1. Citius, Altius, Fortius Records, Medals and Drug Testing John D. Barrow

2. AthleteInd’lG-S-BTotalG+S+BTotal3G+2S+BInd’l+teamG-S-BGrandTotalG+S+B Grand Total 3G+2S+B Phelps * 9-0-1 102814-0-21644 Ewry8-0-08248-0-0824 Caslavska7-1-08237-4-01129 Lewis7-1-08229-1-01029 Latynina * 6-5-314319-5-41841 Andianov6-3-312277-5-31534 Nurmi6-3-09249-3-01230 Shakhlin6-2-210247-4-21331 …. 57 th Redgrave 5-0-16165-0-1616 The Most Successful Summer Olympians

3. G+S+B =M  P 0.73  GDP 0.27 Big variances though Pop in millions GDP in billions USD

4. 1992 Barcelona Games Best Fit S = 3G + 2S + B S = 0.22  P 1/3  G 2/3 P = population in millions G = GDP in billions USD Roughly S = (PG 2 ) 1/3 or S’ = 0.5S 3 = ½ PG 2 = ‘energy of a nation’

5. Peak to peak periodicity of 4T How to Stop Money Killing Competition Ordinary diff eqn Delay eqn Exact soln S(t) = e Ft Model for the ‘Draft’ system in US professional sport Bottom team last year gets first pick of new players Top team gets last pick Premier league model

6. Score = 1 for win, ½ for draw, 0 for loss With T = 2 yr delay there is a clear 8 yr cycle : 8.24 yr for whole NFL 8.24 yr for whole NFL Bufffalo Bills 8.3 yr period What Goes Up Must Come Down

7. Strategy for Success Invest in sports that few countries do Invest in sports that few countries do Pick events with lots of relays, and team awards and ‘double bronzes’ Pick events with lots of relays, and team awards and ‘double bronzes’ Pick sports with strong inter-event similarity (like cycling) Pick sports with strong inter-event similarity (like cycling) Pick team sports where training and organisation can dominate Pick team sports where training and organisation can dominate Don’t do too many different sports Don’t do too many different sports Encourage some to change events Encourage some to change events

8. The Triathlon is Biased Winner spent 16.7% of his time swimming, 28.3% running, 0.8% in transitions, and 54.2% cycling 0.8% in transitions, and 54.2% cycling !

9. The Equitempered Triathlon Roughly equal time on each discipline Current event 1.5 km swim + 40 km bike ride +10 km run 1.5 km swim + 40 km bike ride +10 km run Better to keep the total time roughly the same – say 1 hr 48m with equal 36 min time on each of the three stages New event should be 3 km swim + 24 km bike ride + 12 km run A Major Improvement !

10. Decathlon Running: 100m + 110m hurdles + 400m + 1500m Throwing: shot + discus + javelin Jumping: high jump + long jump + pole vault Times and distances  points scores Heptathlon: 200m + 800m + HJ + 100H + 800m + Javelin + shot put

11. Power-Law Scoring Run Jump Throw Distance achieved = D Time run = T C>1 ‘progressive’ C = 1 ‘neutral’ C<1 ‘regressive’ IAAF 2001 Tables Fix A, B, C

12. Heptathlon 200m C = 1.81 800m C = 1.88 100H C = 1.835 HJ C = 1.348 LJ C = 1.41 SP C = 1.05 JT C = 1.04

13. All-time top 100 performance patterns What you need to do to Earn 900 points in each event for a 9000 points total Which Events Give the Biggest Pay-off ? World record 9026 points Roman Sebrle in 2001 LJ, 110H, sprints ** 1500m, throws xx

14. Could avoid points transformations by having B-Total = LJ  HJ  PV  JT  DT  SP_______ T(100)  T(400m)  T(100mH) T(1500m) List all distances in metres and all times in seconds Units of total are m 6 /s 4 A Different Scoring Scheme It has its own biases! Sebrle (9026 pts): B = 2.29 Dvorak (8994 pts): B = 2.40

15. Best Evers and What Ifs If scoring is made highly progressive C = 2 for all events Dvorak (world no 2) becomes new world record holder with 9468 This change dramatically favours the throwers C = 1.1  2 Daley Thompson missed world record by 1 pt in 1984 Olympics Subsequent change in scoring tables gave him the record! Current world decathlon record = 9026 World record in every event = 12,500 Best ever decathlon performances in each event = 10,485 Usain Bolt’s 9.58s 100m record = 1202 Fastest 100m in a decathlon = 10.22s = 1042 ‘Best’ world record is 74.08m discus (Schult) = 1383

