Even more things considered - on the water performance – extended version

Michael P.C. Watts
Impattern Solutions
2015 Masters Nationals in Camden NJ looking towards Philadelphia                                                                           Head of the Charles                                      
Seeing that age, weight and gender handicaps seem to work well on erg performance results, how about on the water performance?  I analyzed the winning times
over 1k at Masters Nationals, and the Masters events over 4.8k at HOCR for all boat classes, and for both male and female. Much to my surprise,  the decline in
performance with ages match and are comparable to the us rowing handicaps, also the effect of boat classes match, independent of gender and race length, to within
+- 5 secs per K.

Erg tests are much more controlled that rowing, which is why coaches like them – other than satisfying their sadistic streak.  The difficulties of on the water
comparisons include; water and wind conditions, quality of the competition, and an absence of detailed athlete data with regatta results.

Given that we are stupidly competitive (so says my wife), one place to start is the winning times at the 200 + races that are held at US Masters Nationals Regatta. As I
noted earlier, on-water performance has plenty of sources of variation, beyond the natural variation of individual performance. To find the signal in this noise, we
need a large number of independent samples. By selecting winning times of a large number of events, I have a sample of the performance of a consistently highly
motivated, skilled and trained population.

By pooling results for all boat classes, the variability of a single race can be minimized. At Masters Nationals, there are 13 boat classes including; 8+, 4+, 4-, 4x, 2-, 2x,
1x, heavy and light weights, open and club events. Each event typically includes at least 6 age classes.  The order of racing is effectively randomized over 4 days,
and at Camden in 2015 we had consistent conditions over all 4 days.

The raw data for winning men’s times are shown below.


Figure 2 Raw data of winning times from US Masters Regatta 2015 in Camden for men’s all age classes and events. Eights and quads have the fastest times, singles
and pairs the slowest. The general trend of slowing with age, and increased variation with age can be seen.

We know that the different boat types have different speeds, eights faster than fours then pairs, and quads faster than doubles then singles. Statistically these are
known as “blocks”. This is a classic blocked Analysis of Variance analysis problem. Each boat class is averaged across all ages, and each age class averaged across
all boats and subtracted from the average of all data. The result are boat and age class offsets from the average.  The "residual" error is what is left after removal of
average, boat class offset and age class offset.  The uncertainty of each offset can be estimated from the residual error and the number of samples in each offset.

Figure 3 Residual data of winning times from US Masters Regatta 2015 in Camden for men’s events  all age classes and events. The increased variation with age can
be seen. Residual variation is +-10 secs 1 sigma.

The residuals are shown in Figure 3. The variation is noticeably larger for the older age classes, where  the small boats are noticeably slower.

I analyzed the results for male and female separately; and it turns out that the age and boat class offsets match suggesting that this is a robust analysis process. I
then applied the same analysis to 2016 HOCR  4.8k results using the 1k pace for 8+, 4+, 2x and 1x for 4 and age classes 40, 50, 60 and 70. Much to my surprise the
age and boat class offsets also match up also for both male and female.


Figure 4 Age offsets for male and female groups, for National Masters 2015 over 1k, and HOCR 2016 over 5k. All boat types were pooled. There were outliers from
the +- 5 sec (roughly 80% confidence) trend line for over 60 year old women possibly due to light weights and fewer entries.

I added a nominal +- 5 second (80% confidence) trend line through the data to assist in visualizing the trends. The age offsets for the different data sets fit within the
trend line, confirming the  statistical reliability of the underlying trends. There were outliers from the +- 5 sec trend line for over 60 women. As I noted in my erg study,
at Texas Rowing Center we have a number of over 60 women who would meet the cox weight limit and compete successfully in open events. My guess is that this,
and fewer entries, is the underlying reason for the outliers. As noted above, the data for men's small boats for the over 60's are also  notably slower, but when they
were analyzed separately only the over 65 age offset appeared outside the trend line.

The US rowing handicap for 4+ is shown above, and just clips the +- 5 sec trend line. If anything, it is too generous to the 43, 50 and 55 (C, D & E) age classes by
about 5 seconds. By personal experience, these groups are the most competitive in Masters racing. My guess is that this is because the over 40 ex-elites struggle to
beat out the youngsters for seats in the open events and so they reluctantly turn up to Masters. After 60, the perils of old age take over.

A 20 secs offset from 60-70 with a nominal 235 sec pace for age 60 corresponds to 0.8% decline per year from 60-70.

The boat class offsets are shown in Fig 5 ordered nominally from fastest to slowest, showing the offsets generally following the assumption that bigger boats are
faster than small, sculls faster than sweeps.

There is a notable match between 8+, 4+, and 1x offsets for men and women, and over 1k and 5k. I included a trend line with +- 5 secs uncertainty limits (roughly 80%
confidence) to help visualize the uncertainty in the data. The outliers for double scull (2x) at HOCR probably reflect the limited entries for the 2x in the older age
categories with the top scullers entering 1x. The trend line through the H2x 1k data, is consistent with  the fact that 2x and 4+ have the same handicap in the US
rowing handicap table.

Figure 5 Boat (8+, 2x, 4+, 1x) class offsets for male and female groups at National Masters 2015 over 1k, and HOCR 2016 over 5k. All age classes were pooled. The
trend line was added to illustrate the uncertainty in offsets  +- 5 sec (roughly 80% confidence).  The HOCR 2x results are outliers.  

A few more notable observations from these data include;

1) The boat class offsets from 8+ to 1x match, independent of event distance and gender = 39 secs +-4

2) The light weight events were mostly slower than heavy weight on the average by 6 secs consistent with weight correction factors.

3) The coxless events were notably slower than expected (H4-  slower than H4+ and H2-  slower than 1x), presumably a result of the far fewer entries in these
technically challenging events.

In addition, the differences between the data sets are instructive;  

Ratio of Male to female pace is consistent = 0.884 +-0.001

Average 5k pace for HOCR, an international competition, compared to 1k pace for National masters = 20.5 secs +- 1