How did the damage output of Tristana change in 4.18?

From the 4.18 patchnotes:

General ATTACK SPEED PER LEVEL +4% per level ⇒ +2.5% per level

Q - Rapid Fire

DURATION: 5 seconds (was 7 seconds)

BONUS ATTACK SPEED 30/50/70/90/110% attack speed (was 30/45/60/75/90%)

How did the damage output change? Is it more or less?

Solution 1:

4% per level would give 72% at level 18. 2.5% per level gives 45% at level 18.

Rapid Fire at rank 5 now gives 110% instead of 90% - so an increase of 20%

Since speed bonuses are added together then this is a total loss of 27% at level 18, however at mid levels this will not be so bad since rapid fire is usually maxed before level 18.

Note that this doesn't actually mean 25% less damage, since bonus attack speed will almost always be higher than this.

For example BOTRK + Phantom Dancer gives 40+50 = 90 attack speed. Level gives 45 and RF gives 110.

This gives a total of 90+45+110 = 235.

Previously you would have 90+72+90 for 252.

In actual % terms that's a drop of about 8%.

Looking at mid levels: With rapid fire 5 and level 12 you get 12*2.5+110 = 30+110 = 140 Previously you got 90+12*4 = 138

So at level 12 you are actually slightly stronger than you used to be (for the first 5 seconds, after that you are weaker), but you then gain more slowly towards level 18 and never quite reach that peak hyper-carry point that you used to.

Solution 2:

Here is the full sheet

Even with the increase of the attack speed you will do less damage because the duration is a lot shorter.

Note that this is without items.

I calculated everything, in the image below you can see the amount of attack speed per level without and with the ability activated.

You can also see how much attacks you will fire in 7 seconds.