What are the Haste breakpoints for Holy Fire?

Question

Glyph of Smite gives a 20% increase to Smites cast on targets burning with Holy Fire.

At 0% haste, unglyphed Holy Fire allows 4 Smites. Glyphed Holy Fire only allows 3 smites, because the burn begins at the start of the gcd instead of the end of a cast.

At 7.4% haste, I see that holy fire burns for 7.4 seconds, and smite casts in 1.4 seconds. This allows 5 smites during an unglyphed holy fire burn.

What are the haste breakpoints which would let Holy Fire (glyphed or not) burn relatively longer, allowing more smiting?

Answer 1

The GCD (for instant holy fire) and the cast time of Smite at 0% haste are both 1.5 seconds. Haste speeds up all three (ticks, GCD, Smite) equally up to 50% haste (when it stops affecting GCD). While evaluating less than 50% Haste, we can just use ticks instead of seconds. (GCD = 1.5 ticks, Smite = 1.5 ticks).

According to the formula in this article, extra ticks occur at the following breakpoints.

                   0.0% haste for  7 ticks
 7.5/7 = 1.0714 =  7.2% haste for  8 ticks
 8.5/7 = 1.2142 = 21.5% haste for  9 ticks
 9.5/7 = 1.3571 = 35.8% haste for 10 ticks
10.5/7 = 1.5    = 50.0% haste for 11 ticks

So, Unglyphed Holy Fire breakpoints are:

 0.0% haste for  7 ticks and 4 smites
 7.2% haste for  8 ticks and 5 smites
21.5% haste for  9 ticks and 6 smites (exactly)
35.8% haste for 10 ticks and 6 smites
50.0% haste for 11 ticks and 7 smites

And Glyphed Holy Fire breakpoints are:

 0.0% haste for  7 ticks and 3 smites
 7.2% haste for  8 ticks and 4 smites
21.5% haste for  9 ticks and 5 smites (exactly)
35.8% haste for 10 ticks and 5 smites
50.0% haste for 11 ticks and 6 smites