How to calculate start differentials

Mass starts, where everybody leaves at the same time, are pretty rare in distance dog mushing.  Typically the teams start every <n> minutes, in order of bib number.  <n> is usually two or three minutes.

Races want finish results to reflect actual standings.  If someone left the start chute three minutes after someone else but took two minutes less time to complete the trail, it's easier to understand if that person arrives at the finish chute two minutes earlier than the other guy, rather than one minute later.

The way that they make this happen is to apply a "start differential" at some point along the trail, often in conjunction with a mandatory checkpoint rest.  To calculate the start differential for a given musher, you need

• that person's bib number
• the last bib number
• the interval between starts

(note that this assumes that the bib numbers are sequential - always true in the big races but occasionally  clubs putting on small, local races may [ahem] misplace some bibs over the years).

So, to calculate the start differential, all that you need to do is subtract the bib number of the person you're interested in from the highest bib number, then multiply by the interval between starts.  Here's an example from the 2013 Iditarod.  The highest bib number is 67, and there was two minutes between starts.  If interested in figuring out how much time Dave Sawatzky - big number 56 - owes in addition to his mandatory rest, I do this:

67 - 56 = 11

11 * 2 = 22

And so Sawatzky will have 22 minutes tacked onto his mandatory 24 hour checkpoint rest.  His earliest departure time will be 24 hours and 22 minutes after his arrival time.