Tools for looking at run/rest schedules

If you've followed distance mushing for any amount of time you're keenly aware of the role that run/rest schedules play in the sport.  They can be both strategic and tactical, and can reflect the breeding decisions a given musher makes, as well as their training regimen (more on that in a bit).

I've posted a couple of videos on my Facebook page using Trackleaders tools from last weekend's Northern Lights 300 to look at how to use them to get a better understanding of how teams are performing against each other as they move down the trail, and how to use the replay function to watch interesting, and occasionally surprising, things happen during a race, based on how the teams move on the map.  In the latter video I looked more closely at Larry Daugherty, because there were some unusual things happening on his tracker that stood out from the rest of the race.

In Larry's recap of the race he talks about deciding that he was going to try to be competitive, and making adjustments to his run/rest schedule to be more competitive.  Of course, now we know that his team shut down on him twice, and the first place to look given his comments and given what happened is at how he rested his team.

During last year's Yukon Quest I wrote a short Python program to pull rest times out of a Trackleaders musher track.  It's available for download, but for the more visually-oriented, you can take a look at a musher's speed/time plot on their Trackleaders page.  For example, here's Kristy Berington's for this year's NL 300.  She won the race, so clearly the decisions she made worked well for the team she had and the training she'd done:

Reading this is absolutely straightforward.  The x-axis (horizontal) is race time - hours since the race start - and the y-axis (vertical) is speed.  This looks like a pretty standard schedule for a 300-mile race.  Her schedule looked roughly like:

        Run 7 hours, rest 6 hours
        Run 6 hours, rest 3 hours
        Run 5 hours, rest 5 hours
        Run 8 hours, rest 4 hours
        Run 7 hours to the finish

So, the longest of the runs were only moderately long, and pretty much in keeping with what we've seen be successful in other races.  None were what anybody would call very long.  There were four rests.  Note that the longest run was in the last half of the race, the second-to-last one, which was 8 hours.

Now, Larry said that his goal was to run long and rest long, as he'd seen other mushers, notably Allen Moore, do with a great deal of success.  So, let's take a look at Allen's successful Copper Basin 300 race earlier this month:

Again, time is on the vertical axis and speed is on the horizontal axis.  His schedule looked roughly like:

        Run 5 hours, rest 5 hours
        Run 7 hours, rest 7 hours
        Run 3 hours, rest 5 hours
        Run 9 hours, rest 2 hours
        Run 8 hours to the finish

Again, a few moderately long runs, four rests, and the longer runs in the second half of the race (also top speeds of 30mph in a few places - woo, Allen!  But those, sadly, are actually measurement errors).  Note, as well, that in mid-distance races with mandatory checkpoint rest, the run/rest schedule is going to be influenced by checkpoint location and layover rules.

So now we've looked at a couple of successful run/rest schedules, including one that Larry said he was using as a model.  Let's look at what Larry actually did:

        Run 7 hours, rest 7 hours
        Run 12 hours, rest 5 hours
        Run 8 hours, rest 6 hours
        Run 8 hours to the finish

Note that there are places in the third run and the run to the finish where his speed dropped considerably, and in one case where he actually stopped.  Those are the places where his dogs quit on him.

What pops out here is that he only did four runs over 300 miles, while Kristy did five runs in the NL 300 and Allen did five runs in the CB 300.  Note as well that his long run was comparatively quite long (12 hours), that it was in the first half of the race, and that it was not followed by much rest.  His run/rest schedule does not actually look much like that of mushers winning at that distance, and is clearly one possible reason why his dogs quit on him several times.  And this gets back to the training question - if he hadn't been training for very long runs prior to the race his dogs were likely not in condition either mentally or physically to pull one off.

Eyeballing the curves it also looks like Larry lost more speed on the first run than Kristy did.  It might be interesting to fit a regression line to each and see how the slopes compare, but think it would only be a little bit interesting.  More interesting is that many top mushers have talked about leaving the start chute at the same speed they'd like to run their race, or about negative splits, where their speeds towards the end of the race are faster than their speeds earlier in the race.  Sebastian Schnuelle has talked memorably about being passed left and right by other teams towards the start of the race, and telling them "I will see you later."  And nearly always, he does.  Going out fast may or may not hurt but it's not clear that it helps.

This plot (the speed vs. time plot) is an incredibly handy tool for looking at run/rest schedules.  One enhancement I'd love to see would be the ability to overlay multiple mushers on the same plot, which would allow us not only to compare rest durations and locations, but also speeds while moving.  In the meantime, my script has the option to output the results in CSV format, which is handy for loading into a spreadsheet or into a data analysis package like R or NumPy.

A closer look at the Buser shortcuts in the Kusko

I think at this point most distance mushing fans are aware that both Rohn and Martin Buser left the trail during this past weekend's Kuskokwim 300, and that they received no penalty for having done so despite the trail they took being somewhat shorter than the race trail.

The Kusko 300 rules say:

"Racers must follow the marked and/or broken race trail. Leaving the marked and/or broken trail for the purpose of gaining a competitive advantage over other racers is not allowed."

