Typical differences in split times at different distances

[AndyWicks]

I think there is so many variables. I struggle to get my SPM up and therefore will be limited and struggle with the shorter stuff, but maybe find mid distance a bit easier.

I don’t think there are any calcs that will give you perfect answers but are great to use as a rule of thumb.

When I do intervals (and I learnt this from running) always go 3-5% faster than what the effort should be so if I’m doing a 5k effort, my PB is at 1:41-2/500, I do the 5k intervals at 1:40s. Push harder on the intervals and go easier on the recoveries!

[frankencrank]

Go to the rankings page and do a search looking at what others are doing. You can see the difference between the 50th percentile and see the change. This should give you a good sense of what to expect. I saw an approximate 10 sec pace difference in the 30-39 group between 500 and 1000.

[Nomath]

The 50th percentile split times (or any other percentile point) are results from different rowers. The topic starter looks for formulas that apply to one individual on different distances. Some time ago I analysed the performance (i.e. split times) of individuals on different distances in the C2 rankings. They are best described by power laws.

[frankencrank]

The 50th percentile split times (or any other percentile point) are results from different rowers. The topic starter looks for formulas that apply to one individual on different distances. Some time ago I analysed the performance (i.e. split times) of individuals on different distances in the C2 rankings. They are best described by power laws.

That is interesting. I am surprised that it is so simple when there are two non-linear issues involved. Muscle capability will drop off non-linearly and speed for any wattage varies non-linearly. My guess is those who are still improving will drop off differently than those who are in maintenance mode (elites).

[Nomath]

Power laws are non-linear.
If you read my comment in the first entry, you will see that the exponent is indeed different for elite competitors. For example, the split times at the world championship races in speed skating on ice have a much lower exponent than the 500m pace in the C2 rankings for rowers.

You have also to keep in mind that one single parameter (the 'exponent) cannot pinpoint an accurate time. In any race there are a lot of factors that matter, such as weather, competition and psychology.

[frankencrank]

Power laws are non-linear.
If you read my comment in the first entry, you will see that the exponent is indeed different for elite competitors. For example, the split times at the world championship races in speed skating on ice have a much lower exponent than the 500m pace in the C2 rankings for rowers.

Cool

[ArmandoChavezUNC]

I think Paul's Law is an incredibly imprecise model. It gets misused through no fault of his own but I cringe any time I see people using it or recommending it to others. It is flat out bad, even if it's "correct" for some people over some distances (any model will do that with a large enough sample size).

For one, it uses splits instead of watts. Splits are non-linear with watts. Strike one. And a really basic mistake. There's many other reasons it's a terrible model, but this one alone should make anyone wonder why the heck it's so common and used so much (by the way, it's not used at "high" level rowing).

I think the most useful tool for elites is Jensen's Model, which uses watts and is tailored for athletes with incredible aerobic bases. It also uses the 2k as its base, which is what any model should use given this is the most widely tested distance and most representative of any serious rower's fitness. It over-estimates the longer distances but isn't too far off. See below:

10 second all out average power watts be 173% of the 2k average watts.
60 seconds all out watts be 153% of the 2k average watts.
6k watts be 85% of 2k average power watts.
60 minute ‘hour of power’ average power watts be 76% of 2k average power watts.

Now, if you're not an elite rower, your curve is going to look much different, but this can still be used as a guideline and a way to see where you're relatively strong and relatively weak. IMO, anyone who isn't a fairly highly trained athlete is going to massively underperform at longer distances. There's a lot of good 500m/1k/2k ergers who rely on their size to post amazing times but have really bad aerobic engines. This doesn't work in actual rowing.

[Nomath]

....Splits are non-linear with watts. Strike one. And a really basic mistake. There's many other reasons it's a terrible model, but this one alone should make anyone wonder why the heck it's so common and used so much (by the way, it's not used at "high" level rowing).

I think the most useful tool for elites is Jensen's Model, which uses watts and is tailored for athletes with incredible aerobic bases. It also uses the 2k as its base, which is what any model should use given this is the most widely tested distance and most representative of any serious rower's fitness. It over-estimates the longer distances but isn't too far off. See below:

10 second all out average power watts be 173% of the 2k average watts.
60 seconds all out watts be 153% of the 2k average watts.
6k watts be 85% of 2k average power watts.
60 minute ‘hour of power’ average power watts be 76% of 2k average power watts.
.....

Evidence?

I searched the internet for Jensen's Model. I could only find curves and a Power Profile Calculator, but no precise formula. I could not see a way how to predict the times for, say, 500 m, 1000m, 5K and 10K given the 2K time (or watts) using that calculator. Jensen's Model may be fine as an abstract concept, it is nearly useless for the issue discussed here : predict split times at different distances.
The Power-Law and even Paul's Law are much more helpful for this purpose.

Playing for some time with the Jensen numbers, I got a graph that probably shows the gist of the Jensen Model. I plotted the inverse of Power versus the logarithm of time for the 5 points in the Jensen Model (10 sec, 60 sec, 2K, 6K, 3600 sec) for a range of 2K times, and got a set of congruent curves.



