You see, I have been a 30 miles a week jogger for a few years now (excepting the cross-country ski season). When I was younger I ran 30 miles a week. In my middle years I did nothing but watch my middle expand-- now I am trying to undo the middle damage.
I have recently tried the 26.2 distance but cannot seem to get much past the 20 mile mark and while chatting in the driveway I made mention of this sorry fact. He said I was not training enough and said I should look into the 'Collapse Point Theory'. Well, he did not use those words but gave a description that sounded a lot like it. This theory defines the maximum distance you can run is some multiple of your average daily mileage over a week's time.
Here is the math to calculate the required weekly mileage (don't worry we covered this in the 5th grade):
C = {2.5, 3}
26.2 = C * (m / 7)
26.2 / C = m / 7
m = 7 * (26.2 / C)
Which allows me to calculate the number of miles I should average per workout. So as a 5x per week runner I must average 12.2 or 14.7 miles per day depending on whether I feel normal or less than normal. In short, I am screwed.
Just in case I screwed this up and you need to fix my mistakes here is the R script:
#
# simple function to calculate the daily average
f <- function(d, C) { round(7*((26.2/C)/d), digits=1) }
#
# calculate a conservative and standard set of averages
m1 <- sapply(d, f, C=2.5)
m2 <- sapply(d, f, C=3)
#
# create the plot, and legend
c <- c("green", "blue")
d <- c(1:7)
plot(d, type="n", ylim=range(0, m1, m2), main="I'm totally screwed!!", font.main=4, col.main="red", xlab="runs per week", ylab="weekly miles")
legend(1, 8, c("conservative","standard"), cex=0.8, col=c, lty=1:1);
#
# draw the lines leaving gaps for the values
lines(m1, type='c', col=c[1])
lines(m2, type='c', col=c[2])
text(m1, labels=m1)
text(m2, labels=m2)