## My dissertation on damage numbers

Maybe multiplying by 3 and dividing by 2 would work just as well, or perhaps dividing the original number by 2 and adding that result back to the original number will suffice.

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Game Freak does none of these: instead, they multiply by , and divide by So instead of multiplying by 1. Game Freak decided to do this for consistency across all of its modifiers. Division is much easier for computers if the divisor the number on the bottom of the fraction is a power of 2, and so Game Freak just picked and rolled with it for all their modifiers in the damage formula. A good example is Life Orb, which boosts damage by roughly 1. Properly speaking, only the is actually stored; whenever a modifier is applied, it always does the same step of dividing by , then pokeRounds the result.

Here it is as a formula:. This was one of the most confusing parts of the damage formula for me to understand personally, and I would encourage you to check out the examples when we get to our sections that use chained modifiers to help with comprehension. See this proof of concept as a demonstration that normal rounding is used when chaining modifiers, as opposed to pokeRounding or flooring.

When reading, these sections can mostly be tackled in any order, and you can click on the links above to jump around to whatever interests you the most. The damage formula only gets more complex from here. To start off, plug in our values for level, base power, Attack, and Defense:. To tackle solving this, we need to work from the innermost floor to the outermost floor.

First floor taken care of. Like before, flooring means we truncate the decimal, so Floor Previously, we were calculating the base damage.

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These steps are applied in this order for general damage modifiers, one after another. If the weather is Harsh Sunlight e. The exact multiplier for critical hits is currently unknown.

MY DISSERTATION ON DAMAGE NUMBERS IN TF2

The odds of getting a critical hit are dependent on the critical hit ratio:. The current damage is multiplied by a randomly generated number from 85 to , inclusive, then divided by , and finally the result is floored. As a formula, this is represented by the following:. This will give you 16 different possible damage rolls.

You will only use 1 Random Factor per move, and each hit of a multi-strike move has a new Random Factor generated that is independent of the Random Factor of the previous hit. At this point, the game just picks one of these 16 values to use. For the purposes of damage calculators, all 16 possible damage rolls are considered, and all 16 possible damage rolls will need to have the remaining modifiers applied to them individually.

Determine the type effectiveness of a move via the type chart. An example type chart can be found on Bulbapedia. Properly speaking, the type modifier is just a bitshift of 1, 2, or 3 left or right, which is equivalent to multiplying or dividing by 2, 4, or 8 depending on the effectiveness and flooring the result. Electric is super effective vs.

Water-types , while the type effectiveness modifier is the end result e. Electric is 4x vs. These can affect both type matchups and the type effectiveness modifier, and generally follow this order:. See the section on final modifiers for more information. Clangorous Soulblaze into Wide Guard and Protect will still multiply damage by 0. This means it is still possible to do 0 damage, given that you have an move that deals a multiple of 65, damage.

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See this proof of concept of being able to deal 0 damage in Generation 7. For example, if the damage calculated by the damage formula is going be , but the defender only has HP remaining, the move will only deal damage. Def Amoonguss , in Rain, and as a spread move in a Double Battle. Before we begin with general damage modifiers, though, we have to determine the base damage. Chopping off the decimal, Floor So is our base damage for this calculation.

So is our minimum damage. The maximum damage is much easier to find: the maximum damage roll is the same as Current Damage , because the Random Factor is 0, and anything multiplied by then divided by will not change its value. In this case, our maximum damage is , giving us a range of damage.

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There are no modifiers left to apply, so this is the damage Water Spout will do to Amoonguss: Final modifiers are chained together in this order, and the end result is applied in step 9 of the general damage modifiers. The game does not check whether or not the move is single-target for the purposes of screens checks, only what format the battle is in.

As a result, it is possible to have a single-target spread move affected by the Doubles screens modifier at the same time. The duration of Aurora Veil and a regular screen can overlap, but their effects combined do not stack i. Always start with as our first OldCombinedModifier.

The first final modifier we have is Reflect Which evaluates to Next, we plug in as our old modifier, and chain the second final modifier in the list, Shadow Shield Finally, we have something significant! So rather than round down like we do in pokeRounding, we round up on 0. Given , we apply our last modifier: Life Orb This evaluates to NormalRound This makes our final modifier that we would use in step 9 of damage calculation. Our minimum and maximum damage rolls will be Applying STAB gets us to Now, at the final modifier step 9 of the general damage modifiers :.

All of these moves have an internal default base power, which is normally unused; however, the default base power does get used when the move is affected by the Rollout Storage glitch more on that when we get to Rollout. If any of these moves have a base power less than 1 after their calculation is complete, make it 1 BP. For Speed calculations, the Speed used for the attacker and the defender is the Speed after all Speed modifiers have been applied.

For weight calculations, the weight used for the attacker and the defender is the weight after all weight modifiers have been applied.

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Weight calculations are done in kilograms. Happiness is a value that corresponds from Details on happiness can be found on Bulbapedia. A Smeargle or Ditto at base happiness e. The maximum multiplier without Defense Curl is 16x, while the maximum multiplier with Defense Curl is 32x. When Rollout breaks a Disguise, the Rollout counter increases by 1 for the purposes of keeping the attacker locked into Rollout, but Counter does not similarly increment.

If Rollout breaks the Disguise of multiple Mimikyu, the multiplier will be delayed for each time Disguise is broken. Rollout Storage will stay active until some damaging move that uses the damage formula consumes the glitch e.

If the Rollout Storage-boosted move is a move with custom BP, multiply the Rollout Storage by the default BP, and do not undergo its normal calculation e. If the next move is a multi-hit move, Rollout Storage only applies to the first strike of the multi-hit move. Being affected by Rollout Storage is not something copied by Transform. Negative stat drops will not affect these moves e.

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If the base power is greater than , make it If Trump Card is called via a move that calls another move e. Metronome, Sleep Talk , the base power will be determined with respect to how much PP the move that calls another move will have after usage. If the move has custom BP , evaluate its base power first; otherwise, use the regular base power of the move what is listed in the summary screen. Base power modifiers are chained together in this order, and the end result is applied to the starting base power before being used in the base damage formula.

Apply the chained modifier to the starting base power. That is, multiply the starting base power by the chained base power modifiers, divide by , and pokeRound the result. If the base power would now be less than 1, make it 1. Calculate the final base power for a Tapu Koko with happiness that uses Return, affected by the effect of Electrify. Tapu Koko is holding a Zap Plate, and on the previous turn, it had used Charge. To start off, Return is a move with custom base power, so we need to determine that first before we get into chaining modifiers.

So Return has a starting 85 BP. The first BP modifier we have is Zap Plate Next, we plug in as our old modifier, and Helping Hand as our next BP modifier.

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