On marathons and ultramarathons

Many years ago I had drawn the mean velocity for the track world records as a function of the race distance. The part of the curve that was interesting me at that time was the one corresponding to the transition between anaerobic and aerobic processes. However, instead of limiting the graphic to relatively short races, say of up to 5 km, and since I had the world records for all distances at hand I decided to draw the curve all the way to the longest, 1000 km, ultramarathons. I was not able to find that graphic in my archives but it was a matter of a few minutes to draw it again, based on today’s records. The feature that had  attracted my attention the first time was obviously there.

In the figure above  we distinguish three regions: one from 800 m to the marathon, one from 100 km to 24 h events and one for longer events. I have also drawn a thin curve which corresponds to the best fit for velocity vs. distance for races from 800 m to the marathon and which could, in principle, be used in order to extrapolate towards the velocities of races longer than the marathon. However these longer events do not agree with the extrapolation. Two discontinuities are clearly visible. The first is the interesting one. I remember that, back in the days when I was running marathons, the dreaded moment was “hitting the wall” while approaching 3 h of race. All of a sudden it was impossible to keep the same pace. The reason for this is that the glycogen reserves of the organism are depleted and from then onwards one has to burn lipids. Since the rate at which energy is produced through this mechanism is slower than the one of metabolising glycogen, one cannot sustain the same speed as before. (The second, concerning very long races, is very easy to explain: those are multi-day events and the runners must take some time off in order to sleep). 

Marathon champions do not slow down during their races. In fact there exist many examples of record marathons where the second half is run faster than the first.  Top level athletes can sustain a marathon record pace for more than two hours. However a rough extrapolation from the graphic at hand shows that past some distance, around 60 km, an appreciable slow-down occurs. Of course, one can argue that there is substantially less interest in ultramarathons than in shorter races. This is all the more true for the marathon which is meeting with an incredible popularity over the past 20-25 years. A consequence of this is that the best runners do not venture beyond the 42 km races. However I believe that, record-wise, the recent progress in the marathon does not modify the conclusions based on metabolic data. To put it in a nutshell: even the biggest marathon champions would bonk at some point should they attack longer races without the adequate preparation.

The problem with the 110 m hurdles

Let us try a simple calculation and compute the mean velocity of the men’s world record over 110 m and 400 m hurdles. We find respectively 8.59 m/s and 8.55 m/s. The numbers look pretty close. Let me present this result in a more explicit way. If a man were running a 400 m with a 8.59 m/s velocity his time would be 46.55 s, very, very close to the 400 m hurdles world record. So the 110 m hd is run at almost the same speed as the 400 m hd. Perhaps this is a paradox that occurs only at world record level. Well, not so. If I repeat the same calculation for the 1000th performer of 110 m hd (based on the tables compiled by Peter Larsson) I find a performance of 48.11 s again very close to the performance of the 1000th performer of 400 m hd, which is 48.43 s. Could this be something occurring just recently? Again, this is not the case. If look up the first official world record of 15.0 s for 110 m hd, going back to 1908, and obtain a time over 400 m based on the mean velocity for this race, I find a time of 54.6 s again very close to the first, 1908, world record over 400 m hd which was just 55.0 s.

However if we compare the 100 m and 400 m races for women nothing of the sort happens. If we compare the current world records we find that a 400 m run with the velocity of the 100 m hd, 12.21 s, world record would take 48.84 s, a good 3.50 s less than the current 400 m hd world record of 52.34 s. Again this has nothing to do with the world record. For the 1000th performer the corresponding time is 12.68 s for 100 m hd, leading to 50.72 s over 400 m to be compared to the performance of 54.53 s of the 1000th performer over 400 m hd. Again a non-negligible difference of 3.81 s. In fact the women’s differences between 100  m and 400 m hd mean velocities are more in line with the ones observed for the corresponding flat races, both for women and for men.

So what is happening to the 110 m race? What is slowing the athletes down? To put it in  a nutshell the culprit are the rules.

Here is the introduction to the 110 m hd race from the IAAF site

This modern event first appeared in England around 1830 as a variation of the 100 yards using heavy wooden barriers. In 1864, Oxford and Cambridge turned it into a 120 yards (109.72m) race with 10 obstacles three feet six inches (1.06m) high, ten yards (9.14m) apart, with the first and last obstacles 15 yards from the start and finish respectively. In 1888, the French added 28 cm to the distance, to make it the 110m hurdles. It has remained an Olympic classic (in 1896 it was run with only nine hurdles). 
Early hurdling technique was very rudimentary with athletes making 'bundled' jumps by tucking their legs under their bodies. In 1895, the fixed hurdles were replaced with lighter structures with an inverted T-shaped base, allowing them to be knocked over forwards. Athletes were disqualified if they knocked over more than three hurdles and records were disallowed if one hurdle was knocked over. This rule was retained until 1935.

The problem comes from the fact that the distance of 10 yards between hurdles has been fixed at 1864 and now, 150 years later, we are using the same antiquated rule. But so many things have changed since 1868. First, the hurdles themselves, from fixed to inverted T-shaped and finally to L-shaped ones which fall over with a moderate push and minimise (without eliminating altogether) the risk of a fall and injury. Second, the hurdling technique was refined at the beginning of the 20th century, first by A. Kraenzlein who introduced the technique of striding over the hurdles and taking just three steps between barriers and then perfected by generations of hurdlers. Then the old cinder tracks were replaced by the modern synthetic ones which allow for a better rebound of the athlete. Finally, and this is something non-negligible, today’s hurdlers are taller than their predecessors. To a modern hurdler the hurdles are simply too close to each other and he cannot extend his stride to the full length. 

