Revisiting equivalent performances in shoetastic times

A different kind of "flattening the curve"

Despite serious and consequential differences, the joggerscape of the mid-1980’s—when I first took up roving, goal-directed cardio, which may also be performed on skis, in water, or astride a bicycle—had plenty in common with today’s. Ultramarathoners were perceived as free-spirited and shower-averse, and the scene was peppered with Gandalf-bearded men dressed like color-blind vagrants subsisting on unlikely diets. Nike had an elite training group in Oregon that included Alberto Salazar and was later tied to pharmacological hijinks. Cars guided by pipsqueak, Gatorade-swilling adults boasted bumper stickers like RUNNERS KEEP IT UP LONGER and THE DRIVER OF THIS CAR RAN UP MOUNT WASHINGTON. People used long Sunday runs to vent about their spouses, their jobs, their frank insecurities, and each other. And by the end of the Cold War years, there were even multiple track and road distances to choose from, as well as naked, drunken uncertified road miles through various college towns.

As someone who as a ninth-grader ran the 800 and 1600 exclusively, it was natural for me to wonder how to formally compare my times in these two events, and also see how these related to the 5K cross-country races I’d done the previous fall. I had a small sampling of data from older teammates and my coaches. I could look at the state-meet qualifying times in various events. I could go to the library (I know, holdable books, right? But I’ll always love libraries) and look up the world records in all of the distance events, and see how these related to each other mathematically, given that they all had to be almost equally good, measured against some universal quality standard, at any time.

I relied mostly on the latter idea, with a small bit of rounding, and with an assist from the Purdy tables I discovered at the Bailey-Howe library at the University of Vermont in the winter of 1989. Rather than being purely empirical (that is, based on existing datasets of times run in different distance events), these tables rely on basic extrapolations of oxygen-processing curves. This makes them very useful—but a lot less useful today than 30 years ago, or less useful to a greater percentage of regular runners. I hope at least one of you has already figured out why this is.

The men’s WRs in the standard metric track events at the time I adapted this scheme were very close to 3:30, 7:30, 13:00 and 27:18. This establishes a ratio of 7/15 for the 1,500 and 3,000 (or the 1,600 and 3,200, or 1-mile and 2-mile) as well as a 10/21 ratio for the 5K and 10K. What appeared to be true was that, starting with around 5K, the race-pace difference resulting from doubling the distance becomes very close to 5 percent and stays there. That is, someone who can race 5K at 5:00 pace (300 seconds per mile) should be able to hold 1.05(300) = 315 = 5:15’s for 10K, a little slower than 5:30s for a half-marathon, and so on right up through…a point.

So, if you have a 4M time handy, you might be able to use that to estimate your time for an 8M race. But that would be pointless, because there was only one of those worth running in the entire world, and it’s all but gone now, and was hilly anyway. But the lesson, and if you’re still suffering through this you obviously care, is that doubling a shorter time and adding 10 percent, or multiplying by 2.1, is a fair way to get an estimate of capabilities over a longer distance you haven’t raced, assuming proper training and so on.

Turning back to shorter stuff, the 3K-to-5K drop-off is very close to 4 percent. This means that if you can run 80 seconds a lap for seven and a half of the (10:00), you should expect to be able to manage 1.04(80) = 83.2 seconds a lap for twelve and a half laps. It should also force the ratio of times in these two distances to 15/26. From this ratio, and also by grabbing a “reference equivalent” 8K from the Purdy tables, a difference of about 3.3% exists between the 5K and the 8K/5M.

• Should you happen to live at about 5,000’ to 5,300’, 3.3% is also about the cost of running a race 20 minutes or longer at that altitude. Therefore, whatever pace you can run for 5K in a place like Greater Denver or Albuquerque is the same pace you should be able to hold in an 8K/5M race at sea level. For obvious reasons, you can use the same “rule” for a 10K at altitude to get an estimate of your 15K/10M sea-level race pace, although the Bolder Boulder runs more like an idealized sea-level 30K.

One final relationship that emerges from this mess is that the ratio of your marathon time to your 10K time should be about 4.67. At the time I ran 2:24:17, I had never broken 32:00 for 10K, giving a ratio of 4.5, and people with faster bests than this have shown even lower ratios, i.e., have “overperformed” in the marathon.

