See @vemonus answer down below: https://gaming.stackexchange.com/a/288122/75659
Answer: No one officially knows yet. It's frequently a controversial topic in terms of anecdotal evidence: some players say they notice an increase in capture rate, others don't - however, in general, most players seem to be in agreement that it does confer a catch rate bonus.
Below is an explanation of why the capture rate bonuses detailed on certain websites (such as ones in the above answers) are misleading and based on unverified claims.
The closest thing we had to an indication that it does affect the rate (besides anecdotal evidence) is within the protobuf file for the game. This is a list of numbers within the game that detail things like medal achievement requirements, experience bonuses, gym experience numbers, etc. I've provided the link below:
Within this protobuf we can see that there are only two values related to throw types. The first is an item detail for each type of ball, e.g. for greatball:
and the second lists "thresholds" for each type of throw:
Some people saw these numbers and assumed it meant the catch rate multiplier...however others speculate that:
- this doesn't make sense for spin bonus threshold, since it'd cut the rate in half. it makes more sense if the spin threshold meant (as its name indicates) how much spin is required before its counted as a spin throw
- the word threshold doesn't make sense given the context (you'd think something more like GreatThrowMultiplier would be more appropriate) and
- these numbers more accurately line up with (1 - radius) of the size of the inner circle upon impact.
To elaborate on point 3:
The answer here says for nice, great, and excellent the percentage of the inner circle to outer circle diameter required would respectively be: 100%, 70%, and 30%.*
To clarify/reiterate for people unfamiliar with throw types: you have to not only have a smaller circle to get a bonus, you have to hit the pokeball inside the circle as well.
To translate these numbers into the threshold numbers, all you have to do is see that:
let x = the value upon impact based on the distance
- x = 1 means your pokeball hit the pokemon while the inner circle was the same size as the outer circle
- x = 2 means the inner circle had a radius of 0
Take (2 - x) and you see that the thresholds as detailed in the protobuf line up with the percentages.
2 - ExcellentThrowThreshold
2 - 1.7
Here is a link that details actual data communicated with the servers and basically confirms that the values of 1.00 - 1.99 were the thresholds when that protobuf was published (and also explains how these numbers have to do with why there was no bonus exp for throw types for one patch: the 'x' value was changed from 1.00 - 1.99 to 0.00 - 0.99 and thus no one could achieve the 1.3/1.7 required for the bonus except for hackers).
*NOTE: This is not a definitive source, but it lines up so perfectly with the explanation and numbers that it's very likely true.