800 metres 

The Base height is 75.0 cm and the power c is 1.42

The multiplier a​ is 0.8465

400 metres 

The Base measurement is 1.50 m and the power c is 1.05

The multiplier a​ is 25.4347

The Base time is 42.5 secs and the power c is 1.81

The multiplier a​ is 4.99087

The Base measurement is 7.00 m and the power c is 1.08

The multiplier a​ is 10.14

The Base measurement is 1.5 m and the power c is 1.05

The multiplier a​ is 56.0211

The Base time is 254 secs and the power c is 1.88

The multiplier a​ is 0.11193

The standard time for 800 points is 11.28 secs which represents 0.6267 of the base time. Within the range of this chart, each 0.01 sec increases from under one to over two points and is therefore presented on the basis of a score for each increment of 0.01 sec 

The standard time for 1000 points is 23.80 secs which represents exactly 0.56 of the base time, although for 23.81 you would also get 1000 points. Each marginal improvement of 0.01 (one-hundredth) of a second represents fractionally less than a whole point in the score. So sometimes a time is missing, in which case you take the points time for the next slowest time. *

The measurement for 800 points is 15.16 metres.  Each point is the equivalent of just over 0.01 m so if distance is not given, use the next-shortest. *

Women's Heptathlon

For the running events there is a parallel with Interceptions in Passer Rating; you score more points the lower the time as smaller the interception rate.

* If final scores differ by 10 points or less then check the 200m, 800m, Shot Put and Javelin Throw if any interpolations have been involved...

The Base time is 480.0 secs and the power c is 1.85

The multiplier a​ is 0.03768

Athletics

100 metres 

​​This project discusses and examines some of the formulae involved in points-based athletic competitions along with respective Points charts

Jumping Events

Pole Vault

The standard time for 800 points is 261.77 secs which represents 0.5454 of the base time. Within the range of this chart, each point decreases from the equivalent of about 0.20 to under 0.14 secs. Again, work on the basis of the nearest time; if midpoint use the next-slowest published time. * 

The Base time is 28.5 secs and the power c is 1.92

The multiplier a​ is 5.74352

The height for 804 points is 200cm (two metres). Each 3cm increment increases from around 23 points to just under 30 points at the decathlon world best; around 4 secs equivalent in the 1500m

Shot Put 

The standard time for 800 points is 15.42 secs which represents 0.5411 of the base time. Each marginal improvement of 0.01 of a second (one-hundredth) increases the score by just under a whole point (so there are even some time gaps) to around one and a half. If a time is missing, take the next slowest time; as with the 100m Hurdles, duplicate times for points scored have been greyed out.

Running Events

Discus Throw

Jumping Events

The length for 804 points is 694cm (6.94m). Each cm increment is worth from just over two points to nearly three.

The standard time for 1000 points is 13.85 secs which represents 0.5187 of the base time. Each marginal improvement of 0.01 of a second (one-hundredth) increases the score by more than a whole point to nearly two. If duplicated times are shown in the table, score the lower points for that time. For example, a time of 16.30 secs scores 678 points; inapplicable lines have been greyed out.

Javelin Throw

High Jump

The Base height is 100 cm and the power c is 1.35

The multiplier a​ is 0.2797

* If final scores differ by 10 points or less then check the 400m, 1500m, Shot Put, Javelin Throw and Discus Throw if any interpolations were made.

100 metres Hurdles

The Base measurement is 3.8 m and the power c is 1.04

The multiplier a​ is 15.9803

The closest standard time to 1000 points is mathematically 127.64 secs which represents 0.5025 of the base time, although for any time between 127.61 and 127.66 would also achieve 1000 points. Each marginal improvement of 0.01 (one-hundredth) of a second around the standard represents fractionally less than 0.15 of a whole point in the score. Almost always it is safe to take the closest time to that published; if that falls exactly mid-point then take the higher point score. *

The Base height is 75 cm and the power c is 1.348

The multiplier a​ is 1.84523

The measurement for 800 points is 46.58 metres.  Each point is the equivalent of around 0.05 m so if distance is not given, score the points for the next-nearest, rounding down if necessary. *

