Monday, March 1, 2010

Birkie, by the numbers

Without a ton of commentary, here are some statistics about the Birkebeiner. All numbers are based on 2010 finishers, including both men and women, for the freestyle Birkie.

First, wave size. There are obviously more people in early waves than later ones, but how many more? Well, a lot. Waves 1-4, which filled this year, each had between 520 and 560 Birkie finishers, and more Korteloppet skiers, so they were even more crowded during the first 9k. By wave 8, there were only 78 Birkie skiers—surely more in the Korte, but it's still a lot smaller, especially beyond Timber Trail. Wave 10—with new skiers—was larger this year, and perhaps smaller than usual with the early cutoff for registration.
Elite Men 196
Elite Women 70
Wave 1 554
Wave 2 543
Wave 3 530
Wave 4 522
Wave 5 436
Wave 6 223
Wave 7 146
Wave 8 78
Wave 9 142
Wave 10 201

And what of Birkie regionality?
State Avg. Time # skiers State Avg. Time # skiers
S.D. 2:31:01 1 N.M. 3:33:08 5
Alaska 2:50:35 22 Wash. 3:37:14 29
Ore. 2:51:51 11 Ind. 3:37:58 3
Ver. 2:58:48 13 Wis. 3:39:02 1591
Idaho 3:01:20 19 N.D. 3:43:59 6
Mich. 3:02:11 99 Ark. 3:46:44 1
Maine 3:05:40 9 Penna. 3:46:46 8
Wyo. 3:10:12 7 Ill. 3:47:58 154
Int'l 3:16:44 52 Nev. 3:59:20 1
Mary. 3:17:32 3 Ariz. 4:00:46 6
Colo. 3:17:56 102 Calif. 4:01:05 30
Utah 3:17:59 22 Mo. 4:08:10 3
Conn. 3:18:49 2 Ken. 4:14:07 2
Ohio 3:19:37 10 Ga. 4:30:33 1
Mass. 3:19:49 22 Kan. 4:34:30 3
Mont. 3:19:52 25 Fla. 4:37:44 4
Minn. 3:22:01 1254 Texas 5:08:34 4
N.H. 3:23:35 11 Va. 5:16:07 6
Iowa 3:30:04 42 Neb. 5:50:44 2

Well, obviously the most finishers come from Wisconsin and Minnesota, which account for about 75% of the skiers. Beyond that, big states include Illinois, Colorado and Michigan, with sizable contingents from most other states with some decent snow. But who has the best times? Where do the fast skiers come from? Well, the one skier in South Dakota was a first wave qualifier, finishing in 2:30, but he didn't have anyone to drag him down. Alaska, Oregon, and Vermont—all states with development teams (APU, XC Oregon, Craftsbury ) come next, with international skiers following. Of the larger states, Michigan beats out Colorado (and Illinois) and International skaters do well.

However, the most important statistic is who does best between Minnesota and Wisconsin, and while there are more Wisconsinites in the race, the Minnesotans are faster. Apparently, the Gophers beat the Badgers. It would be fantastic if there were a competition between the two states in the next Birkie. Team competition to the max! (Although, to be fair, Chris Cook came 3d, the first Wisconsinite across the line, while Minnesota's first, Matt Liebsch, was 8th.)

Now for some charts! In all the charts, the red dashed line is the elite qualification time (for men). A few things to note: wave 3 is spread out at the top more than wave 2 or 4, as senior citizens (over 65) are allowed to start in wave 3 regardless of their time.

Here are all Birkie skate finishers, sorted by bib number (and thus, by wave). Note how much bigger waves 1-5 are than the rest, as well as the spread of the waves. It looks like they've done a relatively good job seeding skiers.

You can also view this chart by time. Note a couple of things. First, how spread out wave 3 is. Second, how there are contingents in waves 1-7, which are most pronounced in the latter of these waves, which are seeded with lower numbers but slower overall. These are Birchleggings skiers, which get bibs under 200 (i.e. below 1200 or 4200) and generally, since they're older, have lower times. Especially in the smaller, later waves, there is a big gap between the Birchleggings folks and the rest of the skiers, who start at bib 200.

