Predicted Times Algorithm for Tortoise & Hare (2012)

by Paul Patterson, former FCRC President

This algorithm was used from late-January to September 2012. It was a revision of Paul’s algorithm used in years up to late-January 2012. For the latest algorithm, see the Tortoise & Hare page.

The algorithm for predicting the finish time for a T&H race is a two step process. First, for each previous race, using the previous race distance and finish time, a finish time is predicted for the new race distance; the second step is to use all the predicted finish times based on the previous races to calculate a overall predicted finish time; now the messy details.

The formula used to predict a finish time for a new race based on a previous race is

(new finish time) = (previous finish time) * (new distance) / (previous distance) * (adj factor)

where the adjustment factor is either 1.06, if the new distance is greater than previous distance, or 1/1.06 (approximately 0.9434), if the new distance is less than the previous distance. The adjustment factor compensates for the fact that our pace is slower for a longer distance and faster for a shorter distance. For example, if the previous distance was 5K and the new distance was 10K, we can’t just double our 5K time; the learned folks who have studied this problem think an average person slows down by 6 percent of the doubled time. There are a couple other proposed adjustment factors out in internet land; Nick and I decided to use the simplest one.

The overall prediction is based on the races from last season and this season. A point of clarification: a season is seven races, so the 2011 season is October 2011 through April 2012.

Separate predictions are made using last season’s races and this season’s races, and then these predictions are combined. Before discussing how the predictions are made for each season, let’s first discuss how they are combined.

If there are no previous races from this season, then the overall predicted time is the predicted finish time based on last season’s races. (This is the situation for all racers at the first race of the season.)

If there is only one previous race from this season, then there are two sub-cases:

  • There are no races from last season; then use the predicted time based on the one previous race from this season.
  • There are races from last season; then the overall prediction is the average of the prediction time based on the one previous race from this season and the predicted time based on the races from last season. That is:

(1/2) * [(predicted time based on this season’s one race) + (predicted time based on last seasons’ races)]

What this does is weight the one piece of current information from this season more heavily than the old information from last season.

If there are two or more previous races from this season; then the overall predicted time is prediction based on this season’s previous races; that is, ignore the information from last season.

Predicted time based on a season’s races:
If there is 1 race for the season, use the predicted time based on that race.
If there are two races for the season, use the average of the two predicted times.
If there are three or more races for the season, then use the minimum of the following two numbers:

  1. The average of the predicted times.
  2. Fastest predicted time + 1/3 * [Slowest predicted time – Fastest predicted time]

Item 2 above handles the situation where a runner has a large difference between the fastest predicted time and the slowest predicted time and most of the predicted times are clustered around the slowest predicted time.