Pace Curves

[PaulG]

When I first started to erg seriously about nine months ago one of my goals was to become equally proficient at all distances between 500 m and 10000 m. I also wanted some way to estimate the proper pace so I wouldn’t either fly and die, or just go to slow. I wasn’t sure how to measure either of these, but it quickly became apparent that where you stood in the on line rankings was primarily a function of how many people submitted times and how fast, or slow, some of these people were. So instead I thought to compare the paces for my PBs at various distances to the world record paces for heavyweight men in my age group (50-59). The shape of the curve for pace vs. distance for the world record holders (WR) would be considered the ideal curve that I could compare my curve to. In addition, the formula for my curve could be used to predict a proper pace for a PB at any distance, sort of a personal “Paul’s Law”. I have used my PBs not because they represent anything special, but because they are the data I have. At the bottom of this post is a comparison between my pace vs. distance curve and that of the world record holders.

The first thing that is apparent is that I am no threat to set any world records. The r square for both curves is aove 0.9 which indicates the equations describe the data vey well. Closer examination of the curves indicates that my curve (that’s the upper one) has a steeper slope than world record holders (lower). The equation of line reflects this where my coefficient (8.45) is higherv than the WRH (7.45). This means either I am a natural sprinter, or I need more distance work. I suspect the latter. Also my pace for 5000 m is above the curve which indicates that I probably can do better. Solving the equation for 5000 m indicates that the pace I should aim for is at most (slowest) 1:58/500 m. Now this is slightly misleading because the curve may not reflect my current state of conditioning because it is influenced by PBs that may have been set months ago. Therefore any paces calculated from the curve should be considered the slowest paces you should aim for. If I want to set a PB in the 6000 m I should aim for a pace no slower than 1:59.6. The pace for 10000 m is below the line and was my most recent PB and probably better reflects my current state of conditioning.

Taking a look at the WR curve and it is apparent to me that the current 10,000 m record is a tremendous achievement. Torre Foss set this record in 2003 at a pace of 1:40.6, which is only slightly slower than my PB of 1:38.1 in the 500 m! Clearly this gentleman is the descendent of the folks who rowed across the North Atlantic. Also it appears that the record for 6000 m may be a little soft because it is above the line. Any ergo-hero that can row a pace of 1:39.7 for 6000 m will set a world record. In fact, Mr. Foss may have set world records in the 6000 m and the 30 minute row along the way to his 10,000 m record.

I think the approach of graphing pace vs. distance and comparing it to WR pace curve is useful for novice ergers like myself. You could do it on a percentage basis but you would get a flat line that is not as much fun to look at. Plotting the your personal and WR pace curves allows you to see what distances you are weak in, lets you know if you should work on power or endurance, provides an estimate of the slowest pace you should use for a PB, and makes you very humble.

Sorry for the long post and I hope this has not been discussed before. I had fun playing with curves.



EDIT: Sorry folks I can't seem to post the image of the curves. What am i doing wrong?

[schweinlew]

Paul

What a cool idea for a diagnostic tool! I've been playing with the idea of mining the C2 ranking data, but I think your idea is better than any I've thought up so far. Do you think that we might apply a growth curve multilevel model to the rankings data in order to build on your idea? Heck, we might be able to publish it!

(Thank you for the reference to R-square on this forum! Made my night.)


Will Schweinle
Assistant Professor of Biostatistics
Health Sciences, University of South Dakota

[Citroen]

EDIT: Sorry folks I can't seem to post the image of the curves. What am i doing wrong?

The img tag only works when the URL ends in .GIF, .PNG or .JPG

Code: Select all

[img]http://lh6.ggpht.com/paulg9443/SQDzeKWNcUI/AAAAAAAAAGA/Ki2AhqBiNsc/s800/pace%20vs%20D.jpg[/img]

[PaulG]

Thank you Citroen.

Paul

[tdekoekkoek]

Taking a look at the WR curve and it is apparent to me that the current 10,000 m record is a tremendous achievement. Torre Foss set this record in 2003 at a pace of 1:40.6, which is only slightly slower than my PB of 1:38.1 in the 500 m! Clearly this gentleman is the descendent of the folks who rowed across the North Atlantic. Also it appears that the record for 6000 m may be a little soft because it is above the line. Any ergo-hero that can row a pace of 1:39.7 for 6000 m will set a world record. In fact, Mr. Foss may have set world records in the 6000 m and the 30 minute row along the way to his 10,000 m record.

