Citius, Altius, Citius, Altius, FortiusFortius

Records, Medals Records, Medals and Drug Testingand Drug TestingJohn D. BarrowJohn D. Barrow

AthleteAthlete Ind’lInd’l

G-S-BG-S-BTotalTotal

G+S+BG+S+BTotalTotal

3G+2S+B3G+2S+BInd’l+teamInd’l+team

G-S-BG-S-BGrand Grand

TotalTotal

G+S+BG+S+B

Grand TotalGrand Total

3G+2S+B3G+2S+B

Phelps *Phelps * 99-0-1-0-1 1010 2828 14-0-214-0-2 1616 4444

EwryEwry 8-0-08-0-0 88 2424 8-0-08-0-0 88 2424

CaslavskaCaslavska 7-1-07-1-0 88 2323 7-4-07-4-0 1111 2929

LewisLewis 7-1-07-1-0 88 2222 9-1-09-1-0 1010 2929

Latynina *Latynina * 6-5-36-5-3 1414 3131 9-5-49-5-4 1818 4141

AndianovAndianov 6-3-36-3-3 1212 2727 7-5-37-5-3 1515 3434

NurmiNurmi 6-3-06-3-0 99 2424 9-3-09-3-0 1212 3030

ShakhlinShakhlin 6-2-26-2-2 1010 2424 7-4-27-4-2 1313 3131

……..

5757thth RedgraveRedgrave

5-0-15-0-1 66 1616 5-0-15-0-1 66 1616

The Most Successful Summer OlympiansThe Most Successful Summer Olympians

G+S+B =M P0.73 GDP0.27

Big variances though

Pop in millions GDP in billions USD

1992 Barcelona Games Best Fit1992 Barcelona Games Best Fit

S = 3G + 2S + B

S = 0.22 P1/3 G2/3

P = population in millionsG = GDP in billions USD

Roughly S = (PGRoughly S = (PG22))1/31/3 or or

S’ = 0.5SS’ = 0.5S33 = ½ PG = ½ PG2 = 2 = ‘energy of a nation‘energy of a nation’’

Peak to peak periodicity of 4T

How to Stop Money Killing CompetitionHow to Stop Money Killing Competition

Ordinary diff eqn

Delay eqn

Exact soln

S(t) = eFt

Model for the ‘Draft’ system in US professional sportBottom team last year gets first pick of new players

Top team gets last pick

Premier league model

Score = 1 for win, ½ for draw, 0 for loss

With T = 2 yr delay there is a clear 8 yr cycle :With T = 2 yr delay there is a clear 8 yr cycle : 8.24 yr for whole NFL8.24 yr for whole NFL

Bufffalo Bills8.3 yr period

What Goes Up Must Come DownWhat Goes Up Must Come Down

Strategy for SuccessStrategy for Success Invest in sports that few countries doInvest in sports that few countries do Pick events with lots of relays, and Pick events with lots of relays, and

team awards and ‘double bronzes’team awards and ‘double bronzes’ Pick sports with strong inter-event Pick sports with strong inter-event

similarity (like cycling)similarity (like cycling) Pick team sports where training and Pick team sports where training and

organisation can dominateorganisation can dominate Don’t do too many different sportsDon’t do too many different sports Encourage some to change eventsEncourage some to change events

The Triathlon is The Triathlon is BiasedBiased

Winner spent 16.7% of his time swimming, 28.3% running, Winner spent 16.7% of his time swimming, 28.3% running, 0.8% in transitions, and 54.2% cycling0.8% in transitions, and 54.2% cycling !

The Equitempered The Equitempered TriathlonTriathlon

Roughly equal time on each disciplineRoughly equal time on each disciplineCurrent eventCurrent event

1.5 km swim + 40 km bike ride +10 km run1.5 km swim + 40 km bike ride +10 km run

Better to keep the total time roughly the same – say 1 hr 48m Better to keep the total time roughly the same – say 1 hr 48m with equal 36 min time on each of the three stages with equal 36 min time on each of the three stages

New event should beNew event should be

3 km swim + 24 km bike ride + 12 km run3 km swim + 24 km bike ride + 12 km run

A Major Improvement !A Major Improvement !

DecathlonDecathlon

Running: 100m + 110m hurdles + 400m + 1500mRunning: 100m + 110m hurdles + 400m + 1500mThrowing: shot + discus + javelinThrowing: shot + discus + javelin

Jumping: high jump + long jump + pole vaultJumping: high jump + long jump + pole vaultTimes and distances Times and distances points scores points scores

Heptathlon: 200m + 800m + HJ + 100H + 800m + Javelin + shot put

Power-Law ScoringPower-Law Scoring

Run

JumpThrow

Distance achieved = DDistance achieved = D

Time run = TTime run = T

C>1 ‘progressive’C>1 ‘progressive’C = 1 ‘neutral’C = 1 ‘neutral’C<1 ‘regressive’C<1 ‘regressive’

IAAF 2001IAAF 2001TablesTables

Fix A, B, CFix A, B, C

HeptathlonHeptathlon

200m C = 1.81800m C = 1.88100H C = 1.835HJ C = 1.348LJ C = 1.41SP C = 1.05JT C = 1.04

All-time top 100 performance patternsWhat you need to do toEarn 900 points in each event

for a 9000 points total

Which Events Give the Biggest Pay-off ?Which Events Give the Biggest Pay-off ?

World record 9026 points World record 9026 points Roman Sebrle in 2001Roman Sebrle in 2001

LJ, 110H, sprints ** 1500m, throws xx

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 secondsUnits of total are m6/s4

A Different Scoring SchemeA Different Scoring Scheme

It has its own biases!

