Why 1.15? The set adds a 50%chance to proc AA on non-crits. Each heal that doesnt crit, then has a 50% chance to proc AA, right?

The 1.15 is it's own modifier placed within the Crit modifier. A modifier in a modifier. It's a binomial random variable, just like Crit is and you calculate it just as you would Crit.

Ignoring Crit; just the 4P:

1*0.5+1.3*0.5 = 1.15

50% of the time your spells heal for a modifier of 1.

50% of the time your spells heal for a modifier of 1.3 (30% from AA).

On average, each spell cast then heals for a modifier of 1.15.

Because this modifer only affects noncrits, we know we can use it in the binomial formula for Crit to replace the old modifier of 1 for noncrits.

Is your example using averaged numbers?

Technically my example is not, except for the assumption that 1 Crit occurs every 100 casts with 1% Crit. With that example, your one spell that heals for 2.6 literally heals for 2.6. If that confused you, then ignore that statement and just pretend it was.

But it's the same with averages. Just apply it to any example:

Say you have a spell that does 500 HPS. 1% Crit gives a modifier of 1.016 (an average). Thus 1% Crit gives

500*0.016 = 8 additional HPS

Every 1% Crit will give you 8 more HPS.

But with the 4P equipped you get 15% bonus making your new HPS 575, but each additional 1% Crit now gives

500*0.0145 = 7.25 HPS

Thus every 1% Crit you get only provides 7.25 more HPS instead of previously 8. Since Haste and Mastery are unaffected Crit is thus devalued.