# Performance prediction equation for the Valencia Marathon based on time and pacing in the half marathon

## TL;DR

This study predicts marathon performance using half marathon time, age, sex, and pacing, finding it as accurate as existing methods.

## Contribution

A new linear regression model for predicting marathon times using pacing and demographic factors is proposed and validated.

## Key findings

- The model explained 85% of marathon time variance with a 5.9% mean absolute error.
- Adding pacing range did not improve prediction accuracy beyond half marathon time and demographics.
- The model's accuracy was comparable to the VDOT system but varied by runner performance level.

## Abstract

Although pacing is a variable that affects marathon running performance, there is a lack of studies that assessed whether it can improve performance prediction. The aim was to calculate a linear regression model with data such as the half marathon race time, age category, sex and pacing range (difference between the maximum and minimum relative speed of the half marathon) to predict the marathon time. Moreover, the accuracy of the prediction equation obtained was compared with the Daniels’ VDOT.

A total of 8.261 runners, who participated in both events (Valencia Half Marathon and Marathon) in the same year, for the 2022 and 2023 editions, and ran the half marathon faster than the marathon, were included in the study. Three linear regression models were obtained: a first model with only the half marathon time and sex, a second model adding the age category to these, and a final model adding the pace range to the previous ones. Afterwards, the most accurate and simple model was selected, and its fitting was compared with respect to a model contrasted by the literature, the VDOT.

The introduction of the pace range variable did not improve the model’s prediction, obtaining an explained variance of 85% and an mean absolute error of 5.9%. The overall accuracy of the model obtained was similar to that of the VDOT system, but the models behaved differently depending on the level of runners’ performance.

These results allow coaches and runners to establish specific training rhythms to work on the competition pacing.