## 13 September, 2015

### What is Eaton's potential?

A. Eaton's superb decathlon 9045 points world record got me thinking about the level of performance of combined event athletes. I must admit that the results of my analysis were really surprising (for myself at least). I was under the impression that the top decathletes and heptathletes were performing at around 90 % of their potential. This would have meant that if one added the scores of the personal records of Eaton in each of the ten events, one would have found a score of the order of 10000 points.

I did precisely this calculation and here is what I found.

Event Decathlon points Personal points
100 m 10.23 1040 10.21 1044
Long Jump 7.88 m 1030 8.23 m 1120
Shot Put 14.52 m 760 15.40 m 814
High Jump 2.01 m 813 2.11 m 906
400 m 45.00 1060 45.00 1060
110 m Hurdles 13.69 m 1015 13.35 1060
Discus Throw 43.43 m 733 47.36 m 816
Pole Vault 5.20 m 972 5.40 m 1035
Javelin Throw 63.63 m 793 66.64 m 838
1500 m 4:17.52 829 4:14.48 850
Total 9045 9543

Eaton's 9045 points record is a good 95 % of his maximum. To say that I was impressed by this is an understatement. And then I started thinking that perhaps Eaton is not that exceptional in performing so close to his maximum. Thus I went back to R. Sebrle's 9026 world record and computed his possible maximum.

Here are the results:

Event Decathlon points Personal points
100 m 10.64 942 10.64 942
Long Jump 8.11 m 1089 8.11 m 1089
Shot Put 15.33 m 810 16.47 m 880
High Jump 2.12 m 915 2.15 m 944
400 m 47.79 919 47.76 921
110 m Hurdles 13.92 985 13.79 1002
Discus Throw 47.92 m 827 49.46 m 859
Pole Vault 4.80 m 849 5.20 m 972
Javelin Throw 70.16 m 892 71.18 m 907
1500 m 4:21.98 798 4:21.98 798
Total 9026 9314

In fact they are even more surprising that Eaton's. Sebrle was performing at 97 % of his maximum. So the natural question was "how about women?". I decided to analyse the records of J. Joyner-Kersee and of C. Klüft, World and European record holders respectively.

For Joyner-Kersee we have the following results

Event Heptathlon points Personal points
100 m Hurdles 12.69 1172 12.61 1184
High Jump 1.86 m 1054 1.93 m 1145
Shot Put 15.80 m 915 16.00 m 928
200 m 22.56 1123 22.30 1150
Long Jump 7.27 m 1264 7.49 m 1341
Javelin Throw 45.66 m 776 50.08 m 862
800 m 2:08.51 987 2:08.51 987
Total 7291 7597

which means that her world record stands at 96 % of her maximum.

For Klüft things are even better.

Event Heptathlon points Personal points
100 m Hurdles 13.15 1102 13.15 1102
High Jump 1.95 m 1171 1.95 m 1171
Shot Put 14.81 m 848 15.05 m 864
200 m 23.38 1041 22.98 1081
Long Jump 6.85 m 1122 6.97 m 1162
Javelin Throw 47.98 m 821 50.96 m 879
800 m 2:12.56 927 2:08.89 981
Total 7032 7240

Her heptathlon record is at 97 % of her possible meximum.

The trend is now clear. Combined event specialists do perform very close to their possible maximum. In fact compared to the other top deca/heptathletes Eaton is slightly underperforming. Could he reach the 97 % of his maximum, as Sebrle and Klüft did, the world record would soar at a whopping 9250 points.

Combined events champions are often seen as supermen/women and after having carried through the analysis above I find it perfectly justified. It is not rare that deca/heptathletes excel at some individual event.

T. Hellebaut was olympic champion at high jump and world indoor champion of pentathlon the very same year, 2008. (Her ratio of pentathlon score 4877 over maximum personal best 5013 stands at 97 %).

N. Gomes won indoor world titles in both long jump in 2008 and pentathlon in 2004. In fact, had she decided to tackle the women's decathlon record she would have made it quite easily. A feasible 3.40 m in pole vault would have given her more than 700 points. Assuming that she could improve her 35.28 m in discus and performing at 95 % of her maximum she would have scored around 8500 points (the current record of A. Skujyté standing at 8366). Her ratio of pentathlon score 4759 over maximum personal best 5088 is only 93.5 % but one has to take into account that after 2004 she practically abandoned the combined events.

