Despite the prevalence of many calculators on the internet, the scoring of combined-events and the determination of age graded percentages and equivalent open performances remain mysteries to many masters athletes. This article seeks to explain the complexities of and inter-relationships between Age-Factors, the scoring of combined-events, and Age-Standards and Age-Graded percentages.
The relationship of masters athletic performances with other age groups and with open athletic performances has been an issue that has generated considerable interest for some time. This is because people want to compare their performances at various ages against performances of other masters age-groups and open performances and records, taking into account changed implement specifications and weights, hurdle heights etc. Further for scoring masters combined-events some relationships were also necessary for masters athletics to make use of the IAAF combined event scoring tables.
The first age-graded tables were produced in 1989 and published as a National Masters News and WAVA booklet. Masters Age Graded Tables which contained Age-Factors and Age-Standards for mature-age men and women athletes. They were revised in 1994 and extended to younger (juvenile) age groups, and again updated in 2003 and 2006. The Age-Factors are used to convert masters performances to equivalent open athletics performances, while the Age-Standards are standardised “world-best” performances for each event for each year of age from open athletics to masters, that relate closely to world records. The current Age-Factors, which were revised in 2010, are available through the WMA website (www.world-masters-athletics.org).
HOW WERE THE AGE-FACTORS AND AGE-STANDARDS DERIVED?
Determining Age-Factors and Age-Standards involved graphing large amounts of reliable performance and age data for men’s and women’s events, for all ages in masters and open athletic competition. These data showed that beyond a certain point performances decreased with age, however, this decline did not occur at the same rate, nor in exactly the same way, nor commence at the same age for different events or gender. Data for each individual event were compared with graphs of related events (e.g. the walks, sprints, distance runs, jumps, throws etc.) for both men and women, and subjected to statistical analysis to determine a consistent and smooth relationship between the best performances by athletes, open or masters, at all ages (see e.g. <http://home.roadrunner.com/~alanjones/AgeGrade.html#2010 adjustments>. This relationship or curve was used to determine the Age-Standards for each event in one-year age divisions, and is an approximation of the world-best performance at that age. These Age-Standards do not relate exactly to masters world records, as these are determined as the best performance in a 5-year age group, whereas Age Standards were determined for individual years. The smoothing of data has meant some actual age-best performances may be slightly greater or lesser than the adopted relationship.
USING AGE-FACTORS AND AGE-STANDARDS
The ratio between the Age-Standard for each individual year age, and the standard (best) performance in open athletic competition, usually the world record at the time the Age-Graded Tables were established, determines the Age-Factor ‑ as follows:
(1) Age-Factor = Open Competition Standard / Age-Standard
For running and walking events the value of the Age-Factors will be a value of 1 or less, which declines progressively with age, while for throws and jumps the Age-Factor will be a value of 1 or more, which becomes progressively greater with increasing age.
Age-Factors and Age-Standards can be used in a variety of ways to convert, evaluate or compare performances. Thus Age-Factors can be used to generate an equivalent “open” athletic performance as follows.
(2) Equivalent Open performance = Actual performance x Age-Factor (for an event & age)
This conversion is also the first step to scoring performances in combined-events.
The Age-Standards can be used to generate an Age-Graded percentage for a performance which both allows comparison against the “world standard” for the year age group and allows comparisons with other masters athletes. men and women, irrespective of age, particularly in related groups of events. Age Graded Percentage are calculated as follows
(3) Throws & jumps: Age-Graded percentage = Actual performance / Age-Standard x 100
(4) Runs, hurdles & walks: Age-Graded percentage = Age-Standard / Actual performance x 100
The Age-Standard is generally based on the athlete’s actual age not their 5-year age group. Hence there may be situations where a younger winning competitor in a 5-year age group may have a lower Age-Graded percentage than an older competitor in the same age group who may be placed lower in terms of actual performance. From time to time you may also see competitors who have an Age-Graded percentage of over 100% in an event, such as in some women’s hammer age groups. This is because these individuals are performing at levels beyond the “world best” at the time of development of the Age-Graded Tables.
