Is throw bonus for the inner-circle to catch Pokemon continuous or discrete?

Question

When catching a Pokemon, there is an inner colored circle that continuously starts at the outer circle and zooms in to zero. Landing a ball inside the circle gives an XP "throw" bonus depending on how small the circle is when the ball is thrown – Nice!, Great!, or Excellent! That throw bonus also corresponds to an increased catch probability.

Does the catch probability increase continuously as the inner circle size decreases? Or is the effect of the throw bonus discrete and tied to the three named bonus tiers?

Meaning, for example: if I get a Great! throw when the circle has barely shrunk from Nice! size to Great! size, is the catch probability boost the same as if I get Great! right before the circle is about to shrink to Excellent! size?

Answer 1

Gamepress made an analysis about the throw bonus, and these are the results:

Throw Bonuses are not fixed, instead depends continuously on radius! The formula we found for catch bonus is:

Throw = 2−r

where r is the radius of the inner circle, which goes up to 1. That means that when the circle is as big as possible, Throw = 1, and when the circle is as small as possible, Throw = 2.

Since ring size and throw bonus are correlated, we could not be completely sure that the multiplier varies continuously with radius, rather than being a flat bonus for Nice / Great / Excellent.
However, the communication between client and server during a catch suggests that the bonus is continuous. What can be seen in the client-server communication is that a variable named normalized_reticle_size (NRS) is sent to the server when a ball is thrown.
In other words, for a full-sized circle, NRS = 1, and for a circle of minimal radius, NRS approaches 2.

Experimental evidence shows that:

Throw	Nice!	Great!	Excellent!
Target Ring Size	70% - 100%	30% - 70%	~5% - 30%
Bonus (varies with radius)	1 - 1.3	1.3 - 1.7	1.7 - ~1.95

We also have some lines from the game's code that shows:

"excellentThrowThreshold": 1.7,
"greatThrowThreshold": 1.3,
"niceThrowThreshold": 1,