This year D. Schippers, 2013 world bronze medalist in heptathlon, was crowned world champion of 200 m.

But even more impressive is the perfomance of Klüft of 14.29 m in triple jump. I do not know of many deca/heptathlete-triple jumper specialists. Had Klüft jumped at her personal best in Beijing, at the 2008 Olympics, she would have made it to the final but, unfortunately, with a mere 13.97 m she did not make it past the qualifiers. And of course the most impressive of all was the incursion of Eaton into the 400 m hurdles. Not only did he manage to record an enviable 48.69 but he won the Diamond League 400 m hurdles race in Oslo, becoming thus the first ever decathlete to win an individual Diamond League event. As I was writing in my blog post ”what can't this guy do?”.

## 09 September, 2015

### A fabulous championship. Second part: field and combined events.

When I had my first contacts with Athletics, back in the 50s, I remember that the canonical order of jumping events was long, high, triple jump and pole vault. However, when I started interesting myself in Athletics statistics, during the 80s, I discovered that the proper order was high jump, pole vault, long and triple jump, i.e. inversely proportional to the length of the performance. So I will base my summary of the latter order.

Women's high jump reserved a most pleasant surprise: the return of B. Vlasic at high level. Jumping 2.01, the same height as the winner M. Kuchina and bronze medallist A. Chicherova, Vlasic showed that she is still competitive at very high level. Men's high jump took place on the only rainy day of the championships. It is probably the bad weather that pushed my personal favourite, M. Barshim, out of the medals. Although the performances were far from exceptional, the event was a most interesting one since it was the first time to my memory that a tie-break was necessary in order to determine the world champion. All three, D. Drouin, G. Zhang and B. Bondarenko finished the event at 2.33 having passed all heights at the first attempt, missing all three attempts, plus the tie-breaking fourth one, at  2.36. When the bar came down to 2.34 Drouin was the only one to pass it. To my eyes this was a well-merited gold medal since Drouin had the most consistent technique of all participants.

Women's pole vault saw the three best vaulters of the year sharing the medals. Y. Silva had a scare at 4.70 but found the energy to jump 4.90 at her third attempt and clinch the victory. F. Murer had previously established an South American record with 4.85, while Kyriakopoulou after missing one attempt at 4.60 and 4.70 passed 4.80 at first try, securing thus a medal. I was also happy with A. Bengtsson's record of 4.70. Hailed as a great talent for quite a few years, she is now starting to mature.

I had never seen S. Barber jump. Fortunately the qualification of men's pole vault was scheduled in the afternoon and thus I could follow it. I was really impressed his mastery of the vaulting technique and was convinced that he was going to play a role in the final. But never could I imagine that R. Lavillenie was going to going to be in one of his "off" days and would have to contend himself with a (shared) bronze medal. Time is running out for Lavillenie to win this elusive world outdoors title. Be that as it may, Barber had a flawless event up to 5.90 m winning the gold medal at just 21 years of age.

Women's long jump was a fabulous competition. My personal favourite, I. Spanovic of Serbia, went beyond 7 m (in fact twice, with first and last jump at 7.01 m) but had to contend with the bronze medal since S. Proctor had a jump at 7.07 m (and another one at 7.01 m) and T. Bartoletta pushed them down one place in the classification with a last attempt at 7.14 m. K. Johnson-Thompson was clearly affected by the heptathlon debacle and could not do better than 6.63 m for 11th place. The mediocrity which is reigning in men's long jump persisted one more year. G. Rutherford won the competition with 8.41 m; nothing to write home about. Some will argue that he is now Olympic, European and World champion. Does this make him a great jumper? Did the fact that K. Kenteris had the very same titles make him a great 200 m runner? I don't think so.

