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I was looking into the mechanics of Poké balls, and there's a lot of conflicting information about how the bonus from timer balls is calculated.

Earlier than Gen 5, everywhere agrees that the bonus starts at 1 and increases by 1 every 10 turns, to a maximum of 4 at t = 30.
Bulbapedia gives a continuous formula:

C = (10 + T) / 10 

but it's not clear whether that's supposed to be rounded down to the nearest integer.

From Gen 5 onwards, some places claim the calculation has changed to:

C = (1 + X * 1229/4096) 

However, the majority of sites only mention the other formula.

So are these two formulae correct for their respective generations? Are either of them rounded?

1

Generation III and IV

(("Amount of turns passed in battle" + 10) ÷ 10)x
[maximum 4×]

This means:

  • 1× if less than 10 turns have taken place
  • 2× if between 10 and 20 turns have taken place
  • 3× if between 20 and 30 turns have taken place
  • 4× if over than 30 turns have taken place

These are all rounded values.

As explained on Dragonflycave:

The Pokémon games prior to the fifth generation only work with integers. In practice, this essentially means that they round all numbers down, including at every intermediate step in a calculation.

Generation V and VI

(1 + "number of turns passed in battle" * 1229/4096)×
[maximum 4×]

This means you get approximately a 0.3 bonus each turn passed, up to 4x.

Other sources: Bulbapedia, Smogon, Thonky

  • Your sources are contradictory in regards to Generations 3 and 4. – Wrigglenite Jun 10 '16 at 14:31
  • @DanmakuGrazer which part? – pinckerman Jun 10 '16 at 14:32
  • Bulbapedia uses the integer division symbol, which I assume is why you're rounding down for Generations 3 and 4, while the Wikia doesn't. – Wrigglenite Jun 10 '16 at 14:33
  • @DanmakuGrazer oh yes, they use a different notation, but it's an integer division. – pinckerman Jun 10 '16 at 14:35
  • I don't see that mentioned anywhere, so I don't know if I would personally count that as a source. – Wrigglenite Jun 10 '16 at 14:36
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Neither is rounded down, they both slightly increase in potency linearly with each passing turn. And yes, Timer Balls did get stronger in Gen 5.

Source for gens 3 and 4.

  • 5
    do you have a source? – Pyritie Jun 10 '16 at 13:32
  • @Pyritie Not at the moment, this is what I remember from past research I've done. – Wrigglenite Jun 10 '16 at 13:47
  • @Pyritie Added source. It seems the most trustworthy out of Serebii, Smogon, Bulbapedia, all of the usual ones. Bulbapedia could be interpreted either way, so I don't know if I'd call it a source for one interpretation or the other. – Wrigglenite Jun 12 '16 at 14:56

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