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Nobody has actually gone and datamined any solid information yet. To my knowledge at least.
yeah there have been a few YT videos confirming yer capture rate gets worse with a "Better" capture rate, Sucks because i got 5 levels into this before this was confirmed.
The first factor is the displayed percentage before and after the throw. You notice that regardless of the number of shakes, the pal is caught once this number reaches 100. So after each shake the number increases a variable amount. You might also notice that the initial number actually does increase if you have statues applied. For example if you hover your crosshair over a pal with a sphere in hand, and it says "5%", then when you throw, suddenly it says "14%". So it stands to reason that this is the statues working correctly for the first factor.
The second factor is how likely the pal is to break out of the ball on each shake. Regardless of whether a pal has a 5% catch chance or an 85% catch chance, that number still has to REACH 100. Each shake the number increases by a seemingly random amount. Sometimes a 5% can go to 100 after 1 shake, and sometimes 85% can take 3 shakes to reach 100. But after each shake, there is a chance for the pal to break out. And it seems that the liffmunk statues ALSO increase the sphere break chance by the same amount. So even if you have a high catch chance, it's negated by a high break chance.
It also feels like that while playing with a friend. We both catch less often or have to throw a lot more spheres with like level 5 power.
(I also had it happen like the chance already is 90% but the sphere will shake once to go like to 98% and then the second shake will capture it. So its always two shakes for me, never only one.)
So, for example, if it starts at 20%, it will always go up to 60% after the first shake. Because 60% is halfway between 20% and 100%.
100 - 20 = 80 (Total - Current% = Remainder)
80 / 2 = 40 (Remainder divided in half, aka "/ 2" )
20 + 40 = 60 (Current% + Half of Remainder = Halfway Between Current and Total)
The second 'shake' moves it up the other half, meaning you got 100% and you caught it.
Yall love math you know you do.