BUDD handicap system
A level playing field for indoor rowing endurance events
Vianney Koelman
Dutch Eindhoven Rowing Association Beatrix
Competitive indoor rowing typically relies on separating the field of participants into classes for age, bodyweight and gender. This, however, causes considerable fragmentation of indoor rowing competitions. It is not uncommon for these competitions to take the shape of a myriad of separate events in many of which no more than a few athletes compete.
Can we avoid this fragmentation and still be inclusive towards aging athletes and female athletes? The answer is yes. We can fully eliminate any fragmentation while allowing for a fair comparison between male and female athletes of widely different ages. This can be realized by implementing a suitable handicap system that allows competitive events to take the shape of an inclusive-to-all and easy-to-implement single mass event.
Here we focus on long-distance indoor rowing events. Trigger for the development of the current handicap system was the desire to create a single ranking for the annual BUDD (Beatrix Ultra Distance Day) event in which male and female athletes of widely different ages compete on the indoor rower in either a half- or a full-marathon. The whole system relies on the analysis of indoor rowing power data for distinct percentile scores. The percentile scores considered range from the threshold power for top-1% results to the threshold power to make it into the top-6%. Building the whole analysis on percentiles rather than on absolute top scores per age category significantly suppresses noise in the data and - more importantly - strongly reduces over-compensation due to limited competition in specific gender and age categories.
The issue of noise being particularly strong towards the absolute top performances (in the tail of the distribution) is evident from the percentile data (obtained from the Concept2 global database of RowErg verified results) for the half marathon distance (see above figure). Clearly, the 1- and 2-percentile powers show considerably more scatter than the 5- and 6-percentile powers.
The systemic over-compensation for age and gender categories with limited numbers of participants is related to the fact that top scores can be classified as zero-percentile scores only in the limit of very large sample sizes. At the other extreme, for a sample size of N=1, the top score (which also qualifies as the bottom score) should be classified not as te zero-percentile, but as the 50-percentile score. For any finite sample size N, the top score equates to the 50/N-percentile, which ranges from anywhere between 0% (N very large) to 50% (N=1). This means that by calibrating the compensation algorithm to top scores only, one is mixing zero-percentile figures (for age and gender categories with lots of participants) with figures up to 50-percentile (for age and gender categories with few participants).
Sticking to percentile powers, first we investigate their dependency on body weight. The figure above shows for heavyweight and lightweight men the power required to reach top-1% performance. While the top-1% heavyweights overpower the top -1% lightweights by more than 20% on a 500m sprint, this figure reduces drastically for longer events. Parity between the weight classes is achieved for the marathon distance (on which heavyweights outperform lightweights by an insignificant 0.4%). The conclusion to be drawn from this is that for endurance events (half marathon and full marathon distances) body weight compensation would be inappropriate. In the following we therefore focus on an algorithm that realizes age and gender compensation.
Skipping all theory aspects, we jump straight to the resulting correction formula for the power achieved over half-marathon and full-marathon races. This takes the shape:
Here P
To check how well this correction algorithm succeeds in creating a level playing field for long-distance events, we apply it to the male and female top-percentile (1% - 6%) scores on the half marathon and the full marathon distances. The results are shown in below charts.
Comparing these charts to uncorrected carts (like the first chart in this blog post), it is clear that (despite the noise clearly present in these carts particularly for the 1% and 2% scores) a level playing field over sexes and ages is indeed created. However, an obvious feature in all four Pcorr plots above is a performance boost apparent for athletes in their twenties. This behavior is not induced by the correction algorithm (that does not apply any significant age correction for ages below ~35). The higher power scores for athletes in their twenties is plausibly explained by a significantly stronger competition at the top-levels in this age bracket due to the presence of collegiate rowers. To check in more detail for any age-related bias in the corrected power, a scatter plot of the Pcorr data averaged over the 4-, 5- and 6-percentiles, and averaged over male and female results, as well as over both distances (HM and FM) is shown below.
The increased performance for athletes in their 20's can now be located more precisely as an increase for athletes in the early 20's. Around age 70 also a slight upshoot is visible. This is likely related to the scatter in the data. In any case, reducing this upshoot by modifying the above equation would likely cause a downshoot in Pcorr for athletes in their mid-70's.
To check in more detail how well this integrated correction algorithm succeeds in creating a level playing field for long-distance events, we treat the half marathon and the full marathon results for the season 2022/23 as a competition and out of the 4348 results we determine the top 0-40 in terms of Pcorr. The resulting ranking is shown below. Note that distinct genders are color coded, and so are the distinct weight classes, distinct race distances, and distinct age ranges (0-39, 40-59, and 60+). We check for all of these classes if the frequency of occurrences over these classes in the top-40 is according to expectation.
Firstly, the 4348 results constitute 3652 males and 696 females. Hence, a gender-unbiased top-40 would translate into 33-34 males and 6-7 females. We observe 33 males and 7 females in the top-40, thereby confirming a lack of gender bias. Similarly, for the weight classes we have in the total population 3556 heavyweights and 792 lightweights. For the top-40 this translates into 33 heavyweights and 7 lightweights. We observe 34 heavyweights and 6 lightweights, thereby confirming (despite the absence of a bodyweight correction) a lack of bias also for the weight classes. Considering the two distances, we have 3426 participants to the half marathon, and 922 participants to the full marathon. A lack of bias over the two distances in the top-40 translates into 31-32 half-marathon results and 8-9 full marathon results. We observe 30 and 10, again closely in line with expectations. Finally, concerning the three age categories, we have 1183 participants aged 0-39, 2523 participants aged 40-59, and 642 participants aged 60+. Based on these figures one would expect in the top-40 the distribution 11-23-6 over these age groups. We observe the distribution 14-20-6. We attribute the slight apparent bias towards the youngest ages to the more fierce competition amongst rowers in the prime of their physical capabilities (as discussed above).
A last point: organisers of endurance erg events can use the above methodology to create a level playing field for a single mass event across genders, ages and distances (half- and full-marathons). If required, the corrected power can be translated back into corrected duration using the standard power-to-speed equation: P = c (d / t)^3, where d is distance (in m), t is time (in seconds), P is power (in Watts), and c is fixed at 2.8 kg/m.
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