"[Analysis] The effect of the 0.9996 type effectiveness multiplier on damage calculation"

#PokemonGO: Long post aheadWhat is the 0.9996 value?When, during a raid or gym battle, a Pokémon attacks another Pokémon, it does a certain amount of damage. The amount of damage dealt is influenced by many factors as extensively described here by GamePress.One of these factors is type effectiveness, which describes how effective an attack is against the receiving Pokémon, based on this table (by /u/ashiqrh) as found in the game code.Approximately half of all Pokémon have two types. When an attack is super effective against one type and not very effective against the other, you’d expect them to cancel out and equal a multiplier of 1, just like in the other Pokémon games. However, you get an effectiveness bonus of 1.4 * 0.714 = 0.9996 (0.714 is a rounded down value of 1/1.4). In these cases, the game also shows the “Not very effective…” notification.A multiplier of 1 is not equal to 0.9996, so damage breakpoints can be affected.Before type-effectiveness in Pokémon GO changed this was not an issue, but now it might be. So let’s explore!Which Pokémon are influenced?All Pokémon that have a dual-typing could be affected if the type effectiveness matches up just right.For example: Dragonite is a Dragon/Flying type. Electric attacks are super effective against the Flying type and not very effective against the Dragon type, so attacking Dragonite with an electric attack would give a type effectiveness multiplier of 0.9996.In this table all 134 Pokémon are listed that have such a type match-up (also Generation 3 Pokémon inlcuded).Raid Pokémon are bolded, because the potential change in damage dealt to them is a lot more interesting, since they have the same stats every time you battle them (which is not the case for Pokémon in gyms, which are all different).Below, the current raid Pokémon influenced by this are listed again:PokémonTypeIvysaurGround, Poison, BugNidoqueenGrassNidokingGrassVictreebelGround, Poison, BugTentacruelGrassCloysterFire, SteelLaprasFire, SteelOmastarSteel, WaterArticunoFighting, IceZapdosElectricMoltresIceLugiaBugHo-OhIceSableyeGhost, Bug, DarkMost of these match-ups don’t really matter, who is going to take Fire Pokémon with them into a Cloyster raid anyway? Nobody, so any odd damage breakpoints do not matter in that case.Interesting match-ups are cases where you use a generalist. Even though Dark attacks aren’t super effective against Sableye, Pokebattler lists Tyranitar with Bite as one of your best choices. You carefully level Pokémon up to certain damage breakpoints for the best balance between your resources (candy, stardust) and the quality of your Pokémon.What would you think if suddenly, due to a slight change in a damage multiplier (0.9996), this breakpoint is not at the place it should be, making you waste resources? Of course, that would be annoying.Let’s explore such a case:Attacker: Tyranitar, Lvl. 38, 10 Atk IV Bite as quick moveDefender: Sableye, T2 Raid boss (1800HP, CPM: 0.67)Raid Pokémon have 15 IVs in all their stats, so Sableye has 156 as its Defense stat.Damage = floor(0.5 * Move Power * (Atk/Def) * STAB * Type effectiveness) + 1 Damage = floor(0.5 * 6 * (261 * 0.7789…)/(156 * 0.67) * 1.2 * 0.9996) + 1Damage = floor(7.0023 * 0.9996) + 1 = floor(6.9995) + 1 = 6 + 1 = 7Due to the fact that the type effectiveness bonus is only 0.9996, you go slightly under 7 damage. Therefore the damage every Bite does is 7 instead of 8. Sure, if you power your Tyranitar up one more time you would hit the breakpoint, but that would not be needed if the multiplier was 1 instead of 0.9996!In this raid, you have to use bite 258 times instead of 225 times, if the multiplier would have been 1!The same is also the case for a Lvl. 38.5, 9 Atk IV and Lvl. 27, 0 Atk IV Tyranitar. Some examplesAt this point I'm not going to try to convince you that a multiplier of 0.9996 is the worst thing in the world, but I do want to show some more examples to indicate how common it is for damage breakpoints to be affected by this.In the following table, two generalist attackers are shown with influenced breakpoints between Atk IVs 10 and 15 against a Sableye Raid:Atk IVTyranitar - CrunchMewtwo - ShadowballGengar - Shadowball103223, 25.5, 29, 34.5, 35.534.51125.5, 3836, 37231229, 37.530, 38.5, 39.532.5133725, 28, 30.524.5, 311436.520.522.5153620, 21.5, 32.536.5So in all of these cases the attack is doing one less damage than it would have if the effectiveness multiplier was 1 instead of 0.9996.When I found out about this I immediately went through my Tyranitars to see If I was effected by this. Even though the difference is minor, you just want to know if Niantic is swindling you of one extra damage.Maybe you're raiding with some oblivious/random people against a Cloyster or Lapras and they ask you which Pokémon they should bring.The best counters they may have is a Tyranitar (w/ Stone Edge) or Machamp. If that Tyranitar has Iron Tail as quick move (Steel move) or the Machamp has Bullet Punch/Heavy Slam they can be influenced by the 0.9996 multiplier too.Maybe you are doing a quick Ivysaur raid. You might think, Bug moves are super effective against Ivysaurs Grass typing, I'll take Scizor. While forgetting that it is not very effective against it second type, poison. Suddenly your Bug move Scizor can also be influenced by the 