I'm designing a new running calculator - help needed from those proficient in math

Just run baby

it is possible but the math is likely a bit beyond you at this point, since there are multiple functions required for a worthwhile fit.

mileage is a fairly nebulous variable. 8'mi < 7' mi < 6'mi

There's no way 55/2:00 = 4:21. I'd say they can't run better than 4:27

Indicator wrote:

There's no way 55/2:00 = 4:21. I'd say they can't run better than 4:27

I definitely agree with his 55/2:00 = 4:21 calculation. My good friend is your average 1 mile/2 mile specialist guy and his PBs set this year are 54/1:58/4:17 and those are practically parallel times with 55/2:00/4:21. He runs around 50-60 miles per week and averages in the 6' mile range per training run

It's impossible to do what you are trying to do.

Pardon me stewardess, I speak math.

Impossible task!

make sure to include a function for pure hate

If you want to adjust your model for higher training volume, you'll have to justify it somehow, and you didn't post an understanding of how that could be done.

That understanding is more usually of how it can't be done. You can use math to describe things that it succeeds at, but for what it doesn't, it's useless. Biology intervenes. The spectrum of 400, 800, to 1500 and beyond is a simplification of human application of the radically different aerobic and anaerobic energy systems.

Not a total wilderness - obviously a 400 runner untrained in the ways of aerobic endurance will slow more quickly over 800 meters than a 1500 specialist. But how do you model that mathematically?

You can only do that statistically, so you'll need shitloads of data. Otherwise it's best to limit degrees of freedom and limit your model to a single energy system, or at least a single combination of energy systems, i.e. race distance. The classical divisions of sprints, middle distance and long distance formed around these concepts. Compare sprints to sprints, MD to MD and LD to LD.

From 600m to mile, you can approximate equivalent performances - for distances you're equivalently trained for - with the exponent 1.135, or t2 = t1 x (d2/d1)^1.135. For double distances this is about 2.2. For shorter or longer distances, the energy systems involved are too disparate.

alabama runner wrote:

It's an excel spreadsheet that does a calculation much along the lines of statsgangsta's calculator (all credit for the original idea goes to him), but it has more training paces and more distances for which it can calculate times.

Wouldn't the easiest thing be to.... just ask statsgangsta to add the features you want? :p

J. Rexing wrote:

make sure to include a function for pure hate

Pure Hate Factor = A * Pure Rage Power ^ B + C * Pure Rage Capacity ^ D + E * Concealed Rage Power ^ F + G * Concealed Rage Capacity ^ H

A, B, C, D, E, F, G, H all variable per individual.

Pure Hate Factor is expressed as decimal between 0 and 1 with 1 being running on Pure Hate.

Doesn't this data exist? Are you reinventing the wheel?

This general formula I created (whilst similar to many others) is unique, simple, and incredibly accurate to current men's world records. I won't be able to describe it too well, but it goes as such:

it is in 5km intervals starting at 5000m and each interval is applied to the previous distance.

10km=.08/2 -1 or 5km /.96 /1x2

15km=.08/3 -1 or 10km /.97333... /2x3

20km=.08/4 -1 or 15km /.98 /3x4

25km=.08/5 -1 or 20km /.984 /4x5

30km=.08/6 -1 or 25km /.98666... /5x6

et cetera

reversing from 5000m formula is just as simple and accurate

3km=.08/2.5 -1 or 5km x.968 x.6

2km=.08/2.5 -1 or 3km x.968 /1.5

1.5km=.08/2.5 -1 or 2km x.968 /4x3

1km=.08/2.5x1.5 -1 or 1.5km x.952 /1.5

I.E. 130.75 206.01 283.76 439.71 757.09 1577.27 2430.73 ... ...

To statsgangsta: you could add that, but I wanted to make my own rendition to help my coach out if he wanted me to. I also like doing the math. I also thought you stopped posting here for some reason. never mind about that...

To Anti-Logarithm: Your formula works spectacularly for world record performances, but it doesn't account for individuality. El Guerrouj could not have run 12:37. Berkeley could not have run 3:26. For individual athletes, the logarithm seems to work best.

Another problem I'm running into is that after crunching data from HS athletes (my teammates and competitors), performances between 1000m and 3000m seem to be weaker than the logarithmic prediction. Also, 5000m performances are stronger than predicted.

Disregarding the effects of weekly mileage, how would I account for the weakness in middle distance marks? (Like I said, I'm using excel)

your question is ill-posed as the primary limiting factor is not how to get from enough data to a neat mathematical formula, but having "enough" data to start with. the former is rather easy for someone that has some statistical background. the latter is not - unless you have access to Strava's/Garmin's etc. data set (and even then, you have to be careful as not everybody logs every single run).

above_average_joe wrote:

your question is ill-posed as the primary limiting factor is not how to get from enough data to a neat mathematical formula, but having "enough" data to start with. the former is rather easy for someone that has some statistical background. the latter is not - unless you have access to Strava's/Garmin's etc. data set (and even then, you have to be careful as not everybody logs every single run).

I'm sorry, but for the basic calculation (disregarding mileage or age), no statistical data is needed. I use two performances to find the third, so it automatically adjusts to individuals. I'm not even trying to conform everyone to a single formula. Bad Wigins proposed the formula 1.135, or t2 = t1 x (d2/d1)^1.135. That 1.135 is an estimation. Kenenisa Bekele's number is probably 1.085, whereas David Rudisha's is probably 1.145. Even for athletes competing in the same event, there might be differences. A strength-based 1500m runner might have a number of 1.105, and a speed based one might have a number of 1.12.

well, presumably you want to go beyond the basic calculation (since for that we already have online calculators, no?).

I will get tricky once you incorporate mileage and other factors. for example, think about two types of runners. type A is better at converting his 5k pr into marathon pr than type B, and type A is also running higher mileage. now, is that all because he is running more miles? but maybe A is relatively more talented in the marathon compared to 5k, relative to B, and that's why he is running higher mileage. you'd make a mistake in telling B he can get the same 5k to marathon conversion as A if only he ran higher mileage. just an example what can go wrong. in any case, I still think you need lots of data for this to work.

this "pure hate" idea has not aged very well now has it? embarrassing - to say the least.

Pure hate applies to the 800 meters. Has 1:40.91 not aged well?

Go lick all the tiny pebbles off the nearest street, in obeisance to pure hate.