So I did some calculating with this guy's formula and I surprised myself how well I can figure things out with it using a few
assumptions... I know what they say about assumptions, but regardless.
Basically, to start this math assignment, you have to measure your thumb and the distance between your eye and your thumb with your arm extended in front of you. His thumb was .625 inches wide (5/8") and his eye-thumb length was 24.25 for a ratio (thumbwidth/eye-thumb length) of 40. I got a thumb width of .75 (3/4") and an arm length of 24" for a ratio of 32.
The next part of his equation requires you to know the height of whatever you are distance-guesstimating. In our case it's a deer, which average around 36" or so high at the shoulder depending on what part of the country you live in. 36"=3 feet= 1 yard which is very convenient for this situation.
Basically using his arm-thumb ratio and my own, which I would consider a fairly well-encompassing spread, here are some values.
If you hold your thumb out full arm's length parallel to the ground, measure/guesstimate the deer's height in thumb widths.
1/4 thumbwidth= 96-120 yards away
1/2 thumbwidth= 64-80 yards away
1 thumbwidth= 32-40 yards away
1 1/2 thumbwidths= 21-26 yards away
2 thumbwidths= 16-20 yards away
Obviously the ranges get a bid broad as you get up, but for the ranges most of the people on this board will be shooting at (<40 yards) it's a pretty damn good way of estimating once you get past the initial arithmetic!
If you have wide thumbs and/or short arms, hedge towards the shorter end of the range, if you have narrow thumbs and long arms hedge towards the farther edge, or just do the math yourself!
I'm just happy to know that for me, 2 thumbwidths=16 yards, 1.5=21 yards, 1=32 yards, 1/2=64 yards, and 1/4=96 yards.