Ok, I finally found that that missing detail that was confusing me about why people were pursuing higher breakpoints.
From the "Tao of Sentries" thread:
http://us.battle.net/d3/en/forum/topic/12945884471#1
Code:Min APS - Max APS - Sentry FPA - Sentry APS 0.98182 - 1.10204 - 54 - 1.1 1.10205 - 1.25581 - 48 - 1.25 1.25582 - 1.45945 - 42 - 1.42857 1.45946 - 1.74193 - 36 - 1.66666 1.74194 - 2.16 - 30 - 2.0 2.16001 - 2.84210 - 24 - 2.5 2.84211 - 4.15385 - 18 - 3.33333 4.15386 - Cap - 12 - 5
The measured sentry attacks per second you get from your "pet APS" (char sheet APS x T&T bonus) starts at about 1.10x for the lowest breakpoint and increases to about 1.20x at the 4.15 breakpoint.
It still seems like a very minor difference to me. If there were two characters with identical sheet DPS, both using only Elemental Arrow, but one character got there with 2.843 pet APS while the other got there with 4.154 pet APS, the higher breakpoint character would see less than 5% more DPS from their sentries. If it's actually making a bigger observed difference in practice for those two scenarios, I must still be missing something.
Edit: Here's a chart to try to show what I'm talking about here.
Code:Sheet DPS - Sheet APS - (damage) - T&T - Pet APS - Real sentry APS - Sentry DPS (damage x real sentry APS) 1000000 - 1.89474 - 527776.8981 - 1.5 - 2.84211 - 3.33333 - 1759254.568 1000000 - 2.76924 - 361109.9074 - 1.5 - 4.15386 - 5 - 1805549.537 - 1.46x - - - 1.46x - 1.50x - 1.0263x
Why are you factoring in Sheet APS into Sentry DPS (Sheet DPS * Sheet APS * Sentry APS)? Sheet APS shouldn't factor into this number since that only determines the Sentry APS, which is a set number for a given range (hence "breakpoint"). I think Sentry DPS should really just be (Sheet DPS * Sentry APS).
Put another way:
1.89474 <= Sheet APS < 2.76924 ==> 3.33 sentry APS
>=2.76924 Sheet APS ==> 5 sentry APS
Sentry APS is discrete compared to Sheet APS.