The scientist need come down here in to this part of the Ouchita's 34.3268° N, 93.5507° W and tell the deer they are doing it all wrong.
Years of observation in your area will tell you when the peak rut is in you area.
I am lucky in that have lived on this piece of land for 20 years and watch the deer everyday.
Personal observation, 20 years of living and hunting here, peak rut the third week in October.
Fawn drop bears this out as they drop in May.
Speaking to stats I have read studies that a lot depends on where the deer were imported from.
The deer herd in Arkansas was decimated by the turn of the 20th century. Arkansas imported deer from everywhere to rebuild the herd. Where the deer were imported from has an effect on timing of rut. Add to that the inter breeding of deer from different extreme Lat/long and we get mixed up rut wiring. So, I have read.
Good night and good luck.