Why we multiply 'most likely estimate' by 4 in three point estimation? -

i have used 3 point estimation 1 of project. formula

   3 point estimate = (o + 4m + l ) / 6 

that means,

  best estimate + 4 x estimate + worst case estimate divided 6 

here

divided 6 means, average 6 

and there less chance of worst case or best case happening. in faith, estimate (m), take job done.

but don't know why use 4(m). why multiplied 4 ???. not use 5,6,7 etc... why estimate weighted four times as other 2 values ?

i dug once. cleverly neglected write down trail, memory.

so far can make out, standards documents got textbooks. textbooks got original 1950s write in statistics journals. writeup in journal based on internal report done rand part of overall work done develop pert polaris program.

and that's trail goes cold. nobody seems have firm idea of why chose formula. best guess seems it's based on rough approximation of normal distribution -- strictly, it's triangular distribution. lumpy bell curve, basically, assumes "likely case" falls within 1 standard deviation of true mean estimate.

4/6ths approximates 66.7%, approximates 68%, approximates area under normal distribution within 1 standard deviation of mean.

all being said, there 2 problems:

1. it's made up. there doesn't seem firm basis picking it. there's operational research literature arguing alternative distributions. in universe estimates distributed around true outcome? i'd move there.
2. the accuracy-improving effect of 3-point / pert estimation method might more breaking down of tasks subtasks particular formula. psychologists studying call "the planning fallacy" have found breaking down tasks -- "unpacking", in terminology -- consistently improves estimates making them higher , reducing inaccuracy. perhaps magic in pert/3-point unpacking, not formulae.