Right there is an obvious problem: it implies that if someone leaves the trail and follows a shorter route by accident, they will not be penalized.  It requires the race judges to attempt to determine intent, and that's both difficult and unfair, as it introduces a highly subjective element into the decision.  There's also the question of incentives - if you kill a moose with your car in Alaska, you don't get to keep the meat, antlers, or any other valuable part of the animal because the state doesn't want you accidentally-on-purpose killing a moose.  Same with killing wildlife in defense of life and property - you don't get to keep anything of value from the animal because they also don't want you accidentally-on-purpose having a dangerous run-in with a bear.  Setting up a situation in which it's okay to leave the trail under particular circumstances removes some of the disincentives for leaving the trail.

But, this doesn't apply in Rohn's case, as he was told that he was off-course and given the opportunity to return to the race trail, which he did not do.  So.

What interests, I think, a lot of us is whether or not these shortcuts had an impact on the outcome of the race.  We can use several Trackleaders' tools to look at that question and try to sort it out.

First, let's look at the shortcut itself.  If you go to the Trackleaders page for the race, down the right-hand side of the map you'll see a column of buttons.  Click on "Map layers."

That will expand to a series of checkboxed menu items: Weather Conditions, Cloud Cover, All Musher tracks, Tent layer, and Scratch layer.  Click on "All Musher tracks."  That will draw all of the tracks for all of the mushers who are being tracked.  I've done that in the following image, and zoomed in on the trail near Bethel (I've also switched to satellite view, as the tracks stand out better on the map).

Clearly there's no question that Martin and Rohn did not follow the same trail as everybody else, and it appears that the trail they did take was shorter.  So, was it shorter, and if so, how much of an advantage did they gain?

To try to suss that out, let's look at the race flow chart, which can give us a pretty clear look at average traveling speeds and team speeds relative to one another, as well as showing us speed anomalies in the track.  Here's the race flow chart from Tuluksak to the finish.  Note the big vertical jag in Rohn's and Martin's curves - that's where they left the trail (to digress a bit, Trackleaders appears to calculate musher trail mile by comparing the location of the GPS reading to the track that they were given by the race organization).  Note, as well, that both Rohn and Martin had slowed down and were losing speed relative to the teams around them.  On the race flow chart the x-axis (horizontal) represents time since the race began and the y-axis (vertical) represents trail mile.  The steeper the slope of a musher's curve, the faster they're going, and the less steep it is, the slower they're going.  So, that they were losing ground is very clear, and that they got a bump from their shortcut is also very clear.

There are several things we can do in looking at the data.  One thing we can do is look at the bumps and try to figure out what it did to "effective" speed on the trail.  Switching over to looking at Rohn's individual tracker map, it appears that he left the trail right at about mile 253.5 and rejoined at mile 266.   Again, according to his individual track,, that would mean that he left the trail at about 4:37am and rejoined the trail at about 5:36am.  So, as far as the race is concerned he covered 12.5 miles in 59 minutes, or averaged a hair over 12.5 mph over that section of trail (again, as far as the race is concerned).  If you take a look at his traveling speed prior to that (looking at the slope on the race flow chart) at hour 32 he was at mile 234.5 and at hour 34 he was at mile 253.5, so was traveling about 9.5 mph in the two hours prior to leaving the trail.  That is to say, he got about a 1 mph boost.

Now, if he'd stayed on the trail and continued traveling at about 9.5mph, would he still have beaten Jeff King to the finish?  More arithmetic.  He left the trail at about 4:37am, at trail mile 253.5.  The finish in Bethel is at about trail mile 267.3.  That's 13.8 miles.  If he'd been traveling at a constant 9.5 mph over that 13.8 miles he'd have arrived in Bethel about an hour and 27 minutes after the time at which he left the trail, or around 6:04 am.  Jeff got in around 5:58.  That's close enough, I think, to be questionable, but Jeff probably would have finished earlier and gotten the $17,000 check instead of the one for $11,500.

Just for fun, let's try extending Rohn's curve long its original path to see if it results in something much different, and as a way of validating (or not) the values I've been using for time and trail mile.  Also, pictures are just plain easier to understand.  So, what happens if I extend Rohn's line on the race flow chart along its original path?  This, which shows him finishing at about the same time as Jeff:

Note that Rohn's line, however, was not straight - it bulges a bit on top of the straight line because ... he was slowing down.

Running some numbers on Martin's track, he left the trail at about 5:54 am and returned to it at about 7:04am, so as far as the race is concerned he ran that section at 10.9 mph, while otherwise running about 8.7 mph.  If he'd stayed on the trail at a constant 8.7 mph, he would have arrived in Bethel in the general vicinity of 7:30, or right about the same time as Brent Sass.  This one is a lot fuzzier than the Rohn/Jeff situation.

So basically, yes, I think that if Rohn hadn't left the trail Jeff would have beaten him into Bethel, but not by much.  I don't understand why the Busers weren't penalized for leaving the trail and taking a shorter route and I especially don't understand why the race organization has said absolutely nothing. Given that the Kusko organization hasn't said a word about this I think it would be nice if Rohn would take responsibility and then donate the $5500 difference between a 2nd and 3rd place finish to a local charitable organization in Bethel.  The way the race ended just leaves a bad feeling all around.

[Update: KYUK reports that both Busers have been penalized 10 minutes and 10 percent of their winnings.  I do think that both received substantially more than a 10-minute benefit from their adventures on Church Slough, but I'm glad that the problem has been formally recognized by the race.]