The Age-Graded percentages are not without criticism, particularly when these are used for comparisons between event groups. It can be fairly argued that it is considerably easier for say a moderate sprinter to achieve a comparatively high Age-Graded percentage, than for an equivalent athlete in a technically difficult throwing or jumping event. Nevertheless, they are a good basis for comparisons between related events – i.e. sprints with sprints, jumps with jumps, throws with throws.
IAAF SCORING TABLES AND THE SCORING OF COMBINED-EVENTS
The IAAF International Scoring Tables were initially developed for scoring the decathlon, pentathlon, and heptathlon events in open athletic competition, however, these scoring tables are now available for almost every athletic event ‑ male and female. The tables provide point scores, typically between 0 and 1200 points, according to the performance level in an event, with increasing performance rewarded with greater points. The 1000 points level is notionally close to the world record at the time of the creation of the scoring tables. This relationship between performance and scores is not a straight line but curve, which recognizes that a specific improvement in time or distance at a high level should be more highly rewarded than the same improvement at a low level. Thus an improvement in the long jump from 8 to 9 metres gives a much bigger increase in points than an equivalent 1-metre improvement from 4 to 5 metres. The scoring tables also involve the concept of a cut-off ‑ a minimum distance from which scoring commences, or a maximum time beyond which scoring ceases.
The IAAF periodically updates the scoring tables and publishes these both in booklet form, although mathematical formulae that related performance to point scores are most commonly used, which through the use of computers enable an almost instant calculation of the results. The IAAF scoring tables (whose derivation will not be explored here) provide for each event ‑ male and female – a specific Event-Constant, an Event-Power-Constant, and the minimum distance or maximum time beyond which points are not scored. These IAAF scoring tables and factors are available through the IAAF website (www.iaaf.org). The general format of these scoring relationships is provided below:
For throws or jumps:
(5) Point score = Event-Constant x (actual distance – minimum distance) ^ Event-Power-Constant
For runs, hurdles or walks:
(6) Point score = Event-Constant x (maximum time – actual time) ^ Event-Power-Constant
Note that in the above equations the symbol “^” means raised to the power of’ by the Event-Power-Constant. This action allows for the increase in points awarded to better performances.
For masters the Age-Factors used for the scoring of combined-events is the Age-Factor that applies to the first year of a 5-year age group. Thus to score a masters event the actual distance or time first has to be multiplied by the Age-Factor to give an Equivalent Open Performance. This results in a slight modification to scoring equations (5) and (6) above for example:
For throws or jumps:
(7) Point score = Event-Constant x (actual distance x Age-Factor – minimum distance) ^ Event–Power-Constant
For runs, hurdles or walks:
(8) Point score = Event-Constant x (maximum time x Age-Factor – actual time) ^ Event-Power-Constant
World Masters Athletics has recently ‑ in 2010 ‑ updated its Age-Factors, with most changes being associated with throwing events. Some events particularly women’s hammer and men’s javelin were significantly affected by these changes, and apparent discrepancies between past scores and performances and scores based on the new age factors will be particularly noticeable in the throws pentathlon.
HOW DOES SCORING WORK IN PRACTICE?
The following is a worked example of scoring a throwing event:
A 52-year old female athlete competing in the W50 (3kg) Shot Put has a best put of 10.60m:
As the Age-Standard for W52 in the Shot Put is 16.64m;
her Age-Graded percentage as per equation (3) = 10.60 / 16.64 x 100 = 63.70%
The Age-Factor for W50 age group in the Shot Put is 1.3876
thus her Open Equivalent performance as per equation (2) = 10.60 x 1.3876 = 14.71m
(noting here that her Open Equivalent performance is rounded down to the nearest centimetre)
From IAAF scoring tables for the women’s Shot Put we obtain the following factors:
- The minimum distance for scoring in open women’s shot put competition is 1.5 metres
- The Event Constant for women’s shot put is 56.021
- The Event Power Constant for women’s shot put is: 1.05
Her point score as per equation (7) = 56.021 x (10.60 x 1.3876 – 1.5) ^ 1.05 = 841.88pts
However, as points for an event are given as a whole number this value is truncated to 841 pts.