16. Random Records Random Records In year 1 the result must be a record. So the number of record years is In year 1 the result must be a record. So the number of record years is1 In year 2, if the result is independent of year 1, there is a chance of 1/2 of beating the record from year 1 and a chance of 1/2 of not beating it. So the expected number of record years in the first 2 years is In year 2, if the result is independent of year 1, there is a chance of 1/2 of beating the record from year 1 and a chance of 1/2 of not beating it. So the expected number of record years in the first 2 years is 1 + 1/2 In year 3 there are just two ways in which the 6 possible rankings In year 3 there are just two ways in which the 6 possible rankings (123, 132, 321, 213, 312, 231) of the results in years 1, 2 and 3 could produce a record in year 3 (ie a 1 in 3 chance). So the expected number of record years after 3 years is of the results in years 1, 2 and 3 could produce a record in year 3 (ie a 1 in 3 chance). So the expected number of record years after 3 years is 1 + 1/2 + 1/3 If you keep on going, applying the same reasoning to each new year, you will find that after n independent years the expected number of record years is the sum : If you keep on going, applying the same reasoning to each new year, you will find that after n independent years the expected number of record years is the sum : 1 + 1/2 + 1/3 + 1/4 +... + 1/n = H(n) The ‘harmonic’ series

17. But H goes to infinity very slowly H(n) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + …. + 1/n Then H(1) = 1, H(2) = 1.5, H(3) = 1.833, H(4) = 2.083, H(10) = 2.93, H(100) = 5.19 The sum grows very slowly as the number of terms increases: H(256) = 6.124 but H(1000) = 7.49 H(1,000,000) = 14.39. When n gets large H(n) only increases as fast as the natural logarithm of n and approximately H(n) = 0.577 + log e n

18. World men’s 100m record frequency We expect H(100)  5 records since 1910 and H(26)  4 Olympic records So record-setting is not a random process

19. New events Women’s Athletics Records are Very Rare

20. 11 women’s world records are more than 20 yrs old 2 men’s records are more than 20 years old are more than 20 years old

21. Drug Testing Stats Take Drugs (1%) No Drugs (99%) Test + 80%9.6% Test - 20%90.4% Assume 1% of athletes take drugs and 80% of tests detect their presence But 9.6% of tests are positive when no drugs are present (‘false positives’)

22. What If You Test Positive? Took Drugs (1%) No Drugs (99%) Test + 1%  80% = 0.008 true + = 0.008 true + 99%  9.6% = 0.09504 false + Test - 1%  20% = 0.002 false - 99%  90.4% = 0.89496 true - What is the chance you took drugs? Prob you are taking drugs if test + is 0.008/(0.008 + 0.09504) = 0.0776 Only detect 7.8% of drug users because we have 9.5% false positives

23. Thomas Bayes’ Theorem P(A|B) = P(B|A)P(A) = _________ P(B|A)P(A) ______ P(B) P(B|A)P(A) + P(B|notA)P(notA) Prob of Taking drugs if test + 1% 80% 1% False + 9.6% 99% = 7.8% 1701-61 A = taking drugs B = test + not A = not taking drugs

24. Race Walking Start of the 3500 metre walk at the 1908 Summer Olympics

25. ‘Lifting’ in Race Walking ‘Race walking is a progression of steps so taken that the walker makes contact with the ground so that no visible (to the human eye) loss of contact occurs.’ USTFA rules The human eye records at only about 25 frames per sec

26. This film is of an experienced Italian male who, according to the IAAF, has walked a 20K race in 1:23:55 ‘Three warnings from different judges and ‘Three warnings from different judges and you are out’ disqualification rule’

27. Jefferson Perez (Ecuador) 1996 Olympic 20K champion during a 10K race. Note the lack of up down movement of his centre of gravity He averaged just over 6 minutes per mile. He is taking about 186 steps/min. This film is actual speed http://www.eracewalk.com/Tech.htm

28. The Forces That Are With You Stride length S Leg length L Weight Mg V = 2Ld/dt   Vertical accn R-Mg = M d 2 (2Lcos)/dt 2 Rotational accn 4ML 2 d 2 /dt 2 = 2MgLsin

29. g = 9.8 m/s 2, L = 1m, S = 1.3m then max V before contact is lost is V 2 = ½ gL[3(4 - S 2 /L 2 ) – 4] V max = 1.7 m/s World record speed over 20 Km is V > 4m/s Reduce S to 1m still gives V max = 2.42 m/s Increase the effective leg length using hip sway ? Lifting Seems Inevitable

30. Hip Sway can give L eff  S Need 0.7m hip extension !!