Wednesday, March 16, 2011

The Power of Mathematics

Life is the art of drawing sufficient conclusions from insufficient premises. –Samuel Butler

At one point in my life I thought I might want to be an actuary. I am a firm believer that mathematics can be used to explain (and predict) events. Take for instance the heart rate as it correlates to fitness and ultimately race performance.

Theoretically one could collect enough data in order to accurately predict a marathon time. Gather a history of the following training data: pace, course conditions (hills, wind, surface), distance, human conditions (health, fatigue, diet, weight, hydration, sleep, resting heart rate, running heart rate). Develop an equation or some artificial intelligence algorithms based on those factors, and then predict your race given the environment.

One key is to note that most models do much better "interpolating" results as opposed to "extrapolating" results. In other words, if all of the data input distances range between 6 miles and 13 miles then my model will best estimate times between those distances. If I use the model to predict a 20 mile race then I am extrapolating and it's likely to be less accurate. This applies not only to distance but also to heart rate and every other factor for that matter.

There's the rub. Since we so seldom work out at race pace, and never for race pace at race distances, the model will almost always be forced to extrapolate. Of course there are elegant mathematical methods to reduce this limitation, but they can only be so good. I think perhaps the biggest flaw in this approach is probably the general lack of data. If you ran every day for 100 years you probably wouldn't generate enough data to generate a comprehensive set that produced high r squared values. Which brings us to Mr. Butler's quote above. We all go through life making decisions aimed at returning the highest payout (however you choose to measure "payout"), with data sets far too small to be able to know definitively that our choice is correct. In short, we take risks based on our best knowledge. It's the same thing with our race predictions -- I'm going to pick a race goal pace at the beginning of the OKC marathon and hope I can hold on to it for 26 miles. It's risky, and I've almost always crashed in marathons, but I'm hoping this one will be different.

Of all those factors I mentioned above I tend to believe that the heart rate (both resting and running) is the most significant variable that drives predicted performance. To that extent I'm fairly happy with results like I recorded today.

8.29 miles, 1:04:48, 7:48 pace, 130 HR avg


Anonymous said...

pretty good post. I lawful stumbled upon your blog and wanted to command that I get really enjoyed reading your blog posts. Any condition I’ ll be subscribing to your maintain and I hope you despatch again soon christian louboutin platforms.

in America said...

very nice blog...thanks

Serta Mattress said...

thanks for share

sofia123 said...

This is most interesting blog.I like it very much.Keep doing the same.I know some information about HIV which we should always be aware of.

Anonymous said...

Great blog really enjoyed reading it. Have bookmarked you and will check back regular. Please feel free to take a look at my blog...
Cheap Flights to Nairobi
Flights to Nairobi
Nairobi Flights

Anonymous said...

It could possibly be

Hogan Shoes Sale the fact that store nonetheless retains some using the options which have previously gone away from market styles and however the excellence using the products
could induce one to< align="left">Belstaff Mens Bags purchase them. inside the carry out it will not glance remarkable in your circumstance placing on some outdate albeit expensive garments

honeymoon packages maldives said...

Many thanks for such a write-up. I undoubtedly cherished reading it and talk about this it to my friends.

mjshdiif said...

.Christian Louboutin: I love it here! I've got about four days; I will be here through the weekend. I'm going to go to LACMA, to some antique stores on La Brea, to see my friend Mikal, a young European pop star who is recording here.Christian Louboutin Outlet I also love the Pasadena Rose Bowl. Then I go to New York, then Brazil the next day. Sometimes I don't know what city I'm in. But I have many friends here, and I have

holars have long argued against such a broad interpretation of aesthetic functionality. Thomas McCarthy, author of the leading treatise on trademark law, contends that "[t]he notion of 'aesthetic functionality' is anChristian Louboutin Flats unwarranted and illogical expansion of the functionality policy, carrying it far outside the utilitarian rationale that created the policy." Others note that it is contradictory to de

ux de tous, Christian Louboutin s'est montré particulièrement décontracté avec celle qui a pour habitude de dévaliser ses boutiques à chacun de ses passages.Mais n'allez pas croire que le prestigieux chausseur se comporte ainsi avec toutes ses clientes... Pas du tout ! Vu hier en compagnie de Zahia lors d'une soirée célébrant une nouvelle fois sa marque et ses créations, le chausseur des

out of the time, had no choice but to follow study ignore the whole unit of projection in the US view.I seem to have been able to hear her shoulder joint minor noise.We finally arrived at the hospital the garden, sheChristian Louboutin Daffodil sat impassively in parterre edge, then hold your knees, stuffy asked me:" give me a cigarette, okay?"I point a, into her mouth. She is like a drug addict, unable to hold oneself back

termpaperwriter review said...

thanks a lot for the post! very interesting!

masterpapers review said...

Nice effort, very informative, this will help me to complete my task. Thanks for share it keep it up.

custom term papers said...

What a great post! thank you for sharing! i liked it very much)

watch free movies said...

Wonderful blog. Thanks for sharing. Keep posting please.

jiulin said...

.frequent grew for acquiring a strike with grownup males and Onitsuka Tiger Online Store females instantaneously receiving a last final accomplish result of really effective advertising and advertising campaigns undertaken by grownup males and females referred to as Weyden and Kennedy.Hogan Men shoes Of course, this assortment of shoes was named swiftly good ideal after the well-known basketball participant Michael Hogan Men shoes Jordan and was bound to turn in to some strike inside the really bare lowest among the basketball fans, initially. The Jordan sequence of shoes has also been produced for women, which look about in actuality captivating designs. Franklin & Marshall The shoes are obtainable in an exceptionally amount of colors; blue, white, red, black, pink, green, etc. in actuality sporty,Abercrombie Fitch store they get ladies dressed up for that superb game. In add-on they look about in female sizes to fixture the two the tiny footed along utilizing the huge footed.

hotels in pachmarhi said...

Thanks for wonderful article post. One of the best blog post I read in recent past. This post have great content. I can stand up and say superb!

jerseys cheap said...

Hello! I simply would really like to present large thumbs up for the nice information you’ve got here on this post. i’ll be coming to your journal for a lot of before long
cheap nfl jerseys
cheap mlb jerseys

Search Engine Marketing Company in india said...

good job, the squash looks grand
Search Engine Optimization Company in india
Digital Marketing Company in india
Social Media Optimization Company in india
top web design companies
website design company
best website design companies
Website Design Companies
web development company india
web design company india

Anonymous said...

I really like your blog it's really nice.

Search Engine Marketing Company in india
Search Engine Optimization Company in india
Digital Marketing Company in india
Social Media Optimization Company in india
top web design companies
website design company
best website design companies
Website Design Companies
web development company india
web design company india

Anonymous said...

I really like your blog it's really nice.

best deals
travel deals
Cheap Deals
laptop deals
tv deals
online deals
best buy deals
great deals
camera deals