Citius, Altius, Fortius Records, Medals and Drug Testing John D. Barrow.
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Transcript of Citius, Altius, Fortius Records, Medals and Drug Testing John D. Barrow.
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 !!