Simple YTM

Hi all, just a back to basics question. Why in the denominator of the simple YTM formula, is the average price between par and price paid used? I get the math mechanics, but now I'm looking at this from a 1,000 feet view. My rationale is that since this is the simple version of the formula, then it is okay to use bad math, so the denominator is just looking for some "middle ground" to use a reference point?

Any thoughts? Many thanks.

YTM = C + [(F – P)/n] ÷ (F + P)/2

Where C = coupon rate

F = face value

P = purchase price

n = number of years

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