It is worth noting that very few runners demonstrate similar efficacy across the range of everyday “long” distances (1,500m to marathon), not only at a given point in their competitive fitness but across the span of their careers. Eliud Kipchoge is, as he is in many ways, a rare exception, and though Sifan Hassan has yet to run a marathon, she looks to be capable of excelling over just as phenomenal a range. But in general, you’re better off working in smaller ranges with these conversions, e.g., 1,500m through 5,000m or 10,000m through the marathon, depending on your present focus as well as your natural distribution of fast-switch and slow-twitch muscle fibers.

To test the validity of this quasi-Purdy scheme, what did the women’s WRs look like in the late 1980s? Based on the above relationships, the following times should be roughly equivalent:

3:58, 8:30, 14:44, 30:56, 2:24:23, 1:08:45

These are all fairly close to the c. 1985 women’s world records. Of course, almost any conversion scheme you can find will get you “fairly close.”

• If you know how to use Excel, you can even create a plot of your own pace per mile vs. race distance for whatever distances you’ve run, and use this to come up with an estimate for new or nontraditional distances, like 25K or 30K, by instructing the program to create a best-fit curve through the scattered points.

Now I have to get to the bad assumptions that have become baked into this idea over the years; at the time I produced it, those weren’t the issue they are today. One is the advent of EPO in 1990 or so, which didn’t really add much that straight blood-doping had not, but made the cheating process easier. The other is the far more recent introduction of extremely economical racing shoes, which for now—as far as my not-yet-fully-cognizant mind can discern, at least—have more strongly affected the longer races. From what noise I can gather, the same phenomenon is already in play on the track, but with more room to grow yet. So, assuming “my” scheme is as helpful as any other, it does not account for doping (which most of you don’t do) or ultrafast carbon-plated shoes (which almost everyone serious about racing now owns).

Since these tables are based on oxygen utilization and don’t account for pure substrate factors (i.e., fuel), their utility in longer races has proven limited. A better way to say this is that they are almost worthless in this regard. Based on the world record in the 50K run (C.J. Albertson’s 2:42:30 from November), someone “should” be able to run 100K in around 5:41:15. We* may have to wait a few years on that one. It won’t be until someone comes up with shoes that can better protect muscles, a fueling plan that is practically an IV infusion, and most of all the right incentive before anyone gets remotely close to that.

On that note, how weak are the men’s and women’s 50K marks compared to the marathon WRs? It makes little sense to compare the times directly because of the different caliber of athletes involved, but Albertson himself is a great runner with an official marathon best of 2:11:49 on the tough Olympic Trials course in Atlanta and a recent treadmill time of 2:09:58. Crediting him with a 2:10-flat gives him paces of 4:57.5 and 5:13.8 for the marathon and 50K. In reality, Alberton “should” be capable of running back-to-back marathons at his 50K pace. As the man is clearly an animal and does these kinds of things regularly, the “problem” isn’t with anything Albertson is doing. Should he try going out at 5:05 pace in a 50K? I think so. With the right incentive, someone on Earth could hold 5:00 pace for 50K with relative ease, but you’d have to pluck a 2:05-ish marathoner from the marathon ranks to do it. Considering how many of those guys there now are, and the burgeoning incentives for fast runners to go past 26.2, this might even happen in 2021. (The women’s 50K WR, 3:07:20, is so slow—slower than the only 50K result I recorded, even—that it’s not worth analyzing.)

I planned to carry this post into an awestruck description of the HOKA Project Carbon X 2 100K on Saturday in Chandler, Arizona, a town that until this event and the Marathon Project last month only 348 non-Arizonans nationwide had ever heard of. Watching Jim Walmsley perform as relentlessly as any human possibly can at a single task for that long made my entire weekend. I forgot my job is strictly to complain about unfounded complaining, while rewarding efforts to combat it. When I went out for my jog that afternoon, I found myself imitating a runner I had just watched in action for the first time in many years. I have the flapping arms down, and I can get to the manbun over time, but the rest is pure vicarious thrill. The entire production was as great as anything I’ve seen during the pandemic, including the announcing (it was interesting for six-plus hours!) and for some time before it.

Next time I will go into more detail about not only my reaction but those of others as they roll in, as well as what I think this might do for ultramarathon racing generally. I have already seen one predictably disenchanted, hollow response to how the event was managed. But if you want a little fitspo, try this: