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Ability Stacking

With Proper Science For Once

  1. ELStalky
    The test map is a great place for examining the ability to stack abilities as it provides precise metrics. For this experiment we can simply use the damage up ability and see how it affects the damage. Additionally i chose to time the duration of the bubbler, to see how it compares.

    Data
    main denotes abilities in the main slot of the gear (at the top); sub respectively denotes a sub ability of which there can be up to three per gear.

    Splattershot
    Raw: 36.0 dmg
    1main: 39.2 dmg
    1main 1sub: 40.1 dmg
    1sub: 37.0 dmg
    1sub 1sub: 38.0 dmg
    2main: 41.9 dmg
    2main 1sub: 42.6 dmg

    Aerospray
    Raw: 24.5 dmg
    1main: 24.9 dmg
    2main: 24.9 dmg

    Rapid Blaster
    Raw: 80.0 dmg
    1main: 87.2 dmg
    1main 1sub: 89.2 dmg
    1sub: 82.3 dmg
    1sub 1sub: 84.5 dmg
    2main: 93.2 dmg
    2main 1sub: 94.7 dmg

    E-Litre 3K (charged)
    Raw: 180 dmg
    1main: 196.3 dmg
    1main 1sub: 200.7 dmg
    1sub: 185.2 dmg
    1sub 1sub: 190.1 dmg
    2main: 209.8 dmg
    2main 1sub: 213.2 dmg
    3main: 220.3 dmg

    1main (Head): lacking gear
    1main (Clothes): 196.3 dmg
    1main (Shoes): 196.3 dmg

    1sub (slot 1): 185.2 dmg
    1sub (slot 2): lacking gear
    1sub (slot 3): 185.2 dmg

    Bubbler
    Due to the audio measured for the raw loadout being close to 5 s, it will be assumed that this is actually the default length. More precision could possibly be achieved using visual measurement via high speed video recording.

    Raw: 5.00 s
    1main: 5.555 s
    1main 1sub: 5.749 s
    1main 2sub: 5.874 s
    1main 2sub 1sub: 6.004 s
    1sub: 5.151 s
    1sub 1sub: 5.324 s
    2sub 1sub: 5.509 s
    2sub 1sub 1sub: 5.656 s
    2sub: 5.323 s
    2main: 6.055 s
    2main 1sub: 6.182 s

    Swim Speed Up
    Roughly measured time swimming from one wall of firing range to the other. (No Ninja Squid ability has been used which is said to reduce speed.)

    Raw: ~5.0s
    1main: ~4.6s
    2main: ~4.4s
    3main 1sub: ~4.25s

    (Measured this because it was suggested that Swim Speed Up does not stack.)

    Results
    Now for some observations and calculations based on that data.

    Weapons
    The stacking appears to work the same for the different guns, with one exceptional behaviour: Capping.

    Damage Up stacking caps for certain weapons at some point. This is believed to be due to the amount of shots being needed to splat someone with that weapon being made constant. So if a weapon takes three shots to splat someone without any abilities then it will also splat at three shots with 3main abilities. Chargers are not affected by this. (Likely because in the charged state they all kill at one shot.)
    This effect can be seen with the Aerospray already when applying 2mains. The damage caps at 24.9 => 24.9 * 4 = 99.6, thus five shots are required. If 0.1 more damage where done that number would go down to four.

    The larger damage counts yield more precise results so calculations are done based on the E-Litre 3K:

    Raw to 1main: +9.06%
    1main to 2main: +6.88%
    2main to 3main: +5.00%

    Raw to 2main: +16.56%
    Raw to 3main: +22.39%

    1main to 1main 1sub: +2.24%
    2main to 2main 1sub: +1.62%

    Raw to 1sub: +2.89%
    1sub to 1sub 1sub: +2.65%
    Raw to 1sub 1sub: +5,61%

    (These are still fairly inaccurate, to control for rounding errors one could calculate the ratios for all different damage profiles and average them.)

    Bubbler
    Raw to 1main: +11.1%
    1main to 2main: +9.00%
    Raw to 1sub: +3.02%
    1sub to 1sub 1sub: +3.72% | What is going on here...