It takes some mathematical juggling to combine these different curves into a single formula. I will not detail that formula here, but it reproduces the Jensen points accurately. Still it does not help a lot in predicting times for the common distances 500m, 5K and 10K given the time for 2K. To predict those times requires an awkward iterative process that is far beyond the time and ability of most.

Regarding your criticism that splits are non-linear with watts: that is obvious, because watts ares proportional to 1/splits³. But the point is: does that make splits less suitable for making predictions ? In the Power Law it doesn't matter whether you use splits or watts. The Power Law uses logarithmic linearities. The percentual change in watts with distance is three times bigger then the percentual change in splits with distance.

[robbiep]

Have you considered using the Nonathlon site to see what you (theoretically) should be able to 'score' for distances, compared to what your current times and paces are ?

It works by calculating a theoretical best for your age for each distance (it takes data from the C2 site, I believe), and then gives you points based on your percentage of that pace (I've probably really worded that badly)

For example, my current points are :

500m - 1:36.3 - 820 pts
1000m - 3:32.3 - 822 pts
2000m - 7:39.0 - 798 pts
5000m -19:59.3 - 817 pts
6000m -24:36.7 - 805 pts
etc, etc

It than (and this is the clever bit) calculates what time you need to do to increase your points for each distance. For example, my 2k points are low (I did it a while ago, and hate the 2k so haven't done one since to improve), to get 25 pts more (taking it to 823 pts, equivalent to the 500m and 1k set at the Scottish virtual champs), I'd have to do 7:25.4 - but it also means I SHOULD be able to do that.

I've probably explained this all terribly - nonathlon.com is a lot better !

[ArmandoChavezUNC]

Regarding your criticism that splits are non-linear with watts: that is obvious, because watts ares proportional to 1/splits³. But the point is: does that make splits less suitable for making predictions ? In the Power Law it doesn't matter whether you use splits or watts. The Power Law uses logarithmic linearities. The percentual change in watts with distance is three times bigger then the percentual change in splits with distance.

Well, yes. I don't know what the Power Law is, but using raw splits is absolutely less suitable than using raw watts.

Imagine telling someone their 60' should be 12 splits slower than their 2k.

For someone with a 1:28 2k, that's a 1:40 60'. For someone with a 1:50 2k, that's a 2:02 60'. If we convert that to watts that's a 164 watt difference for the faster athlete, but only a 70 watt difference for the slower athlete. It would be ludicrous to suggest using raw splits is a suitable way of making predictions. This illustrates my first (but not the only) problem with Pau's Law or any other model that uses raw splits.

If you're advocating for a model (Power Law) that converts the raw splits logarithmically and somehow adjusts them to where they can be accurately compared then that's a fair way to go about it, but why do that instead of just using watts? Why the extra steps? Watts should be (and are) the gold standard for high level rowing.

[Nomath]

Well, yes. I don't know what the Power Law is, but using raw splits is absolutely less suitable than using raw watts.
...

The Power Law is a simple mathematical expression for how total time depends on distance : t(D)/t(Do) = (D/Do)^x .
t(Do) is the time for a reference distance Do, e.g. 2K. The number x is called the exponent. If x=1, total times would be directly proportional to distance, which evidently they are not. For indoor rowing I found that x is close to 1.08 for individuals doing different distances between 500m and 10K. Hence if t(2K) = 480 sec (8:00), then the predicted time for 5K = 480 x (5000/2000)^1.08 = 1291 sec (21:31).

This relationship has been extensively tested and used in sports like running, cycling, swimming and speed skating on ice. In several of these sports, e.g. running and swimming, measuring power is very difficult. It turns out that the time-distance exponent is very similar for different sports.

Of course, 'distance' is an artificial result in indoor rowing, just as speed, because the erg does not move in reality. It measures power and translates that power into an imagined boat speed via the relationship Power=2.8/(t500/500)³, where t500 is the split time in seconds for 500m. The same applies for the BikeErg and the SkiErg, although the power-to speed conversion formulas may differ. My analysis of the times of individuals listed in the C2 rankings on the BikeErg for 1K to 40K distances yielded an average exponent of 1.06. The SkiErg data of individuals doing distances between 1K and 10K also yielded an average exponent of 1.06.

The Power Law is just a convenient tool for analysing and predicting performance. The word Law may suggest that it has a basis in physics. That is not the case. It is purely empirical!

Often covering a certain distance is taken as doing a number of laps. In indoor rowing the usual lap is 500 meter and the 500m pace is mostly used for comparisons. E.g 2K consists of 4 500m-laps and 5K is 10 laps of 500m. The same Power Law can be used to describe how 500m splits change with distance : split(D)/split(Do) = (D/Do)^y .
Mathematically, y = x-1. So splits increase slowly with distance. In the above example for a 2K in 8:00, hence split = 120 sec, the predicted 5K split will be 120 x (5000/2000)^0.08 = 129 sec.

Discussions often focus on whether you can cover anaerobic and aerobic exercises in one formula. There is evidence from many sports that the exponent for the splits in anaerobic distances is about twice as big as for the aerobic distances, for example y=0.17 for the anaerobic distances in running and y=0.07 for the aerobic distances in running. I haven't done this analysis for rowing data, but would expect roughly the same difference.