Psionic Equations

The equations governing psionics are as follows:

 Attack Strength (AS) = INT( Psi Strength * Psi Skill / 50 )
Defense Strength (DS) = INT( Psi Strength + ( Psi Skill/5 ) )
  
   Attack Chance (A%) = 100/56 * ( Constant + AS - DS - Distance )

               where
             Constant = 25 for Mind Control
                        45 for Panic

Attack Chance (A%) is a number (0 to 100), not an actual percent (0.00 to 1.00). Values less than 0 mean guaranteed failure, and greater than 100 mean guaranteed success.

The further away a target is from its attacker, the lower the chance an attack will succeed. Distance follows the "walking TUs" method, where a distance 10 tiles directly lateral equals 10 in the equation, but diagonal distances are more. For example, 10 tiles away on a pure diagonal is considered to be 15 tiles away; see this for more on Walking TUs distance. The distance factor means that beyond a certain point, aliens can only panic a unit, not mind-control it.

The OSG Speaks

The text of the Official Strategy Guide section on Psionics (p. 227) is reproduced here, for comparison. Thanks to Zombie for transcribing this:

Chances for Success in Psionic Combat

Only soldiers with high ratings in psionic strength and psionic skill should use this form of combat, because it is difficult to master. A soldier's psionic combat strength is determined as follows:

(Psionic strength) x (psionic skill) = (psionic combat strength)

A soldier with a psionic strength of 20 and a psionic skill of 50, for example, has a psionic combat strength of 1000.

When you use a psionic attack on a target, the base chance of success is determined by subtracting the target's psionic defense from the attacker's psionic combat strength. The defense value against mind-control attacks is higher than the defense value against panic attacks.

The psionic defense against panic attacks is determined as follows:

(Psionic strength) + (psionic skill/5) + (10) = (panic defense)

The psionic defense against mind-control attacks is determined as follows:

(Psionic strength) + (psionic skill/5) + (30) = (mind control defense)

So the base chance of success for a psionic attack is determined as follows:

(Attacker's psionic combat strength) - (target's psionic defense) = (base chance)

For example, a soldier with a psionic combat strength of 1000 attacks an alien with a psionic defense of 950. The base chance of success is 1000 - 950, or 50%.

Psionic attacks decrease in effectiveness over distance.

Defending X-COM Soldiers Against Psionic Attack

When X-COM soldiers fall under alien psionic attack, there is a brief flash around the soldier being attacked. If the attack is successful, the victim either panics or falls victim to alien mind control.

Psionic defense for X-COM soldiers uses the same formula as shown earlier. It is best to have soldiers with the highest possible psionic abilities because they are much less susceptible to psionic attack. This is especially true late in the game, when more psionically endowed aliens tend to show up.

Taken together, the equations as presented in the OSG would look like this, if re-written in our format:

 Attack Strength (AS) = Psi Strength * Psi Skill
Defense Strength (DS) = Psi Strength + ( Psi Skill/5 )
  
   Attack Chance (A%) = Constant + AS - DS

               where
             Constant = -30 for Mind Control
                        -10 for Panic

As can be seen, while what the OSG shows is more or less correct in and of itself, it omits important details:

The Attack Strength portion (PST * PSK /50) doesn't show the divisor of 50
The slope factor (100/56) is missing
The distance factor was not shown (1 per tile)
The constants (OSG 10 and 30 versus actual values of 25 and 45) are 15 points low. Also, as presented (as part of the Defense Strength which is subtracted), they result in negative values which are subtracted, when the constant should be added. This leads to a final variance of -35 for Panic attacks (+25 missing, then -10 more) and -75 for MC (+45 missing, then -30 more), versus the correct results.

The absence of the 50 AS divisor was probably the most egregious omission (a.k.a., "these numbers don't make a bit of sense!"), although the constants being so far off didn't help one bit. One could've gotten a close approximation (results that at least made some sense in the game) if only the slope and distance factors had been omitted. But notice how the OSG author himself (David Ellis) lists an incorrect example - how'd he ever get 950 for a Defense Strength?

All in all, it suggests that Ellis never knew the full equation. This can readily happen when an author talks to developers and they tell him a ton of new, important things, but then later he finds that despite the avalance of information, it still wasn't the whole story... but he doesn't have time to follow up amidst the many other things in the book. Not to put down the OSG... It's a remarkably long and comprehensive game guide, relative to many other single-player game guides. Inevitably, some deep game details don't make it, in the all-important shuffle to get the guide out quickly, so it can hit the streets the same time the game does (the peak buying period).

Be that as it may... due to incompleteness, the OSG's psi equations have long frustrated players attempting to use them.

Psionic Equations

Psionic Equations

The OSG Speaks

See Also

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