How to create a level playing field across ages

 

The P/AR ratio 

Vianney Koelman 

Dutch Eindhoven Rowing Association Beatrix 

 

Cyclists are used to a power-to-weight (measured in Watts per kilogram) performance metric. The power-to-age-reserve ratio (abbreviated as P/AR and measured in Watts per year) provides us with a similar metric. The objective of this novel metric is to create a level playing field across sexes and ages for ergometer events such as RowErg and BikeErg competitions. 

So what is 'age-reserve'? We are all aware that once we enter our thirties, the power our bodies are capable of generating will gradually drop. Every year we grow older, the odds are our power figures will be less than those from a year before. This also holds for world-class athletes. As an example, below figure shows the power delivered by male and female RowErg 2k world record holders against the athlete’s age. 

Straight lines fit nicely through both sets of data points. These straight lines effectively represent the age decline of world-record level fitness for males and females.  When extrapolated to high age, both straight lines will cross the age-axis, indicating a vanishing power figure. This happens at around an age of 120. So the age at which world-record level fitness drops to zero corresponds to the maximum age achievable by humans (also roughly 120 years), as it should be. 

The age-reserve measures the number of years an individual is away from the age above which the athlete's power is expected to vanish. In other words, the age-reserve for an individual equates to 120 minus the age of that individual. 

In above plot, as both male and female power performances follow straight lines that crosses the age-axis at the same age of 120, it follows that by a re-scaling both straight lines can be made to overlay. Effectively, if one multiplies the powers generated by females by 1.56, the female and male performances nicely overlay. We use these sex-corrected powers to define the P/AR ratio. So, for males this ratio is the power generated divided by the age-reserve. For females it is 1.56 times the power generated divided by the age-reserve.  

By construction, this power-to-age-reserve metric creates a level playing field across the sexes and across a wide range of ages. This is demonstrated in below figure for the indoor rowing world-record 2k performances. This time these performances are not expressed in terms of raw power (Watts) but in terms of the power-to-age-reserve (P/AR) ratio (Watts-per-year).

Therefore the P/AR metric can be used to create fun competitions in which bothe sexes, regardless their age, can participate. All one has to do is to measure the athlete's performance in terms of this power-to-ageReserve ratio. This will work equally well for RowErg, BikeErg and SkiErg events.   

Below table lists an all-time bests (top-50) P/AR RowErg 2k leaderboard. A mix of males and females with ages varying from 25 till 76 results. This age diversity corresponds to age reserves ranging from 44 to 95. As expected, diversity in body weights is not achieved (can you spot the single lightweight?). 

The all-time top-50 for BikeErg 4000m P/AR personal bests shows a similar diversity over sexes and ages (see below).

As we saw, in RowErg competitions, the P/AR metric itself does not achieve diversity over weight classes. One way to realise this, is to introduce the P/AR-intensity metric measured in milliWatts per year of age reserve per kg of body weight. Another way is to expand the use of weight factors (introduced above to create a level playing field between males and females) so as to create a level playing field also between weight classes. The latter approach is calibrated more easily with available data (which includes weight classes but excludes specific body weights). We achieve diversity accros sex and body weight classes using proportionality factors of 45, 48, 69 and 75 for heavyweight males, lightweight males, heavyweight females, and lightweight females, respectively.  

The P/AR metric can also be used to create all-rounders competitions. To achieve this, one simply aggregates for each participant the P/AR scores achieved for the various events. For instance, see here for the 2022/23 BikeErg all-rounders P/AR competition.