Renaldo Nehemiah, world record holder (the first to dip under 13 s)

The same problem does not seem to exist for women. In some sense they are lucky because not only hurdling races were introduced much later for women as compared to men but also a major change intervened in 1969: while up to 1968 women were competing over 80 m, from 1969 onwards this race was discontinued and women compete over 100 m. This change was the occasion to increase the distance between hurdles from 8 to 8.5 m. 

My proposal concerning the 110 m hd is simply to discontinue it and replace it with a 100 m race with just 8 hurdles (after all the number 10 is not magical). This would allow to increase the distance between hurdles. I do not know what is the optimal distance: this is something to be fixed by the international coaches’ and athletes’ community. (In fact Juilland suggests that each athlete be allowed to place the hurdles at his preferred distance but I find this proposal rather difficult to implement in practice). Were this proposal to be adopted (a zero probability), we would be looking forward to a world record of less than 11 s.

Another thing that has bothered me for a long time was the assimilation of hurdles to flat races as far as wind assistance is concerned. I do not think that the assistance of wind plays the same role in the two kinds of races. While for a flat race there is not limit to the benefit an athlete can obtain from a strong tailwind, in the case of a hurdle race too strong a wind will cause problems, “pushing” the athlete into the hurdles. I have, just for fun and knowing that the result is not significant statistically, computed the mean wind speed for the world records over 110 m hd and 100 m since 1980. For the former the mean value is 0.4 m/s while for the latter it is 1.1 m/s. In fact two of the world records were established by a hurdler running into a headwind. Another interesting information can be found in the compilation of the best regular and wind-aided times. If we take the time of the 50th performer under regular conditions and ask how many perfomances better than this are there in the wind-aided list we find 20 for the 100 m but less than 10 for the 110 m hd. So, the assistance of wind in a hurdles race must be appreciated in a way different from the wind assistance in flat races. The only possibility for this is the one I am mentioning in my post, namely use a modelling approach in order to adjust the registered times so as to correct them from the effect of the wind. In the case of the 110 m hd this approach should take into account the fact that too strong a wind may have a negative impact on a hurdles race.

Another point I would like to comment on is the one mentioned at the end of the IAAF Introduction quoted above.
Athletes were disqualified if they knocked over more than three hurdles and records were disallowed if one hurdle was knocked over. 
Somehow jumping the hurdles without knocking them over was a left-over from the period when the hurdles were fixed. If we consider that this rule was introduced in parallel with the new hurdles around the first Olympics, it took a good 40 years for it to disappear (1935). Even today the rules stipulate that   

Each athlete shall jump each hurdle. Failure to do so will result in a disqualification. In addition, an athlete shall be disqualified, if:
(a) his foot or leg is, at the instant of clearance, beside the hurdle (on either side), below the horizontal plane of the top of any hurdle; or
(b) in the opinion of the Referee, he deliberately knocks down any hurdle.

I see a real problem in this. 

First if one must jump the hurdles one should be able to jump at least 1.067 m (the height of each hurdle) and moreover do so with a reduced, rectilinear, run-up. Still, the scoring tables for combined events award points for high jump for performances inferior to the hurdle height all the way down to 0.77 m. Is this illogical? As I shall explain, I do not think so. 

At this point a remark is in order. The previous, 1962, tables had the scoring for high jump start at 1.07 m because of the hurdles height and as a consequence the lowest part of the tables was pushed upwards. I find this quite unfortunate. In fact, as I have argued in my publication in New Studies in Athletics, I am convinced that the 0 of the tables should correspond to a zero performance (zero length or zero velocity). The current tables get closer to this by pushing the threshold for acquiring points all the way down to 0.77 m for high jump or 2.25 m for long jump. 

Going back to the argument in favour of the current tables choice I believe that   the tables should not be adapted to the rules of the hurdles race but, on the contrary, the rules for the hurdles should be modified so as to be consistent with the scoring tables. This can only be done if the rule of disqualification when the athlete deliberately knocks down a hurdle is not applied for performances worse than 23.71 s. This is the performance that gives 116 points, exactly the same as a high jump of 1.07 m. The rationale of this is that if the athlete is not able to jump the hurdle he should be allowed to knock it over. For performances better than 23.71 s the athlete must jump the hurdles. One can even imagine a proviso in the tables whereupon if the athlete knocks down hurdles he cannot have a score better than 116 points. It goes without saying that if the athlete knocks down a hurdle he should not obstruct another competitor lest he be disqualified. A famous video of a chinese guy destroying everything in his path can be found in YouTube. In extreme cases like this the athlete should not only be disqualified but get a suspension for his behaviour, which is contrary to any sense of fair-play. However, just as in the case of the  proposal of a 100 m hurdles race, I am not very optimistic concerning a change of rules for knocking down hurdles. Some things are too deeply ingrained and will not change even in view of patent inconsistencies.