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Posted on 6 Aug 2009 at 12:52

 

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He may be used to fixing runtime errors, but David Robinson finds that writing a program to work out handicap races for his local running club is much trickier.

The hard-working secretary at our running club asks, "Have you started that program yet?" We'd spoken, ages ago, about the problem of calculating handicap times for some of the club races - in particular, what a tricky job it was and how the burden might be alleviated by the right software.

Having handicap races is an essential part of club competition, otherwise the same few - usually young - people win everything in sight and the rest of us trudge round without a hope of any glory.

You'd think calculating target times would be simple enough, but it's fraught with gotchas. For a start, the only person who thinks they got a fair handicap time is the person who won - everybody else thinks the winner's target was too easy and theirs was too hard. In fact, being the handicapper could be the most unpopular position in the club.

I discovered that successive handicappers had been using a spreadsheet constructed anonymously back in the mists of time. This had a column storing a base time for each club member; it was supposed to be a representative 10K time, but the innocent-looking word 'representative' hides several cans of worms. Suppose the next race to be run is a half marathon (21 kilometres); you have the task of working out what is the 'right' target time for the longer distance.

Common sense says that if someone runs 10K in, say, 50 minutes, the answer's not going to be 105 minutes (50/10 x 21), because the further you run the slower you go. If this weren't true, then Usain Bolt would be running marathons in just over an hour.

Formula one, and two

There are at least two recognised formulae for converting times run at one distance to a projected time for a second distance. The simplest is t2 = t1 * (d2 / d1)^1.06 and was devised by Peter Riegel. It's a shorthand way of saying that speed declines by six per cent when the distance run is doubled. The exponent 1.06 was determined by research among elite and semi-elite runners, so while most people apply the Riegel formula 'as is', there's no reason to assume that other numbers don't work better for mere mortals such as me.

The Cameron formula is a more exotic affair that goes like this:

a = 13.49681 - 0.048865*olddist + 2.438936/(olddist**0.7905)

b = 13.49681 - 0.048865*newdist + 2.438936/(newdist**0.7905)

newtime = (oldtime/olddist) * (a/b) * newdist

This formula uses distances in miles and times in seconds. Often the results are remarkably similar to those from the Riegel formula.

Our spreadsheet used the Riegel formula without modification. After entering the distance of the next handicap race, the spreadsheet kicked out a column of target times based on the 10K base time.

So what's wrong with that? Well, there are a number of flies in that ointment: how representative is the base time? What if the target race is a hilly one and the base time was on a course as flat as a pancake (or vice versa)? What if, as a runner, your times don't vary according to Riegel's six per cent decline?

To compound the problem, several handicappers had tweaked calculated times in the (perhaps misguided) hope of correcting anomalies. There was only one happy person per race and the rest thinking they'd been robbed. At the end of a race one runner felt so disgruntled he ripped off his number, swore a lot and refused to cross the finish line - not what it's all about.