test whether these variables are relevant and decide whether to include them.
- Fit your model (without the term for year) to just the 2021–2022 data. Use it to make predictions for the running finish time for runners in 2023–2024. For each prediction, also produce a 95% prediction interval, and compare the interval to the runner’s actual finish time. Do the prediction intervals have 95% coverage?
- Write code to make models to predict from each time point. That is, predict finish time from the 5K time, then (separately) predict finish time from the 10K time, and so on. Fit on the 2021–2022 data again. Show or plot the estimated error variance \(\hat \sigma^2\) from each model. We’d expect the model uncertainty to decrease as we get later in the race, so the 40K time is the most precise predictor of finish time and the 5K time is the least precise; does this show up in \(\hat \sigma^2\)?
References
Data scraped from the website of the Boston Athletic Association by Brandon Onyejekwe and Eric A. E. Gerber for the paper “Quantifying uncertainty in marathon finish time predictions”, presented at JSM 2026. Code and data available at https://github.com/bonyejekwe/Marathon_Predictor.
Additional historical data available at https://github.com/adrian3/Boston-Marathon-Data-Project.