Revision as of 07:54, 20 May 2007

The master hit chance formula is:

where

• BaseHitChance is the chance of hitting the attack would have if there were no modifiers at all – no Enhancements, no buffs, no level differences, nothing
• ToHitMods is the sum of all ToHit buffs and debuffs (the debuffs will be negative)
• DefMods is the sum of all relevant Defense buffs and debuffs (ditto)
• AccMods is the product of all Accuracy multipliers, and
• Clamp(x) limits x to the range of 5% to 95%

ToHitMods and DefMods are additive, so they default to 0. AccMods is multiplicative, so it defaults to 1.

BaseHitChance

If a player is attacking a critter, BaseHitChance depends on the critter's level relative to the player. The critter's rank is irrelevant. Roughly speaking, for critters close to the player's level, BaseHitChance will be 75% + 5% per level of difference if the critter is lower, or 75% – ~9% per level if it's higher. An exact table is at the end of this article.

If a player or critter is attacking a player, BaseHitChance is 50%.

Accuracy, ToHit, and Defense

ToHit and Defense work the same way, but in opposite directions. What they do is pretty simple: they directly modify the chance of hitting by the same amount as the modifier. (That is, they would be that simple if Accuracy didn't exist, but we'll ignore that for just a moment.)

Example: Let's say you're attacking something with a power that has a 65% chance of hitting. If you then got a +20% ToHit buff, your chance of hitting would go up to 85% (65 + 20). If your target then got a +10% Defense buff, your chance would drop to 75% (85 – 10). If you then had your ToHit debuffed by -23%, your hit chance would drop further to 52% (75 – 23).

Accuracy is subtly different. It modifies an attack's chance of hitting by a fraction of itself instead of by a fixed amount.

Example: Consider an unbuffed, unenhanced attack that hits 30% of the time. If it got a +50% ToHit buff, its hit chance would rise to 80% (30 + 50). If it got a +50% Accuracy bonus instead, its hit chance would only rise to 45% (30 + (50% of 30), or, alternately, 30 * 1.5).

Accuracy is applied in a second step, after all ToHit and Defense modifiers are applied.

Accuracy for Players

If the attacker is a player, he gets Accuracy multipliers from two places. These two numbers are multiplied together to get AccMods.

First, every power has an inherent Accuracy multiplier built into it. It might be greater than or less than 1.0, depending on whether the power is intended to hit more or less reliably than normal. Often, though, it's exactly 1.0 .

Second, a player can get an Accuracy multiplier from Enhancements. Accuracy Enhancements (not ToHit Buff!) in the power itself are the primary source for this kind of Accuracy. Invention Origin Enhancements Sets that give global Accuracy bonuses can also add small amounts to every power. This multiplier starts at 1.0, and Enhancements can only improve it.

So for players, AccMods is calculated using:

AccMods = InherentPowerAcc × EnhancementAcc

= InherentPowerAcc × (100% + that power's Accuracy Enhancements + all global Set Accuracy bonuses)

Accuracy for Critters

If the attacker is a critter, it gets Accuracy multipliers from three places. First, critter powers each have their own inherent Accuracy modifiers, just like player powers do. Second, critters get an Accuracy multiplier based on Rank. Third, if the critter is attacking a player, it will also get an Accuracy (and possibly a ToHit) modifier if it's of a higher or lower level.

So for critters, we have a slightly longer formula for figuring AccMods:

AccMods = InherentPowerAcc × RankAcc × LevelDifferenceAcc

Caps and Floors

Final hit chances are forced to stay in the range of 5%–95% to preserve a measure of uncertainty and prevent modifiers from making a power automatically hit or miss. This range limit is also applied once in the middle of the calculation, after adjusting for ToHit and Defense modifiers but prior to applying Accuracy, to prevent situations where strong Defense buffs and/or ToHit debuffs render Accuracy irrelevant no matter how high it was.

The Streak Breaker

On top of all the calculations above, there is a special feature in the game called the streak breaker. Its purpose is to prevent long streaks of misses, and it works by sometimes forcing a hit regardless of probability depending on how high the upcoming attack's final hit chance is and how many consecutive misses the attacker has had so far. This is a direct quote from Cryptic developer Weirdbeard:

Final to-hit : misses allowed

>.9 : 1
.8-.9 : 2
.6-.8 : 3
.4-.6 : 4
.3-.4 : 6
.2-.3 : 8
0 -.2 : 100
Auto-hit powers are not included in the system.
Critters get the benefits of the system as well.
The system does not track each power individually; instead it tracks every miss you make in a row, regardless of power (or target). Otherwise you could have nine different powers, each with a 0.95 to-hit, and if you executed them all in a row you could miss each attack (note a caveat at the bottom of the post regarding this).
[AoE] attacks are considered distinct sequential attacks on indivudual targets for the purpose of the system (so if you [AoE'ed] two targets and had 0.95 to-hit for both, you be guaranteed to hit one of them).

To determine the to-hit used in the table above, you take either the current to-hit, or the worst to-hit in your current miss series, whichever is lower.

Inaccuracies and Errors

Since launch, both players and developers have used the term “accuracy” interchangeably to mean all the following things:

1. actual Accuracy, as described here
2. ToHit
3. final hit chance

In fact, all powers and Inspirations currently in the game that provide ToHit bonuses or penalties are labeled as “+Acc” or “-Acc” in their descriptions. These are almost all incorrect. Only Accuracy Enhancements and global IO Set bonuses actually give Accuracy. All other powers and effects modify ToHit instead, regardless of game text.

Also, some older character builders contain data on inherent power Accuracy modifiers, but add it in with the Accuracy bonus from Enhancements rather than multiplying it as a separate factor. This is technically incorrect, though the resulting final hit chance is off by very little.

Results, Notes, and Observances

• The more Accuracy an attack has, the more every single ToHit and Defense modifier affects its chance of hitting.
• A ToHit bonus of X gives you a better increase to your chance of hitting than an Accuracy bonus of X will. The less likely you are to hit to begin with, the more extreme this difference becomes.
• Any attack with more Accuracy bonuses than penalties will have a guaranteed chance of hitting greater than the well-publicized 5% minimum. To be exact, it'll be 5% × AccMods.

Data Tables

References

• Arcana's Guide to Defense v1.4 - Updated for I7