Thank God, while long jump is stagnating, triple jump is rewarding us with great competitions. The battle between P. Pichardo and C. Taylor was breathtaking, ending in a fabulous performance for the latter at 18.21. He has now the mythical record of J. Edwards in his sights. Who would have guessed a few years back that we would be having three jumpers over 18 m. If next year in Rio, Tamgho is back and at the same level as the two others, the triple jump will be the event one should not miss. Women's triple jump saw the crowing of C. Ibargüen, who is the indisputable number one triple jumper of the last three years, with a jump of 14.90 m. I hope that she will continue to dominate the event in the same way next year and add an olympic gold to her extensive collection. The one newcomer I will be keeping my eyes on is G. Petrova of Bulgaria who jumped 14.66 for fourth position and showed a great potential.

Men's shot put saw the defeat of the reigning champion D. Storl by J. Kovacs 21.74 m to 21.93 m. The bronze medal went to a representative of Jamaica, O. Richards, with a throw of 21.69 m. The Caribbeans are becoming a nursery of athletics' champions also for the "heavy" events (following a road already paved by Cuba). In this event I was really pleased by the return to high level of J. Gill, of New Zealand. Once a wunderkind of shot put he was given for lost these last two years. At 21 he has all the time in the world. With V. Adams  out of the race C. Schwanitz was the logical favourite. Still she had to fight hard and in the end only 7 cm separated her from L. Gong, 20.37 to 20.30 m.

P. Malachowski after being the "eternal second" could at last bring home a gold medal. With 67.40 m he dominated a so-so discus event. Again a representative of Jamaica was distinguished here. F. Dacres threw 65.77 m in the qualification which would had sufficed for a bronze medal but could only manage 64.22 m in the final for 7th place. Still he is only 21 and so we will surely see more from him in the years to come. When I read in June that D. Caballero had thrown her discus at 70.65 m I was really impressed. She is a most gifted thrower and had already thrown over 65 m in 2012 but her last two years had seen rather lacklustre performances. Still, she was a finalist in the last two World Championships and her victory here, with a superb 69.28 m, was no surprise. For this she had to beat the "sacred monster" of women's discus, S. Perkovic, the only other seventy-plus'er of the last fifteen years who could only manage a 67.39 m throw to save the silver medal. I will be keeping an eye on the second cuban thrower, Y. Pérez, who with 65.46 m barely missed the bronze medal. I think that she has a potential at least equal to that of her team-mate.

Men's hammer throw was the proof that we are down to just one top-class thrower: P. Fajdek. He confirmed his class by winning his second world tile with a confortable margin and a 80.88 throw. I must say that I am little bit disappointed by M. El Gamel 7th place but this is probably due to a lack of experience at high-level competitions. What I said about men's hammer throw applies also to the women's event, unless there is a question of perspective, given the total dominance of this event by A. Wlodarczyk. She won the championships with two throws over 80 m but was somehow unlucky. Hadn't she not broken the world record less than a month before, her 80.85 m championships throw would have garnered her a very substantial extra prize. I am little bit disappointed with the 6th place of K. Klaas. This time I was really hoping she would be among the medalists. The new talent to follow in this event is S. Hitchon who missed a medal for just 16 cm.

Women's javelin throw led to a fierce competition for the honour places although the overall performances were somewhat below-par. K. Molitor managed to win with a last attempt throw of 67.69 m, her first medal in a major championship. The three big names of women's javelin throw, back from maternity leave had various fortunes. C. Obergföll obtained a not-so-bad fourth place, while M. Abakumova was ignominiously eliminated in the qualifications. B. Spotakova, who came back in good shape in 2014, threw a promising 65.02 m in the qualification and then collapsed in the final, ending in 9th place. But the most exciting throwing event was undoubtedly men's javelin throw. I. El Sayed took the lead with a great second throw of 88.99 m but then J. Yego retaliated with an incredible 92.72 m, third performance of all times. I have been following Yego since the Moscow, 2013, World's where he was pushed out of the medals at the very last throw. This time he squashed the competition with a fabulous throw. He is still a little bit inconsistent technically, but given his great talent, once he manages to tame completely his technique, sky is the limit. My minor disappointment at this event was the elimination in the qualifiers of K. Walcott the only other thrower to have surpassed 90 m this year.

