Did you even read what I posted? Here is a blow up of it so you can see it addresses a scenario very close to what you posted, and illustrates how you don't have a 15:1 ratio. Number 5 in the chart places the post season/mortality at 90 to 1, which is a worse ratio than your example.
Go back and actually read what was posted, either the screen shot I put up or the link provided by Pathman.
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Lets take your example of 75 deer, and 7 of them button bucks. That leaves 68 females, if you are correct and they were all does and not shed bucks, and we'll assume that the 7 button bucks were the only bucks around. Zone 10 has great habitat, so I would assume each doe having twin fawns is not out of the question. So that gives us 136 fawns, given an even male/female birth rate, that gives us 68 females, and 68 males. So, we have 136 females and 75 males in the herd. That's a little better than a 2:1 ratio.
If each doe only has one fawn, it's 34 female and 34 male fawns, and that means 102 females to 41 males, or a little worse than 2:1 ratio. And that's assuming there were no shed bucks in your count, or buttons you missed.