The field slows hardest between 25 and 35 km

Start · the question

Runners name different miles

Ask marathoners where the wall is and you hear mile 18, mile 20 or mile 22. One runner's handful of races is too few to show a shape. One field of 31,655 is plenty.

Every Boston finisher leaves a cumulative time at 5, 10, 20, 25, 30, 35 and 40 km and at the finish. Each segment's time divided by its length is that runner's pace through it, and the median across the field, segment by segment, is the average shape of the race.

The curve

Flat, then a corner, sharper at the back

Drawn along the course, the field's numbers make a corner. The first 20 km add only 2.4%. If fatigue built up evenly from the gun the line would slope from the start, and it doesn't: something changes after 25 km.

Pick a finish-time group to see the same corner at different strengths, each measured against the group's own 5 to 10 km pace. Runners under 3:00 end about 8 to 9% slower than their early pace. Runners over 4:30 are 33 to 35% slower between 30 and 40 km, then ease to 25% over the last 2.2 km.

How the model was built

One linear model per mat, tested on a year it never saw

At each mat the model predicts how much slower than even pace the rest of the race will be. Its inputs are the average pace so far, the last 5 km against that average, the first 5 km against that average, those terms against each other, and optionally gender and age. The training years are 2014 to 2017 and 2021 to 2023 (176,059 finishers). 2024, the latest year with splits, was held out: nothing about it was used to fit or choose anything.

I compared four ways to predict, by leaving out one training year at a time: even pace from the latest split, the 2014 field's median curve scaled to your time (the rule behind the split card above), this linear model, and gradient-boosted trees. The trees were 0.6 to 4% better than the linear model. I kept the linear model because it is a few hundred coefficients that the browser and Python evaluate identically; the trees would have been a large export for a small gain. The table shows all of them on 2024, the trees included for the record.

Mean absolute error in minutes on the 2024 race (25,377 finishers; 25,376 scored at each checkpoint); lower is better. The Brier score compares the wall-risk probability with what happened (0 is perfect); the base rate always predicts the training share, 17%. From tables/model_eval.json, written by train_model.py.

From 10 km on the model beats both baselines. At the half its typical miss is 7.9 minutes, against 18.1 for even pace and 9.9 for the 2014 curve. At 5 km it does not: the 2014 curve was slightly closer on 2024 (15.0 against 15.4 minutes), probably because 2024, like 2014, had a big fade (see the panels above).

The ranges are split conformal intervals. For each mat and each fifth of the field by pace so far, the model's errors on the left-out years set the width, so year-to-year swings in weather are already in them. The chart shows how often 2024 finish times fell inside.

Coverage is close to target early and slips late: by 35 km the 80% range held 74% of runners and the 95% range 92%. 2024 faded harder than most training years, so the late ranges were a little too narrow for it. At the early mats the misses sit with the slowest finishers; by 35 km they are spread across the field.

Wall risk is weak early and useful late. At 5 and 10 km it barely beats the base rate (Brier 0.172 against 0.179), and for most runners it runs low, because 22.7% of 2024 runners hit the wall against 17% in the training years. The few given a very high risk at the half hit it less often than predicted. By 30 km the score is 0.117, and at 35 km 0.091.

Pacing types

Four shapes, and a field that drifts between them

Each training runner's eight segment paces were divided by their own average pace and grouped with k-means. Three to six groups all came back the same from different random starts, but the groups are slices of a continuum: the silhouette score for four is 0.28, low. I kept four because each has a shape a runner would recognize, and named them by that shape.

From model/pace_model.json and tables/model_eval.json.

The shapes hold from year to year (clustering one year alone puts the same runners in the same type 72 to 92% of the time), but the mix does not: Even was 29% of the 2014 field and 65% of 2023. In the tool, the type is the nearest shape to the segments you have run, scaled by your predicted finish. Read early it is a guess. On 2024 it matched the runner's full-race type 40% of the time at 10 km, no better than always answering Steady fade, then 53% at the half, 70% at 30 km and 81% at 35 km.

Limitations

What this doesn't show

Split data locates the slowdown and can't separate the causes. Glycogen depletion, muscle damage, heat and a too-fast start all produce a late fade.

Boston's course is part of the result. The Newton hills run from about 16 to 21 miles, or 26 to 34 km, which is where the corner is, and the net-downhill opening makes early pace look quicker than it would on a flat course. A flat course would probably show a softer corner, but this study has no flat-course data to test that.

The main results above are one edition of one race, and the multi-year panels show it was an unusually hard one. The model adds eight years but is still Boston only, and it knows nothing about the weather: a hot year shifts everyone at once, which is why its 2024 ranges ran narrow late in the race. The 2015 to 2024 files come from public mirrors of the official results, not from the B.A.A. directly. The companion study on negative splits now has the per-year counts too.

For a runner

The damage shows after 25 km and starts earlier

The groups that stay closest to flat late are the ones whose early pace left them something in reserve. The data shows an association and says nothing about mechanism. For a runner the reading is still the familiar one: the first 25 km are where you choose how the last 17 go.