110m Hurdles 

The Base measurement is 4.00 m and the power c is 1.10

The multiplier a​ is 25.4347

According to various sources, including Wikipedia, the formulae were devised by a Viennese Mathematician, Dr Karl Ubrich and consist of three formats:  

Running Events

The Base length is 220.0 cm and the power c is 1.40

The multiplier a​ is 0.14354

The measurement for 800 points is 64.09 metres.  Each point is the equivalent of around 0.07 m so if distance is not given, score the points for the next-nearest, rounding down if necessary. *

For the running events (100m Hurdles, 200m and 800m) the formula used is:

P​ = a * ((b - T)^c) or solving for T, T= b - ((P/a)^(1/c))

For the jumping events (High Jump and Long Jump) the formula used is:

P​ = a * ((HL - b)^c)

For the throwing events (Shot Put and Javelin) the formula used is:

P = a * ((M - b)^c) or solving for M, M=((P/a)^(1/c)) + ​b

In these formulae P is points and for each event the "Standard" is around 1000

a is the multiplier applied once the rest of the equation has been solved

is the base for each event, for which there is no score

is the power by which the difference between score and base is raised before       being multiplied by a to give the Points for the event

Note: You cannot score negative in any category; the absolute minimum is zero

T is the time in seconds for the running events

HL is the Height or Length for the jumping events in centimetres

M is the Measurement of throwing events in metres

Throwing Events

The measurement for 1000 points is 17.06 metres. In competition terms each cm recorded, or more correctly 0.01 m for the formula is worth somewhat less than a point. So, given the nature of the projectile, round distance down to the next shorter measurement for which a score is given. Thus 15.06 m, for example scores 865 instead of 866. * 

Men's Decathlon

High Jump

Long Jump

1500 metres 

The Base time is 82.0 secs and the power c is 1.81

The multiplier a​ is 1.53775

Shot Put

The Women's Heptathlon consists of seven events:

Day 1: 100m Hurdles, High Jump, Shot Put, 200m

​Day 2: Long Jump, Javelin Throw, 800m

Long Jump

Javelin Throw

Throwing Events

The measurement for 1000 points is 57.17 metres. In competition terms each point is is the equivalent of just over 0.05 m for the formula. Score the points nearest to the exact measurement. *

The Base time is 18.0 secs and the power c is 1.81

The multiplier a​ is 25.4347

The length for 1001 points is 648 cm. In competition terms each cm recorded is worth approximately 3 points; sometimes 2 for shorter and 4 for longer; for example 6.07 m is worth four points more than 6.06 m and the same for 6.16 m over 6.15 m

The same formulae as used as for the Women's Heptathlon. Only the High Jump, Long Jump and Javelin may be compared and to obtain 1000 points, required performance is significantly greater. It may be fairer to equate 800 points in Decathlon comparable with 1000 in Heptathlon.

200 metres 

The Men's Decathlon consists of ten events:

Day 1: 100m, Long Jump, Shot Put, High Jump, 400m

​Day 2: 110mH, Discus, Pole Vault, Javelin, 1500m

The standard time for 800 points is 50.32 secs which represents 0.6137 of the base time. Within the range of this chart, each 0.01 sec increases from about 0.37 to over 0.52 of each point, so work on the basis of the nearest; if the step between each point is 0.02 secs round the time to next slowest. * 

There is no comparison other than the Hurdles and even the information has to presented slightly differently. 

The Base length is 210 cm and the power c is 1.41

The multiplier a​ is 0.188807

Points are awarded according to Height or Length, which is measured in centimetres subject to a very low minimum

The height for 799 points is 463cm (6.94m). Each extra 3cm achieved is worth from 7 to 10 points.

The height for 1004 points is 182 cm. In the Rio Olympics the bar was raised in 3 cm increments representing around 39 points, or about 2.5 seconds in comparison with the 800 m.

Points are awarded according to Measurement in metres to the nearest centimetre subject to a very low minimum

The Base time is 26.7 secs and the power c is 1.835

The multiplier a​ is 9.23076

Last updated 19th July 2017
Copyright Hugh Nightingale 2014-2017

​2MW