The Statistics of 1. Which is the best world record? Running Faster
[Pages:5]The Statistics of Running Faster
Howard Grubb Department of Applied Statistics The University of Reading, UK rdg.ac.uk/ snsgrubb/athletics
Questions: 1. Which is the best world record? 2. What will the mile record be in 2040? 3. How much do we slow as we get older?
1. Which is the best world record?
dist(m) 100 200 400 800
1500 1609 3000 5000 10000 42195
Men Women 9.79 10.49 19.32 21.34 43.18 47.60 101.1 113.3 206.0 230.5 223.1 252.6 440.7 486.1 759 868 1583 1772 7565 8447
ratio 93% 91% 91% 89% 89% 88% 91% 87% 89% 90%
The Statistics of Running Faster, BAAS, September 17, 1999
All-time best performances
number
45
100m (22/163) 98%
40
35
30
25
20
15
10
5
0
9.79 9.81 9.83 9.85 9.87 9.89 9.91 9.93 9.95 9.97 time (s)
number
45
400m (21/42) 98%
40
35
30
25
20
15
10
5
0
43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 44.0 44.1 time (s)
The Statistics of Running Faster, BAAS, September 17, 1999
time (s)
time (s)
The Statistics of Running Faster, BAAS, September 17, 1999
Men 100m (816)
10.0
9.8 1960
1970
1980
1990
2000
Men 400m (227)
44.5
44.0
43.5
1960 1970 1980 1990 2000 year
The Statistics of Running Faster, BAAS, September 17, 1999
distance(m)
time (s)
105
104
103
102
6
number
45
200m (13/46) 97%
40
35
30
25
20
15
10
5
0
19.32 19.38 19.44 19.50 19.56 19.62 19.68 19.74 19.80 19.86 time (s)
Men 200m (46)
19.8
19.6
19.4 1960
1970
1980 year
1990
2000
The Statistics of Running Faster, BAAS, September 17, 1999
speed (m/s)
8
200 best speeds
10
Performances at other distances
Time doubles with distance
Time (secs)
10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 0
1999 world records
Men Women
10000
20000 30000
Distance (m)
40000
50000
Speed shows more features
Speed (m/s)
11 10
9 8 7 6 5 4
100
1999 world record speed
Men Women
1000
10000
Distance (m)
100000
The Statistics of Running Faster, BAAS, September 17, 1999
dist(m) 100 200 400 800
1500 1609 3000 5000 10000 42195
%WR speed Men Women
99.2% 100.1% 100.9% 99.3%
99.9% 99.9% 99.7% 99.3% 99.8% 99.8% 99.5% 98.4% 100.1% 101.5% 100.1% 98.9% 101.1% 102.0% 99.4% 99.5%
Use % WR speed to compare
Individual athlete has own speed curve - calculator: rdg.ac.uk/ snsgrubb/athletics/runcalc.html
The Statistics of Running Faster, BAAS, September 17, 1999
British Records
dist(m) 100 200 400 800
1500 1609 3000 5000 10000 42195
Men Women 9.87 11.10 19.87 22.10 44.36 49.42 101.7 116.2 209.7 238.1 226.3 257.2 452.8 507.4 780 884 1638 1827 7633 8756
%WR speed 98.4% 94.6% 98.1% 95.9% 97.2% 96.2% 99.1% 96.8% 98.1% 96.7% 98.1% 96.6% 97.4% 97.3% 97.4% 97.2% 97.7% 99.0% 98.5% 96.0%
The Statistics of Running Faster, BAAS, September 17, 1999
time (s)
2. What will the mile WR be in 2040?
- 1913 ? mile record = 4:14
- 1954 ? 4 minute mile - 1999 ? 3:43 mile
? 7:58 2 miles - Komen 20/7/97 ? 10km @ 4:15/mile ? 3:26 1500m
240
Progression in 1500m times
235
230
225
220
215
210
205
200
195
190
1900
1950 Year 2000
2050
The Statistics of Running Faster, BAAS, September 17, 1999
speed (m/s)
Performances in other years All distances - speed
10
Progression in speeds
9
8
7
6
5
4
1900
1950 Year 2000
2050
Putting them together with model for speed gives more information on progression
How fast will we run?
Chapman-Richards
Dist(m) Record, 1999
Predicted lower Diff bound
% of limit
400 43.18 40.80 2.4 94.5
800 1:41.1 1:34.8 6.3 93.8
1500 3:26
3:13 13.0 93.7
5000 12:39 11:55 44 94.2
10000 26:23 25:00 1:23 94.7
42195 2:06:05 1:55:25 10:40 91.5
The Statistics of Running Faster, BAAS, September 17, 1999
The Statistics of Running Faster, BAAS, September 17, 1999
3. How much do we slow down?
Age-group WRs 21 (of 8x2x12=192) records broken at WAVA Champs (Gateshead, August):
AGE 50
dist(m)
M
W
100 11.20 12.90
200 22.90 26.52
400 51.60 58.51
800 119.5 142.0
1500 245.2 294.3
3000 533.1 624.0
5000 896 1046
10000 1861.9 2211
42195 8370 10127
M/W 87% 86% 88% 84% 83% 85% 86% 84% 83%
ALL/50 MW
87% 81% 84% 80% 84% 81% 85% 80% 84% 78% 83% 78% 85% 83% 85% 80% 90% 83%
propn. WRspeed
Performances by athletes of different ages/gender
Age-WR speeds - relative to overall WR
age-group WRs
1.0
0.8
0.6
0.4
0.2 30 40 50 60 70 80 90 age
The Statistics of Running Faster, BAAS, September 17, 1999
propn. WRspeed
men
1.0
0.8
0.6
0.4 log(dist)
80
women
0.2 30 age
1.0
0.8
0.6
0.4 log(dist)
0.2
30
80
age
propn. WRspeed
The Statistics of Running Faster, BAAS, September 17, 1999
The Statistics of Running Faster, BAAS, September 17, 1999
Comparing athletics performances - Data - WRs, all time best times
how far from these is a WR? - Speed - slowing with distance
reference curve - %WRspeed - WR progression - Age-group WRs - slowing with age
The Statistics of Running Faster, BAAS, September 17, 1999
4. How good was my race?
Reading half marathon 1999: 4500 runners, 3500 men
Reading Half 1999, time
0.0004
0.0002
0.0000 4000
6000 8000 10000 time(secs)
Hill race
10km, but climbing (304 men, 81 women)
0.0008 0.0006 0.0004 0.0002 0.0000
2000
2.0 1.5 1.0 0.5 0.0
0
Carnethy 1999
4000
6000
time (s)
Carnethy 1999
2 "speed" 10k/t
7000 6000
(time (s))
5000
4000
3000
2000
8000
-3 -2 -1 0 1 2 3
Normal
4.0 3.5
("speed" 10k/t)
3.0
2.5
2.0
1.5
1.0
4
-3 -2 -1 0 1 2 3
Normal
distribution
The Statistics of Running Faster, BAAS, September 17, 1999
The Statistics of Running Faster, BAAS, September 17, 1999
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