- Converted open equivalent distances are always rounded down, and times rounded up, after multiplying by the Age Factor.
- Calculated points are always rounded down so that the value never corresponds to a performance better than that actually achieved.
- See also hand-timing corrections next page.
IAAF COMBINED EVENTS SCORING FORMULAS & FACTORS
The official IAAF scoring tables, as published in the IAAF “Scoring Tables for Men’s and Women’s Combined Events Competitions” are generated by the following mathematical formulas. The results of the formulas must be truncated to the integer and not rounded up. So a formula result of 674.999 is 674 points, not 675, and 872.001 is 872. The actual points formulae are as follows with the three constants listed below for all of the standard combined events. Note that performances must be expressed in seconds, centimetres, or metres as indicated. Note that only events relevant to the decathlon, heptathlon, outdoor pentathlon and throws pentathlon are provided here.
Running and hurdling events: Points = a x (b – Performance)^c
Throwing and jumping events: Points = a x (Performance – b)^c
If combined events running events, from 400 meters down including hurdles, are hand timed, the times have to be corrected before multiplying by the appropriate Age-Factor. Then the corrected score must be looked up in the automatic portion of the scoring Tables (The hand-timed part of the IAAF scoring tables are not used in masters combined-event scoring). The IAAF corrections to apply are:
All track events up to 300 meters add 0.24 seconds to the hand time
400 meters add 0.14 seconds to the hand time
Events above 400 meters do not require any addition – that is use the hand time as is.
IAAF Scoring Factors ‑ Men
100m a=25.4347 b=18s c=1.81
200m a=5.8425 b=38s c=1.81
400m a=1.53775 b=82s c=1.81
1500m a=0.03768 b=480s c=1.85
short hurdles a=5.74352 b=28.5s c=1.92
high jump a=0.8465 b=75cm c=1.42
pole vault a=0.2797 b=100cm c=1.35
long jump a=0.14354 b=220cm c=1.40
shot put a=51.39 b=1.5m c=1.05
discus a=12.91 b=4m c=1.10
hammer a=13.0449 b=7m c=1.05
javelin a=10.14 b=7m c=1.08
weight a=47.8338 b=1.5m c=1.05
IAAF Scoring Factors ‑ Women
100m a=17.857 b=21s c=1.81
200m a=4.99087 b=42.5s c=1.81
400m a=1.34285 b=91.7s c=1.81
800m a=0.11193 b=254s c=1.88
1500m a=0.02883 b=535 c=1.88
short hurdles a=9.23076 b=26.7s c=1.835
high jump a=1.84523 b=75cm c=1.348
pole vault a=0.44125 b=100cm c=1.35
long jump a=0.188807 b=210cm c=1.41
shot put a=56.0211 b=1.5m c=1.05
discus a=12.3311 b=3m c=1.10
hammer a=17.5458 b=6m c=1.05
javelin a=15.9803 b=3.8m c=1.04
weight a=52.1403 b=1.5m c=1.05
REVISED WMA 2010 SCORING TABLES
Following the decision to lower implement weight for older men and women, World Master Athletics has issued completely revised scoring tables (see www.world-masters-athletics.org under Laws & Rules and then under Appendices. Individuals and statisticians involved in scoring such events should note that the revised Age-Factors for the M80+ hammer and shot put, and W75+ discus, shot put and heavy weight have been provisionally calculated without any existing performances and will be adjusted and redefined after a certain test period. A mooted change in the older women’s javelin weight would similarly be affected.