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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download