0.9996 multiplier. This is also found in gym battles. But as far as I am aware the current mechanics of how the stats of Pokémon in gyms change as their motivation (and visible CP) decays is not currently exactly known. Therefore it is hard to predict any influenced damage breakpoints, except for Pokémon at full motivation.Maybe one day when PvP arrives, and Pokémon are set at a certain level during battle, it will be easy to predict the influenced breakpoints. Hopefully, this is fixed by then and none of our concerns anymore.Back on topic: Pokémon that are often seen in gyms and are influenced by this are for example the previously mentioned Electric attacks against Dragonite. But also Grass attacks against Gyarados (I’ve used my Venusaur against them before, if a Rhydon was the next Pokémon in line, thinking it would do super effective damage, not thinking about the fact that grass is not very effective against flying.)Other Pokémon that are commonly spotted in gyms and influenced by this: Lapras (Fire, Steel), Steelix (Grass, Ice), Scizor (Fighting, Flying, Ground and Rock) and Wigglytuff (Fighting). At this point you might feel like this can only work against you. But actually, a raid boss is also attacking you and maybe it is doing reduced damage every time due to the 0.9996 multiplier!Some examples of this:A Raikou (both Volt Switch and Thunder Shock) does one less damage against a Lvl. 31.5 10 Def IV Dragonite. Thunderbolt does one less damage against a Lvl. 35 14 Def IV and Lvl. 35.5 13 Def IV Dragonite. (just noticed a small mistake here)A Raid-Boss Thunder Shock Raikou does one less damage against a Lvl. 29.5 8 Def IV Dragonite. Volt Switch does one less damage against a Lvl. 36.5 9 Def IV and Lvl. 30.5 7 Def IV Dragonite.And in approximately 3-4% of all cases, a raid boss Raikous Charge move does 1 damage less too.Ground attacks of the raid bosses Rhydon, Golem, Nidoqueen, Nidoking, Snorlax, Omastar, Marowak and Sandslash may affect Victreebel, Vileplume and Venusaur, Pokémon that you often use as attackers against them.About 3% of the Earthquakes coming from the tier 4 bosses do reduced damaged to Victreebel , Vileplume and Venusaur (counting over the range of Lvl. 30 to 40 attackers and Defense IVs 0 to 15).So maybe you should be happy that the type effectiveness bonus for a super effective and not very effective move canceling each other is 0.9996.But also in gym battles you might be lucky and receive less damage than you would if the multiplier was just 1.Some Pokémon that I’ve not mentioned yet but can be used as attackers are: Charizard (Ice), Jynx (Fighting), Kabutops (Steel, Water), Articuno (Fighting, Ice), Zapdos (Electric), Moltres (Ice), Houndoom (Fairy, Bug), Kingdra (Grass, Ice, Electric). If you’ve read through all examples, you can probably imagine the relevance of the peculiarity that is the 0.9996 effectiveness bonus. Sometimes it works in your favor, sometimes against, but overall, you will hardly ever notice it (but it will be there).Proving its existenceAt some point while I was writing this, I figured I should probably add some proof that the 0.9996 does actually exist. It could be that Niantic somehow coded it as being 1 all along (which is not the case if we believe the type charts).So I decided to do a raid that can be influenced by this. To exclude influences from other players, soloing Ivysaur (600 HP) or Sableye (1800 HP) were the obvious choices.I did some research with Rhydon and Scizor against Ivysaur. Since Ground and Bug type moves both give an type effectiveness multiplier of 0.9996.In this case, the used Rhydons Mud-Slap deals 15 or 16 damage and Scizors X-Scissor deals 50 or 51 damage. Where both are dependent on the type effectiveness multiplier being 1 or 0.9996. After recording some raids I counted the amount of attacks that were needed to take down the raid boss (40 or 38 for Rhydon, dependent on amount of X-scissors in Scizor case). In both cases the Pokémon did damage as if the multiplier was 1! This was absolutely not as expected. After exploring a bit I figured the difference is not because the 0.9996 effectiveness multiplier is different, but the raid boss CPM value is not precise enough.The CPM values for raid bosses were estimated by doing battles similar to these, so are not written in stone. If the CPM value for tier 1 raid bosses would be 0.599 instead of 0.600 it would already explain why my Pokémon did more damage.To be precise, Scizor would deal 51 damage with CPM values of 0.59981 and lower and Rhydon would do 16 damage with CPM values of 0.59986 and lower. So overall, the Tier 1 CPM value is probably 0.59981 at the highest (further research might lower it more). Fine Tuning the CPM of tier 1 raid bosses was not the goal of this post. So, even though the practical research I did does not really matter anymore, I'll still report it in a bit of detail (because I had already written it, so didn't really want to delete it). First, I decided to try this with a Mud-Slap Rhydon against an Ivysaur raid boss. A level 27.5, 15 Atk IV Rhydon does 15 damage if the type effectiveness multiplier is 0.9996 and 16 if the multiplier would be 1 (You can confirm that it becomes 16 by temporarily changing the multiplier in your favorite-breakpoint calculator. (Note: Here I’m using 0.60 as CPM for tier 1 raids instead of 0.61 as was commonly used before. With a CPM of 0.61 the damage dealt would be 15 with both effectiveness bonuses due to higher Defense of Ivysaur.)Here is a link to the battle video.I tried to overlay the video with damage counts but it didn't work out since I am not proficient with video editing.Sadly, the video does also not show me IV checking the Rhydon to proof the stats since the recording would stop as soon as I started GOIV or CalcyIV. Here is a screenshot of the IVs taken afterwards.As you can see, after 19 attacks the health goes into yellow (285 or 304 dmg) and after 29 attacks the health was about to go in the red (435 or 464 dmg), but the damage of that attack got reset due to the Rhydon fainting here. So the second Rhydon (a random one, 16 dmg/Mud-Slap) finished the battle in 10 attacks. The thresholds at which Ivysaur had 50% and 25% health remaining already indicated that the first Rhydon was doing 16 damage.This concludes that the effectiveness multiplier should be 1 (or as already explained above, the CPM value probably needs fine tuning). Since the experiment with Rhydon wasn't flawless, I decided to gather more data with Scizor vs Ivysaur (Scizor resists Grass moves, Lvl. 32 & 12 Atk IV).Scizor doesn't have any interesting influenced breakpoints with Fury Cutter (4 dmg) so I had to use a damage breakpoint for X-Scissor.In this case, for every 4 X-Scissors I would have to do 1 quick moves less if the damage dealt would be 51 instead of the expected 50.The first try didn't go as well because I was spamming Fury Cutter to fast and couldn't reliably count it afterwards, so didn't upload that footage. The second time I took some time in-between the quick moves to make it easier to count. Here is a link to the video. I managed to take down Ivysaur in 8 X-Scissors and 48 Fury Cuts. This correlates with either 48 * 4 + 8 * 50 = 592 or 48 * 4 + 8 * 51 = 600 damage. So it’s pretty evident that also Scizor was doing more damage than the damage calculations suggested, which indicates that the effectiveness multiplier is 1 (or as stated earlier, the CPM value probably needs refining and the effectiveness multiplier is 0.9996). So I wasn’t able to either proof or disproof that the type effectiveness multiplier is 0.9996.Maybe it is possible to proof it by doing tier 3, 4 or 5 raids since the CPM for those have actually been confirmed by information requests with the server and are therefore assumed correct.This also means that any specific breakpoints influenced by the effectiveness multiplier for tier 1 and 2 raids that I mentioned before are incorrect, since the CPMs are probably not precise enough (but can ‘easily’ be refined by doing some experiments with breakpoints like this).Any specific ones mentioned for tier 3, 4 and 5 should be correct.What’s left to tell you about the 0.9996 multiplier is some Pokémon (and potential raid bosses) that will be influenced by this that are coming out with the Generation 3 launch.Looking forwardNiantic promised that more Generation 3 Pokémon should be appearing as soon as this december. Therefore I thought that I should also say something about new Pokémon that are affected by the 0.9996 multiplier.In the table that I also linked somewhere near the top of this post all the Generation 3 Pokémon that influenced were also listed.Of course Pokémon placed in gyms will be affected by this, but as stated earlier, you can’t really predict those breakpoints since Gym Pokémon continually degrade their CP.I also ran some calculations for Generation 3 Pokémon as raid bosses (T4 Gardevoir and starter evolutions for example) but didn’t find any interesting results.However, if you can come up with any interesting match-ups where a new Pokémon can be influenced by this, please say so and I will run the calculations to see where Niantic is crediting us one damage to little (also for other/specific Gen 1 or 2 match-ups)I made this post because one day I was questioning if any attacks would be influenced by this. I couldn’t find any research towards this, so decided I would do it.Note that you probably won’t ever notice any breakpoints being lowered due to the type effectiveness multiplier being only 0.9996 instead of 1.Most Pokémon have a lot of damage breakpoints across different levels and IVs and maybe a handful of combinations result in 1 less damage due to this multiplier.Personally I think it would be nice if Niantic changed it to 1 because that is what it is supposed to be if a super effective and not very effective attack cancel each other out.Like I said earlier, the CPM values of tier 1 and tier 2 (probably) raid bosses are not 100% accurate. Therefore all damage or breakpoint calculators are showing incorrect values for a handful of data. This is not really important since it only influences very specific Pokémon at very specific IVs and Levels and besides that, they are easily beatable anyway, you probably don’t have to collect specific counters for them.However the CPM values can be fine-tuned by battling tier 1 bosses with Pokémon at different breakpoints where the unfloored damage is just above a damage threshold. I did all calculations in Excel and used macros to run through IVs and Levels of attackers. As far as I know, it is not common use to give download links for files. So here is a link to a Google Sheets version of it, where you can make a copy if you want to. via /r/TheSilphRoad http://ift.tt/2BiO1o8