Neat idea. Just wanted to point out however that the world record on Concept2 for 10K was set in 2001 and is 31:36.5 for an amazing pace of 1:34.4. Also the WR for 6K is 18:54 which oddly enough is 1:34.5.

There are quite a number of people who row under 1:40 for 6K. In fact I think pretty much all elite heavy weights even trying to get on the team would be in that category.

[Snail Space]

Paul

Could you plot "Split pace" vs "Log Distance"? It should be a straight line.

Mine is like this: [my 1000m time is the rogue reading - must try harder ]

[PaulG]

Paul

Could you plot "Split pace" vs "Log Distance"? It should be a straight line.

Mine is like this: [my 1000m time is the rogue reading - must try harder ]

Snail: I thought of that but I find the curve more visually pleasing and I find it easier to deal with the original units. The point is the same: Any outliers represent either a very good effort (below the line) or where you can improve (above the line).

Paul

[PaulG]

Trevor:

I was limiting the WR curve to the 50-59 age group that I belong to because I suspect the pace curves may look different for younger age groups. It would be interesting to look at and I think they may show a greater slope.

Paul

[bloomp]

heh, my 1k is also an anomaly... but everything else seemed to fit together... even my year old 2k time worked in well (which doesnt make sense seeing my 5k splits)

but to the point of WR 6k's, i know that PennAC requires a 19:40 6k which is a ridiculously fast split of 1:38.3, nothing i'll achieve without a few more inches and pounds

anyhow, i love this curve idea, gotta get back to erging now that i'm not sick anymore!

[M. Podolsky]

I find the online rankings are great for helping me figure out a target pace for a given distance. I don't care so much about the overall ranking - instead I find someone who has scored close to me in a couple of distances, and look at their pace in the chosen test. I use the country filter, so the names have become familiar. After a few months I know who will be faster than me, and who will be slower. In almost all cases your body type and VO2Max will impose a limit on your erg times, so any formula or curve that doesn't take these into account will be less useful than finding someone with a similar physiology who has been there already.

I think it's a good idea to try the test distances at least once a month. It doesn't take too many iterations to find your current best pace for any distance. Once I set a season best, I increase the target pace by very small amounts - unless I notice someone in the online rankings who posts similar times for other distances but is way ahead on the target row.

I'm definitely a "poke it and see what happens" person, but I've worked with enough "let's think about this so we know what to expect" people that I can see the value of both approaches. So I like these graphs - even though I find the online rankings a little more useful.

[PaulG]

Another thought on the pace curves is that they can be used to identify the best overall erger over a defined range of distances. The difference between your pace curve and the WR pace curve for an age group may be considered an index of your overall ability. For example, if you are the world record holder in all distances between 500 m and 10000 m there is no difference between the curves and you are the best. The differences between the curves can be calculated either through the calculus by subtracting the areas under the curves, possibly through statistic analysis using an analysis of covariance approach, or modifying Mr. Snail’s approach and turning the curve into a straight line and algebraically subtracting the lines. Someone more clever than me could set up a website where you: (1) enter either your times or pace (splits if you come from track background) for various distances, (2) your pace curve is calculated, and (3) the current WR pace curve for your age group is subtracted. The smallest difference wins.

[johnlvs2run]

This is all set up for you in the new Perathlon.

[pmacaula]

Paul - very cool & as you say, humbling.

Not sure how much more or less informative it is to use Average Watts (instead of s/500m), but did the same graph using both sets of units.
Watts are even more humbling.

For me, Pace (s/500m) ranges from 13% to 23% above the WR (40-49 MH). Using Avg Power, the gap is between 31.8% and 46%.

Cheers. Patrick.

[PaulG]

instead I find someone who has scored close to me in a couple of distances, and look at their pace in the chosen test. I use the country filter, so the names have become familiar. After a few months I know who will be faster than me, and who will be slower.

I think it's a good idea to try the test distances at least once a month.

I'm definitely a "poke it and see what happens" person, but I've worked with enough "let's think about this so we know what to expect" people that I can see the value of both approaches. So I like these graphs - even though I find the online rankings a little more useful.

Despite my penchant for curves, poke and see what happens is exactly what I am going to do this weekend. My PB for the 1K is right on the curve so there is little use in calculalting a new pace. Instead I will look at someone ahead of me in the rankings and see if I can better the pace. Using pace curves to estimate PB paces works best when you are in a period of improvement in your training and the points are off the curve.

[Godfried]

I keep my graph simple, see a selection of male heavy 40 49 with all distances