**Aleksandr Sorokin** from Lithuania, the world record holder for the 100 km, 100 mi, 12- and 24-hour runs, has announced a new record attempt for the 100 km, which will take place on May 14, 2023. The athlete’s current achievement of 6:05:41 was recorded in April 2022. Preparing for the race, Sorokin ran a marathon in Seville (February 19, 2023) with a new personal best of 2:25:33. Is it possible, based on this, to predict Aleksandr’s chances of becoming the first person in history to run 100 km in less than 6 hours?

## A Simple Equation – From A Simple Mind

Exactly one week before the announcement of the new record chase by Sorokin, a paper titled “Prediction of performance in a 100-km run from a simple equation” was published in the PLOS ONE magazine. Author **Jeremy B. Coquart** collected detailed data on 58 French athletes. The data for each athlete included:

- Gender, birth date, weight, and height;
- Race times for both 100-km run and marathon, attainment (or not) of a personal record during the marathon, and the dates of participation in the marathon and the 100-km run;
- For each 100-km race, the city, minimal and maximal air temperatures, wind speed, total amount of precipitation, relative humidity, and barometric pressure.

Based on the results of the regression analysis, two equations for predicting the result for the 100 km were obtained; one of them features wind speed as a variable, while the other works solely with the marathon result. Of course, the second one is more applicable to predicting Sorokin’s performance, since guessing what the weather might be like during the race in May is rather pointless. So here is the “simple equation”:

Perf_{100} = 131.574 + 2.53 х Perf_{42} + 30.113 х PR_{42}

*wherePerf _{100 }is the 100-km prediction time in minutes,Perf_{42} is the result of the last marathon in minutes, andPR_{42} can be set to 1 if that last marathon was a personal best, and to 0 if not.*

Substituting Sorokin’s result in Seville into the formula, we get a 100-km run prediction at… 8 hours and 50 minutes. Facepalm.

If we look at the athletic performance of the 58 runners that were included in the sample for analysis, we will see a fantastic spread of results from 2:35 to 5:10 (!) in the marathon and from 7:13 to 17:20 (!!!) for the 100 km. This is what happens when so-called scientists try to do something they are completely incompetent in; anyone who has even the slightest understanding of running would never use such a random sample for any kind of analysis. In all fairness, the PLOS ONE journal does not hold much gravitas in the world of science, and this work is mentioned only because it is the latest on this topic. Anyway, this is amusing overall.

## Closer To The Truth

A much more plausible prediction is given by the good old Rigel’s formula. **Peter Riegel** (1935–2018) was an American research engineer, and in a 1977 article for the Runner’s World magazine, he already proposed a simple formula for comparing relative performances at different distances:

T_{2 }= T_{1 }× (D_{2 }÷ D_{1})^{1.06}

*whereT*

_{1}*is the time achieved for D*

_{1}*,*

T

T

_{2}*is the time predicted for D*

_{2}*,*

D

D

_{1}*is the distance over which the initial time is achieved, and*

D

D

_{2}*is the distance for which the time is to be predicted.*

Thus, based on a 2:25:33 marathon result, Riegel’s formula gives a prediction of 6:03:17 for the 100 km, which would be a new world record for this distance yet still falls short of the 6-hour mark.

## What Do They Think Of It In Running Expert?

The idea of predicting the 100-km performance based on marathon achievement, as the author of the PLOS ONE publication attempted, is correct in and of itself. Now, elite athletes (yes, elite – not the recreational runners who spend more than 5 hours to complete a marathon) run 42 km at the level of the so-called *aerobic threshold,* and this is why it matters.

The aerobic threshold is the maximum level of oxygen demand from the working muscles that the cardiovascular system is able to satisfy. This is quite a steady state, which, in theory, can last for hours but, in practice, does not exceed 2 to 2.5 hours. The fact is that energy for the working muscles is provided by the oxidation of either fats or carbohydrates, but these two substrates have different oxygen efficiency.

When one glucose molecule is oxidized, 30 ATP molecules are produced (ATP is the final “fuel” that is “burned” directly by muscle fibers), which requires 6 oxygen molecules. In the case of the palmitic acid, 108 ATP molecules are generated in the process, but it requires as many as 23 molecules of oxygen. Thus, it is possible to calculate the efficiency of energy production per unit of oxygen for both glucose (G) and fatty acids (FA):

30 ÷ 6 = 5 (G) vs 108 ÷ 23 = 4.7 (FA)

That is, carbohydrates are 6% more efficient than fats, which is quite a lot. For example, if we take Sorokin’s pace in Seville of 3:27/km, then the pace “on fats” would be 6% slower: already a 3:39/km. If he ran like this, his overall result would not have been 2:25:33 but nine minutes worse.

However, the body never limits itself to burning just carbohydrates or just fats: it always uses both sources of energy, but in different proportions – depending on running speed. An elite marathoner runs the distance mainly on carbohydrates, but as they are depleted (and their reserves in the body are enough, roughly speaking, for a couple of hours of running), the muscles switch increasingly to the oxidation of fats, which require more oxygen to maintain the same power. Yet the cardiovascular system can no longer meet oxygen demand adequately. Hence, the runner slows down.

In fact, this is the first reason why the pace at one’s aerobic threshold cannot be maintained for longer than 2 to 2.5 hours. A logical question: is it possible to replenish carbohydrate reserves using, say, energy gels? In a nutshell, not fully.

No runner has yet been able to consistently ingest more than 120 g of carbohydrates per hour: the gastrointestinal tract has its own capacity limitations. Since the 1960s, the “Margaria constant” has been known, which determines the energy costs of running: 1 kcal/kg/km. More recent data on elite runners (Arcelli, Canova) show that these costs are lower – up to 0.8 kcal/kg/km, but even if we start from these figures, we get a 60-kg runner moving with speed of 17 km/h and spending more than 1,000 kcal in one hour, while gels can provide no more than 500 kcal/h and most often even less (since 1 g of carbohydrates contains 4 kcal).

So, the first reason for a slower pace in an ultramarathon is carbohydrate depletion, but it is not the only one. The second reason is the so-called *exercise-induced muscle damage* (EIMD). Anyone who, even after a marathon (not to mention an ultra), has difficulty going down the stairs knows firsthand what EIMD is. But this muscle damage is not only the cause of pain *after* the race; it is also the reason for the slowdown along the distance due to the fact that the damaged muscles no longer absorb the impact and push the runner forward as efficiently.

It is impossible to calculate the influence of these factors, especially since each of them can be targeted and affected by training, including the athlete’s consumption of carbohydrates per unit of time (so-called “gut training”). In any case, it is useful to recall Sorokin’s pace chart when he set the current 100-km record.

He ran in Bedford, UK, on the track; the first 50 km at 3:01:50 and the second 50 km at 3:03:51, with the pace drop of only 1.1%. This is great. Theoretically, if he starts next time at a pace 3% slower than his marathon pace (remembering that the difference between carbohydrates and fats is 6%) and slows down in the second half by as much as 1.5%, then his result prediction reads as follows:

2:57:40 + 3:00:20 = 5:58:00

So good luck to Aleksandr!