Women's heptathlon did not offer us the thrilling finale we were expecting. One of the two  big favourites, K. Johnson-Thompson managed to foul all her long jump attempts and dropped out. So it was an easy victory with 6669 points for J. Ennis-Hills, since, moreover, B. Theisen-Eaton was not in optimal shape. I watched the third attempt of Johnson-Thompson and I must say that she was really unlucky. She fouled, by just a few millimetres, a jump around 6.90 m. Had this jump been valid and assuming that she could perform over the two remaining events at 95 % of her maximum she would have had a final score very close to that of the winner. I always keep an eye open for new talents and this time I was impressed by the new product of the Dutch combined events school, N. Visser, who finished at the 8th place. On the other hand, I was really disappointed by the performance of N. Thiam who should have been among the contenders for a medal. Finally I would like to draw attention to the tenacity of B. Nwaba of the US team: she crashed out at the very first event clipping the second hurdle. Still she hanged on and finished the event managing even to improve her personal bests in the throws.

Men's decathlon on the other hand offered us even more than what we expected with the fabulous world record of A. Eaton. I plan to write a special post on Eaton and his record in a near future so I will not comment further on his performance. Still I must confess that when he entered the final stretch in the 1500 m I did not believe that he could make it. Fortunately I was proven wrong. D. Warner continued his progression and is now hand-down the second best decathlete of the world. The two athletes that did impress me with their progress were L. Bourrada of Algeria (he improved his own African record, finishing 5th) and K. Felix from Grenada who managed to complete a major decathlon this time (he had not finished one neither in the Moscow, 2013, World's nor in the London, 2012, Olympics) finishing 8th. I will keep an eye on both in the years to come.

While I was compiling this report on the World Championships I realised that it was going to be way too long (even after I split it into two parts) for any technical digressions. So, I plan to return, in some future posts, to the discussion of some more technical points inspired by what happened in Beijing.

## 07 September, 2015

### A fabulous championship. First part: track events.

The World 2015 Championships are over and I must say that I have never watched a better one. The time difference between Greece and China made it practically impossible to follow the morning session and thus I missed the two Marathon races and part of the combined events, but apart from that I have watched every evening session and I must say that I was enthralled. Thus I could not resist the temptation to write a short account with my impressions with just a sprinkle of technical analysis.

Perhaps the most important conclusion one can draw from the 2015 World's is that U. Bolt is the best sprinter ever. (In fact, I was convinced about this even before the championships). He did not come into the competition as the favourite for the first time in many years. Short-sighted people had let themselves be impressed by J. Gatlin's performances and, to tell the truth, Bolt had hidden his game almost perfectly. After a relaxed 100 m quarter final he stumbled out of the blocks in the semi and had to power hard in order to qualify. So, coming into the 100 m final, we knew nothing about his real condition. It turned out that it was excellent and Gatlin cracked. In fact having watched the replay several times I do not think that Gatlin had been ahead of Bolt at any moment.

Then came the 200 m and it was clear to all, apart from hardcore Gatlin fans, that Bolt was going to make short work of Gatlin (he did with an excellent 19.55 time). By the way, are there Gatlin fans, apart from his family, friends and training partners? The only people I can think of are some journalists, the very ones who were ecstatic about the dominance of Marion Jones. In the semi-final we had a déjà-vu with Bolt "chatting" in the last 50 m with A. Jobodwana on his left just like he did at the Moscow, 2013, World's. In fact I was thinking that this relaxed race costed Jobodwana a sub-20 time. I should not have worried. The South African sprinter not only clocked a 19.87 in the final but he secured a bronze medal, his first in a major championship.

Women's 100 m saw the crowning of S.A. Fraser-Pryce in 10.76. (My regret is that my preferred female sprinter, M. Ahouré of Ivory Coast, could not make the final despite an excellent 10.98 in the semis). But the most important element of this race was the second place of D. Schippers in 10.81. To my eyes she became immediately the great favourite for the 200 m race. Some journalists started grudgingly granting her such a position after the usual incantations: "Felix is not running", "Fraser-Price is not running" etc. I am convinced that, had they run the 200 m, Schippers would have inflicted them a stinging defeat. In fact the one thing that surprised me was the superb race of E. Thompson. She was leading most of the race but, with a fantastic finish, Schippers managed to catch up and secured her victory by executing a perfect dip.

She has now, with 21.63, the second best performance in the world after F. Griffith-Joyner (and I refuse to acknowledge the 21.62 of M. Jones, which, moreover, was registered at the 1753 m altitude of Johannesburg).