Sebrle (9026 pts): B = 2.29Sebrle (9026 pts): B = 2.29Dvorak (8994 pts): B = 2.40Dvorak (8994 pts): B = 2.40

Best Evers and What IfsBest Evers and What IfsIf scoring is made highly progressive C = 2 for all eventsIf scoring is made highly progressive C = 2 for all events

Dvorak (world no 2) becomes new world record holder with 9468Dvorak (world no 2) becomes new world record holder with 9468

This change dramatically favours the throwers C = 1.1 This change dramatically favours the throwers C = 1.1 2 2

Daley Thompson missed world record by 1 pt in 1984 OlympicsDaley Thompson missed world record by 1 pt in 1984 OlympicsSubsequent change in scoring tables gave him the record!Subsequent change in scoring tables gave him the record!

Current world decathlon record = 9026World record in every event = 12,500

Best ever decathlon performances in each event = 10,485

Usain Bolt’s 9.58s 100m record = 1202Usain Bolt’s 9.58s 100m record = 1202

Fastest 100m in a decathlon = 10.22s = 1042Fastest 100m in a decathlon = 10.22s = 1042

‘‘Best’ world record is 74.08m discus (Schult) = 1383Best’ world record is 74.08m discus (Schult) = 1383

Random RecordsRandom Records In year 1 the result must be a record. So the number of record years isIn year 1 the result must be a record. So the number of record years is

11 In year 2, if the result is independent of year 1, there is a chance of 1/2 of 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 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 expected number of record years in the first 2 years is

1 + 1/21 + 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

((123123, 132, 321, , 132, 321, 213213, 312, 231) , 312, 231) of the results in years 1, 2 and 3 could produce a record in year 3 (ie a 1 in 3 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 chance). So the expected number of record years after 3 years is 1 + 1/2 + 1/31 + 1/2 + 1/3

If you keep on going, applying the same reasoning to each new year, you will If you keep on going, applying the same reasoning to each new year, you will find that after find that after nn independent years the expected number of record years is the independent years the expected number of record years is the sum :sum :

1 + 1/2 + 1/3 + 1/4 + ... + 1/n1 + 1/2 + 1/3 + 1/4 + ... + 1/n = = H(n)H(n)

The ‘harmonic’ seriesThe ‘harmonic’ series

But H goes to infinity very But H goes to infinity very slowlyslowly

H(n) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + …. + 1/nH(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 + logH(n) = 0.577 + logeenn

World men’s 100m record frequencyWorld men’s 100m record frequency

We expect H(100) We expect H(100) 5 records since 1910 and H(26) 5 records since 1910 and H(26) 4 Olympic records 4 Olympic recordsSo record-setting is not a random process So record-setting is not a random process

New events

Women’s Athletics Records are Very RareWomen’s Athletics Records are Very Rare

11 women’s world records 11 women’s world records are more than 20 yrs oldare more than 20 yrs old

2 men’s records2 men’s records are more than 20 years oldare more than 20 years old

Drug Testing StatsDrug Testing Stats

Take Take Drugs Drugs (1%)(1%)

No DrugsNo Drugs

(99%)(99%)

Test +Test + 80%80% 9.6%9.6%

Test -Test - 20%20% 90.4%90.4%

Assume 1% of athletes take drugs and 80% of tests detect their presenceBut 9.6% of tests are positive when no drugs are present (‘false positives’)

What If You Test Positive?What If You Test Positive?

Took Drugs Took Drugs

(1%)(1%)No DrugsNo Drugs

(99%)(99%)

Test +Test + 1% 1% 80% 80% = 0.008 = 0.008 true +true +

99% 99% 9.6% 9.6%= 0.09504 = 0.09504 false +false +

Test -Test - 1% 1% 20% 20% = 0.002 = 0.002 false -false -

99% 99% 90.4% 90.4%= 0.89496 = 0.89496 true -true -

What is the chance you took drugs?What is the chance you took drugs?

Prob you are taking drugs if test + is 0.008/(0.008 + 0.09504) = 0.0776Only detect 7.8% of drug users because we have 9.5% false positives

Thomas Bayes’ TheoremThomas 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%

80%

1%

False +9.6%

99%

= 7.8%

1701-61

A = taking drugsB = test +not A = not taking drugs

Race WalkingRace Walking

Start of the 3500 metre walk at the 1908 Summer Olympics

‘‘Lifting’ in Race WalkingLifting’ 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

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 andThree warnings from different judges and you are out’ disqualification rule’

Jefferson Perez (Ecuador) 1996 Olympic 20K champion Jefferson Perez (Ecuador) 1996 Olympic 20K champion during a 10K race. during a 10K race.

Note the lack of up down movement of his centre of gravityNote the lack of up down movement of his centre of gravity

He averaged just over 6 minutes per mile. He averaged just over 6 minutes per mile.

He is taking about 186 steps/min. This film is actual speedHe is taking about 186 steps/min. This film is actual speed

http://www.eracewalk.com/Tech.htm

The Forces That Are With YouThe Forces That Are With You

Stride length SLeg length L Weight Mg

V = 2Ld/dt

Vertical accnR-Mg = M d2(2Lcos)/dt2 Rotational accn

4ML2 d2/dt2 = 2MgLsin

g = 9.8 m/s2, L = 1m, S = 1.3m then

max V before contact is lost is

VV22 = ½ gL[3 = ½ gL[3(4 - S(4 - S22/L/L22) – 4]) – 4]

VVmaxmax = 1.7 m/s = 1.7 m/s

World record speed over 20 Km is V > 4m/s

Reduce S to 1m still gives Vmax = 2.42 m/s

Increase the effective leg length using hip sway ?

Lifting Seems InevitableLifting Seems Inevitable

Hip Sway can give LHip Sway can give Leff eff S S

Need 0.7m hip extension !!