    1sub 1sub to 2subs: ~0% (When chalking up difference as measurement error)

    When plotting the times for the number of subs (0 to 4), treating them all as equal, we get this:

    Screenshot from 2015-06-03 07:18:10.png

    Weapons vs. Bubbler
    Falloff (Raw -> 1sub) to (1sub -> 1sub 1sub):
    Weapon: 91.62%
    Bubbler: 123.2%​

    Is this even possible? My hypothesis is, that the initial duration simply is not exactly 5 but something smaller. Looking at the bubbler plot the first point also seems out of line and looks like it should be lower. Also subsequent measurements were all affected by the initial assumption, which may further change the data.

    This is why the damage numbers are better: They only contain rounding errors, not measurement errors.

    Discussion
    The count relative results from the bubbler trials are ignored for now, as the trials appear to have been faulty.

    The results seem to suggest that stacking is in fact quite real, and that the falloff becomes fairly steep once the already applied bonus is high. For example, when already being equipped with one damage+ on main, an additional damage+ main will only be 75.9% effective. When adding a sub to another sub the additional sub is still 91.7% effective.
    The penalty appears to go down again, as a third damage+ on main is still 55.2% effective. If it were still increasing one would expect a value below 51.8%.

    If the slot position of a sub ability matters, then it is quite unintuitive, as at least between slot 1 and 3 there is no difference. The sub slots being the same was to be expected; while the exact values of falloff and absolute gains may not be public, it would be odd to have such a mechanism. Likewise, the type of the gear does not appear to matter either.

    The results also show that weapon damage caps at the amount that still yields the same number of shots on one target necessary to splat. This is probably a mechanism very specific to Damage Up. Other abilities might have their own peculiarities, for example i doubt that Ninja Squid stacking has any effect (though it would be interesting if it lowered the swimming noise or made the trails disappear).

    The two bubbler data points for 1sub 1sub and 2sub seems to suggest, that having abilities spread over different gear does not affect their bonus.

    I will investigate this further once i acquire more gear with damage+. With more data points it might be possible to calculate a falloff curve.

    Other things that need to be investigated:
    • Is the falloff the same for other abilities (might be hard to measure for other abilities though)
    We must science this at once!

    Notes
    • Damage capping does not render the ability useless! The other direction is not capped, so if an enemy equips defense abilities the needed amount of shots can go up. Also, when in a firefight with your team you can combine your added damage with theirs, e.g. a .96 Gal does 62 damage, a Splattershot 36, so if two people equip these weapons and hit an enemy once each they do 98 damage, now if the .96 Gal user is equipping 1main damage+ it does 67.6 damage; the total now is 103.6, which is one splatted enemy.

    [​IMG]

Recent Reviews

  1. VideoGameVirtuoso
    VideoGameVirtuoso
    5/5,
    Some reasonably accurate data, however limited the set of values are.
  2. Robotoboy20
    Robotoboy20
    5/5,
    This is really good data! Thanks for putting it together.
  3. Giraff3
    Giraff3
    5/5,
    I really felt like you were going to say that damage + bonuses didnt matter until the end when you combine shots with your teammates.
  4. Figy
    Figy
    5/5,
    I like how everything is organized into one thing.
  5. Squelchior
    Squelchior
    5/5,
    Reading everything and humming until I found the graph and insane number crunching.
    We Maylay now guys.
  6. Necrosis
    Necrosis
    5/5,
    This is what I have hoped for the splatoon community to turn into. Number crunchers. :)
  7. ChivalRuse
    ChivalRuse
    5/5,
    Useful guide. I hope more gets added to it.
  8. Chewypuck
    Chewypuck
    5/5,
    Extremely helpful, glad someone's doing science. Keep it up!
  9. SolarTrifle
    SolarTrifle
    5/5,
    Looking forward to more! Keep up the work, I can't wait to see if there's a curve for stacking
  10. PerfektNerD
    PerfektNerD
    5/5,
    Very science! Much math! Thanks for all your work.
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