The two 400 m races were exciting in quite different ways. For men's 400 m my favourites were, in that order: K. James, L. Merritt and L. Santos. I admit that I did not believe in the braggadocio of I. Makwala. But I would never had thought that W. Van Niekerk could win the race despite the fact that he had run a sub-44 (short-lived) African record. Still he executed the perfect race and won in an amazing 43.47 (fourth all-time best). In the case of women's 400 m A. Felix was hands-down the favourite. She run an almost suicidal first 150 m, which had a serious effect, psychological and otherwise, on her opponents, slowed down for the next 100 m and then accelerated again to finish in a brilliant 49.26. (What is even more impressive is her 47.72 split in the 4x400 relay, but more on this later).

When a friend of mine who couldn't watch the championships asked me about the results of the men's 800 m and I told him that D. Rudisha won in 1:45.84 he pouted and said that that was a shitty time. Well, with his two most dangerous rivals Amos and Aman out, Rudisha knew that the race was his to win. He used the best tactique for this. After a first fast 200 m Rudisha took control and slowed the race to an almost snail pace (54.15 at mid-race). He controlled the first attack at 550 m and managed to contain the opposition and when he reached 700 m he went off at full speed. He was never caught. Remember, at the World Championships, or at the Olympics, the important thing is to win.

I have been following M. Arzamasova since 2012 when she was going to qualify for the semis in 800 m at the London Olympics but was hit by a cramp over the last 20 metres. I had the right intuition because she won the European championships in 2014 and, after a great race, was crowned world champion in Beijing. But the women's 800 m was doubly interesting for me. As I wrote already in a previous post I was keeping an eye open for C. Semenya. And I must say that I am perplexed. In the heats she entered the final stretch at 7th position and managed with her well-known powerful sprint to win the qualifying third place. In the semi, on the other hand, she was last and apparently did not even try to catch the girls in front of her. In her interview she said that she was not "that much disappointed" and that she will be preparing for the Olympic Games. So no solution to the Semenya puzzle yet (but, boy, isn't she masculine in everything from looks to voice tone to gestures).

The women's 1500 m saw the crowning of G. Dibaba. It would have been a major surprise if, just after having improved one of those "haunted" world records, she were to lose the world title. But as we'll see below Dibaba is not a bionic woman, just a great champion. At men's 1500 m with 100 m to go there were practically 10 athletes competing for the medals. While one of the favourites, A. Kiprop, did win, the most astonishing race was that of the silver medalist, E. Manangoi. With 30 m to go he was still fifth but with his incredible finish he ensured the one-two for Kenya with the first five athletes separated by less than half a second.

Men's 5 and 10 km were a mere formality for M. Farah. He showed that he could equally win a (very) slow race, the 5 km, as a fast one, the 10 km. In the latter, the Kenyans did their best in order to blunt Farah's finish, but to no avail: Farah was the one to cross the line first. Women's 5 km was an exhibition of power by A. Ayana. I have not been paying much attention to this superb Ethiopian runner, despite the fact that she was bronze medalist in Moscow at the 2013 World's. From 2000 m onwards she imposed a 2:49, 2:44, 2:47 per 1000 m rhythm which nobody could follow. I will not be astonished if she were the one to break the 5000 m world record.  Dibaba, unable to follow, gave up on the race to the point that when she was caught up by S. Teferi she had to sprint in order to save the bronze medal. The African domination was total in this race with three Ethiopians finishing at the first three places followed by four Kenyans. The situation was less clear-cut in women's 10 km who saw the victory of V. Cheruiyot, four years after her Daegu 2011 gold medal: the first 9 places were occupied by three Ethiopians, three Kenyans and three Americans. It was in fact the latter who provided the most thrilling moment of this race. M. Huddle was arriving third at the finishing line and started celebrating when E. Infeld, coming from behind with a very strong finish and a timely dip managed to filch the precious bronze medal.

The lesson here is clear: first cross the line and only then celebrate. You have all the time in the world once you have secured your medal.

