Paul's Law vs. actual results

[dschwick]

I decided to graph my best times against the values predicted by Paul's Law to see where my weaknesses are. I found it interesting that some of my best times in terms of online ranking percentile are my worst times according to Paul's Law and my best time according to Paul's Law is my worst in terms of online ranking. Not quite sure why, but it's food for thought.

It's a neat graph. It would be great if you could automatically generate one of these from your logbook here.

http://danwork.blogspot.com/p/pauls-law.html

[djh]

I've done similar work. Here are some things I do differently:

Try using a log scale on the x-axis with doubling between labels i.e. 500, 1000, 2000, 4000 etc. (You can do this in Excel.) No, you won't get a straight line due to the shorter distances benefiting more from anaerobic respiration (and subsequent crash) but I still prefer that layout. Also, you can format the y-axis in Excel as m:ss which looks nicer in my opinion.

I agree that the Concept2 percentiles have too much bad data in them to be very useful. Try instead basing your stats on your http://nonathlon.com/ scores.

Paul's Law is an approximation and doesn't scale perfectly. I've also heard "Double the D, add 3." My personal regression-based "law" is 3.8 this year, but it shifts every time I have a new best time.

If you include a regression-based trend line in your graph you can easily see which event needs to be worked on because it will be highest above the line. My regression ignores 500 meters (too fast), 4 minutes (too similar to 1,000 meters) and anything longer than one-hour (too slow).

Nice if this could be done automatically, but I've customized my analysis so much over time that it could never become a standard canned product.

[Carl Watts]

Depends on you level of fitness as to how well it lines up.

You will notice that your results can be a seesaw either side of the 2K. Some people have a great 500m but there 5K is rubbish and some people have a great 5K but no power to produce a great 500m. Once you finally improve your weaker side the "Double the distance and add 3sec to your average pace" works pretty well.

[gregsmith01748]

I tend to grade myself against the online rankings, rather than Paul's Law. I do use Paul's Law when I am trying interpolate between two distances that I have done. For example, if my 2k and 10k PBs are more recent and I want to set a target for a 5 or 6k, I use Paul's Law from each direction to estimate what to shoot for.

[dschwick]

Thanks for the pointer to nonathlon, What a neat idea. I went ahead and signed up so now I have an incentive to do a full marathon BEFORE the global marathon challenge rolls around.

I took the suggestions about the labels and the logarithmic distance scale and wrote some javascript to generate a graph based on your "Ranked Workouts":
http://dl.dropbox.com/u/39744416/Concep ... gbook.html

Would this be a welcome addition to the site? I'd be willing to contribute my code if so. I'd like to add a "best fit" regression line as soon as I figure out how to do the math involved. It would be easy to make this graph optional and show only when you click a "Graph" button. Thoughts?

[Bill]

Hello,

I liked the graph.

Is that 10 minutes worth of time or 10 hours or 10 days to write something like that ?

Am keen to learn how to do that sort of thing.

Bill

[dschwick]

It took me more like 10 hours. The steps involved were:
*Parse the table data from the logbook, convert times to milliseconds since that's the easiest way to convert it to a date/time and do math based on the value.
*Figure out how to do the math for Paul's law with only a natural log function. I knew I'd eventually use those college math classes for something!
*Find the best/worst times based on Paul's law for 500m.
*Graph the data. It took me a while to find a free/open source graph API that gracefully handles dates. I tried Google's chart API first, ended up using Flot (http://code.google.com/p/flot/).
*Add mouse-over effects that show the exact time and tweak the distance scale for maximum readability for any possible Ranking page.

You can see all the code here http://dl.dropbox.com/u/39744416/Concep ... c2graph.js. The Concept2 folks are welcome to add this to their site if they'd like. Otherwise, this code can be be converted to a Chrome Extension or a Greasemonkey (Firefox) script without too much work so you can at least see it on your own Ranking page.

To keep all this related to training, I used the graph to predict my 6k time for the Nonathlon. I didn't quite make my goal pace but I still put up a good time so I was happy. A neat thing about this graph is that it motivates you to hit a PR not just for the given distance that you're rowing but for all distances by hitting a new "best" on Paul's Law.

[slwiser]

Nice work..maybe they will put that up.

[djh]

http://dl.dropbox.com/u/39744416/Concep ... gbook.html

Would this be a welcome addition to the site? I'd be willing to contribute my code if so. I'd like to add a "best fit" regression line as soon as I figure out how to do the math involved. It would be easy to make this graph optional and show only when you click a "Graph" button. Thoughts?

I think what you did is really good. I'd love it if this was built into the Concept2 log book.

[mikedepetris]

Is it still possible to draw the interpolation graph from erg results? I'm testing myself over all distances up to 60 minutes and it seems I have some values far from the predicted/golden curve, so I'm not sure what should I adjust in my training or in the calculations.

[Bob S.]

Is it still possible to draw the interpolation graph from erg results? I'm testing myself over all distances up to 60 minutes and it seems I have some values far from the predicted/golden curve, so I'm not sure what should I adjust in my training or in the calculations.

It wasn't intended as a predictor. It's intent was to give you an idea of what your strength/endurance balance is. If your long rows are faster than what the law would say but the short rows are slower, then you endurance is better than your strength - and vice versa.

Of course it is often used for prediction and works for a few people who happen to have the right balance. Interpolation, of course, is far better than extrapolation, which is the basis of the prediction applications of the so-called Law.

Bob S.

[teddyDK]

What about using this

http://www.ergrowing.com/2k-erg-power-p ... alculator/

http://www.machars.net/

[mikedepetris]

I am sorry my question was not so clear, I tested myself over all distances:
100m 1' 500m 1k 4' 2k 5k 6k 30' 10k 60'
will soon try the HM.

I want to graph the results and compare with the "golden curve" or other kind of calculations, it seems to me simple to do in Excel, what would you suggest?

The suggested .js does not work on my system, and the other sites only use 4 or 5 points, that are too few for a good approximation.