Composite bow maths

Can someone help me understanding the maths behind composite bow?

In the patch update:

In game it says the upgrade increase attack speed by 33%.
Base archer attack speed is 1.5s

If i do 1.5 / 1.33 i get 1.12
If i do 1.5 x 0.67 i get 1.00

How do i reach 1.25 exactly?

Also 33% more attack speed should imply 33% more damage before armor no? And to deal 33% more damage you would need the upgrade to be a reload time of 1.12s.
Example with archer dealing 5 damage:
5 / 1.5 = 3.33 dps
5 / 1.12 = 4.46 dps
5 / 1.25 = 4 dps
4.46 / 3.33 = 1.33 so 33% more damage.
4 / 3.33 = 1.20 so 20% more damage.

So with the patch the attack speed bonus is only 20% but it still says 33% on the upgrade?

Completely agree with your calculations.
Similar issues come with the economic upgrades like horticulture.
The description often does not refleft the real values.

For the attackspeed it’s a little trickier, as multiple components come into play here.
As far as I know there are aim-time, animation-time and reload-time.
The attackspeed is all 3 combined.
So the description maybe should be 33% less animation time or they should just re-calculate the saving on time of the full cycle and correct the mentioned percentage to the true value.

The current system is very missleading and 33% more attackspeed would (ignoring piercing armor of the target) mean 33% more dps, which is obviously not the case.

Devs either have to change the description or the number in the description.

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Isn’t their starting attack interval 1.625 not 1.5?

That still gets me an attack interval of 1.22 seconds though, not quite 1.25.

The displayed in game "attack speed " is a contrived value that is NOT directly used. I keep losing the link but if you go into Frequently Ask Questions you can find it.

It details that “attack speed” is a combination of aiming + winding up animation + attack animation + winding down animation. The attack animation (ROF) is the ONLY metric affected by attack speed increases. What worse!!! Is they don’t multiple bonus by the standard ROF… rather they divde (1- decimal_value_of_the_speed_buff).

So instead of 1.33 x standard rate of fire; they do ROF/(1 - 0.33) = 1.49 x ROF