Hurdles are a discipline of precision. As P. Iakovakis, the 2006 European champion over 400 m hurdles, has said '"the hurdles are there to make you fall". So, as was natural, the titles went to the people with the best technique over the hurdles. Shubenkov, in the 110 m was the only one in the final who managed to pass over every hurdle without even a single contact, scoring a new Russian record at 12.98. A serious last hurdle mistake costed T. Porter the title in the 100 m in a race won by D. Williams in a so-so time of 12.57 (it wouldn't have sufficed for a medal two years ago in Moscow) with second place, after a flawless race, to heptathlete-turned hurdler C. Roleder. Who in their right mind would have thought that the men's 400 m hurdles was to be won by a Kenyan. And moreover, N. Bett, the winner in a time of 47.79, was not the only Kenyan in the final, the fifth place going to his team-mate B. Tumuti. The big pre-race favourite M. Tinsley foundered, finishing last, after three huge mistakes over hurdles number 4, 7 and 8. What is amazing with Kenyans is that while their technique is far from perfect they do not seem to suffer a slow-down because of the hurdle jumping.

The same ease was exhibited by the Kenyans in the men's 3000 m steeplechase. They managed to kill the competition with a humongous acceleration over the last 300 m finishing in the first four places. E. Kemboi was first for the fourth consecutive time with a time of 8:11.28. Here again the technique over the barriers was essential. C. Kipruto was strongly attacking Kemboi coming into the final stretch but then he fumbled with the final barrier and he barely saved the silver medal. (Mind you, given the ease with which Kemboi finished the race I do not think that anybody stood a chance again him in Beijing).

A similar mistake over the very same last barrier costed my personal favourite, H. Ghribi, the title of the women's 3000 m steeplechase, the victory going to H. Jepkemoi with a time of 9:19.11. Now I just hope that Y. Zaripova, a well-known doping offender, gets stripped of her London, 2012, olympic gold medal, in which case Ghribi will cease being an eternal second.

Relays could have been a clean sweep for Jamaica but they managed to lose the men's 4x400m. I was disgusted by the journalists' attitude who were practically rooting for the US in the 4x100 m men's relay. It is as if they were wishing for Bolt's team to lose the race. (It is understandable: they were the same who, before the championships, were promoting Gatlin as the big favourite). Jamaica, in fact did help them a lot with two messed up exchanges when A. Powell received and passed the baton, but I cannot tell whether Powell was responsible for this just from watching the video. Be that as it may, when it came to the final exchange the US had a slight lead on Jamaica, but nothing Bolt could not make up for. And of course the American team managed to miss completely the exchange and get disqualified, thus allowing the Canadian team to take the bronze medal home (and thus A. De Grasse, whom I consider the future of men's sprint, barring injury, is leaving his first World Championships with two bronze medals). The women's team of Jamaica won easily in 41.07 the second best performance ever. I would have been interested in their splits, even unofficial ones (although I know that they do not mean much in the 4x100 m).  Let us hope they surface one day. Just in case you were wondering: the best split that I know of is a 9.88 by F. Griffith-Joyner in Seoul, 2012, in third position. (Other athletes have done better but only when running at fourth position).

Women's 4x400 m was probably the most exciting relay race. The US team could have won if the team were anchored by Felix provided that she received the baton close enough to the Jamaican team. So, despite Felix' blistering 47.72 split, that brought US to the head of the race her team had to contend with the silver medal. I cannot resist the temptation to mention the split of F. Guei, the very one who managed to win gold for France last year at the European championships. This time she had to retrieve the baton from her fallen team-late, tripped by the Nigerian athlete, and still managed to clock a 49.95. The men's 4x400 m was the only one won by the US. In this they were greatly helped by Jamaica, with R. Chambers, at second position, running a below-par 45.30, and R. McDonald, on third, running a suicidal first part resulting in an utterly disappointing 44.56 (while he had registered a 43.93 in the heats of the individual event). J. Francis, anchoring the relay, repeated the same mistake and, although he clocked a superb 43.52, managed to lose even the bronze medal. On the other hand, had the competition been fiercer, L. Merritt would most probably have run faster than his 44.19 anchor. (And had the Bahamas not been disqualified we would have witnessed an even more thrilling final). K. Borlée run an incredible 43.58 spilt at third position, confirming his 43.78 at anchor position at the semis, but making his elimination at the individual semis even more difficult to understand.