And here is a chart of all the skate finishers in the race, sorted in to five minute categories. A bell curve with a long tail, it seems.

Now, we come to some more fun. Here is the chart above, but sorted by starting wave.A few things to note. First, that, since the elite wave is based on a number (top 200) and not a time, its tail has a different shape, as it drops off much more quickly. The first and second waves look like rather normal curves, although the third wave, owing to the older skiers in it, has a second peak. Beyond that, the fourth and fifth waves, while still rather normal, are much more spread out, since they have the same number of skiers finishing in longer times (with the fast snow, the modal finish time was 3:10 this year). And the color doesn't show up well in the legent, but the light yellow of wave 10 has a very flat curve.

This can also be shown by charting time versus place in wave—to look at the times for each wave. The large waves, 1-4, are not surprisingly quite flat—only a few minutes separates the first and last finishers, although there are, of course folks at the back whose times skew up. A few things to notice are the old folks in wave three posting long times, the fact that almost everyone in wave 1 finished in under 3:30, and almost everyone in wave 2 was under 4:00, and that the front of wave 4 was actually a tad faster than the front of wave 3 (the line is slightly lower on the chart). A couple more interesting tidbits: wave 9 is faster than waves 7 and 8, and even than the start of wave 6. The fast pieces of waves 3, 4 and 5 are all about the same speed (perhaps because everyone got stuck in the same traffic jam on the hills).

These data can also be shown by comparing the place in the wave to the overall place. The trends are similar: elite wavers avoid relegation as long as they stay near the second point of inflection, the early part of the fourth wave beats the early third, which is comparable to the early part of the fifth, and the 7th through 9th waves don't really line up as expected. There's more variability in later waves, too. Most first wavers finish within the first 850 or so and will be right back in the first wave. Second wavers mainly finish between 750 and 1500. But there are quite a few wave 5 skiers who will qualify in to the top two waves, even as most of their co-wavers ski wave 5 times.

Finally, we can plot all of the finishers. I'm not sure what the inflection point here, but the curve is very flat from about 2:40 to 3:50—where most of the skiers finish.

It's pretty minor, but there seem to be points of inflection around 100th place, and then a very minor change in the slop right around the elite qualification mark. I have no idea what that means. Probably nothing. Then there's avery constant slope from about 400th place to 2400th place, before the stragglers come in.

These charts are fun and don't tell us much, but they definitely confirm Birkie wave creep (everyone tries to, and often does, qualify in to the top waves), but this is also due to the fact there is not much of a difference in time between a wave 1 skier and a wave 2 skier (see all the overlap in the "bell curve by wave" chart). So, yeah, unless you're in the elite wave, or wave 6 or higher, you'll have a lot of company on the trail.


  1. Holy data boner.

    This graph confirms that if I can win wave 2 next year, I can get to the elite wave.

    To the rollerskis!

  2. Yeah, and usually there are more qualifiers out of wave 2. This year the early waves were on faster enough snow that only one guy made it.

    Just don't knock me out of the Elite Wave, please. (To the rollerboard to get some of this so-called "upper body strength".)

  3. This needs to be done for the Classic skiers. I bet as the temps got warmer you will see a big difference with the classic times.

  4. Ari, you start your blog with "without a ton of commentary." I'd dispute that. ;)

    Nice pictures. Care to predict the percentages the Birkie will use for wave cutoffs?

  5. No love for us classic skiers? I second the need for analysis of the classic race (if you've got the time). Thanks for the fun factiods!

  6. Something I'd like to see is my finish position relative to the skiers in my wave. Should be fairly easy to do. your average skier will never win the race but he might win his wave. Interesting info if you assume most people in your wave are about your ability. probably works better for the earlier waves

  7. I think the numbers will dictate that at least the 1st wave, like the elite wave, will need to go a year by year qualifing rank with no more grandfathering. Set a number you want (adjust for the Korte influx) and it's how did you do last year that gets you into that wave. May the "plug" be with you.

  8. Can we expect to see one for the 2011 Birkie?

  9. 2011 statistics can be found at the all new site,!

  10. Wow, Colin, how prescient of you. You didn't win Wave 2 (but you come close) and got in the elite wave. And then 2012 happened.