I have not been able to follow the Marathons and so it would be unfair to go into details but reading the results of the women's Marathon one can easily conclude that it should have been a most exciting race, the favourite, and winner, M. Dibaba (no relation to the other Dibabas) being chased all the way to the finish line by four kenyans (one running for Bahrain). The men's Marathon was won by a famous name, Ghebreslassie, belonging to an, almost unknown, Eritrean teenager, the youngest man to win a world title at this race.

And for questions of principle, I am going to ignore the race-walking events (although I firmly believe in the athletic value of race-walkers). It is just that the rules as they stand allow them to run instead of walking which to my eyes is condemning the discipline.

## 01 September, 2015

### On the abuse of the logistic extrapolation

I was riffling through the book of Juilland when I stumbled upon tha page with record projections and predictions. Juilland obtains these predictions by extrapolating, based on exponential curves (his terminology), from records established between 1950 and 1999. (I surmise that by "exponential curves" he means a logistic expression, but more on this later).

It was the Discus throw that grabbed my attention where the predictions were really out of this world. Juilland predicts more than 77 m for 2000, 92 m for 2050 and 101 for 2100. Today we know that Juilland's predictions will never materialise. Since the 80s and the 90s, women's throwing events have taken a serious downturn and it took 25 years for women to reach again 70 m (with just two performers above this mark and a still more than 5 m below the world record).

How could Juilland's predictions be so wrong? A first answer to this is that whatever you do you cannot predict the evolution of the world record. Last year, while presenting a talk on athletics, I chanced the prediction that we should see the first throw beyond 80 m in women's hammer this year. That was a easy one and I would never chance a more daring prediction. So, why are people, including really serious writers like Juilland, think they can make sensible predictions? The answer is: "too much confidence in mathematics", especially by people who are not really trained in mathematical modelling.

So let us see how the predictions can get off the mark. The usual tool for extrapolating from a set of given data on athletics is the logistic equation. It has the expression
$$L={A\over 1+\exp({b-t\over c})}$$
and its graph has a sigmoïd form.

It is supposed to represent the mean evolution of records over time, with a period of rapid progress followed by a slow-down. For very large times the value of L approaches asymptotically A. The way the logistic equation is applied in practice is by obtaining the best fit of such an expression to a set of given data, which allows to fix the values of the parameters. Once the latter are know one can obtain the value of L for any time and thus make predictions for the future evolution of records.

While the assumption that the progression of records follows a sigmoïd curve is quite reasonable, the blind faith in logistic-based predictions may lead to absurd conclusions. We can illustrate this through some examples. The fit below was based on the women's discus world records registered between 1923 and 1965 i.e. just before the 60 m barrier was broken.

The values I obtained were A=58.87 m, b=1923 and c=9.664 (both in years). This is really funny: the prediction for the future evolution of the world record gives a value which is lower than the already registered record! Once you have seen this, how much confidence can you have in logistic-based predictions?

But how about the future, the "real" future now. I haven't tried to reproduce Juilland's predictions but rather used all existing world records from 1923 to 1988. In fact, I am not 100 % whether he has used a logistic fit or he just opted an exponential one of the form
$$L=A(1-\exp({b-t\over c}))$$ In the figure below you can see the best fit corresponding to parameters A=90.31 m b=1939 yr and c=31.52 yr leading to prediction for today of almost 83 m.

However we know now that the discipline of discus throw for women did not continue to evolve as it did in the 80s and thus the fit based on the pre-88 records is misleading. Not having a good criterion that would allow to eliminate suspicious performances I decided to redo the fit by adding a ficticious 2015 world record equal to the current 76.80 m one.

The change in parameters is dramatic. We find now A=83.28 m b=1934 yr and 27.29 yr which would lead to a 2015 prediction around 79 m.

What can we deduce from these analyses? For me the main conclusion is that a logistic fit is next to useless when it comes to predicting the future in athletics. And I am convinced that this is not just a fluke of the logistic equation. (In a future post I will review some of the expressions commonly used in order to make extrapolations based on a set of existing data). It is the very nature of athletics that makes the evolution unpredictable in the long run. Rules, equipment, training methods, to name but a few, do evolve over time with, as a consequence, serious bumps in the record evolution, which cannot be smoothed out by some mathematical tool.