Psionic Equations

This page is an in-depth exploration of equations used for psionics.

Conventions:

• PST = Psi Strength
• PSK = Psi Skill
• MC = Mind Control
• Values such as "95/16" represent a unit with Psi Strength 95, Psi Skill 16.

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
```

For this equation, Attack Chance (A%) is always 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.

Things that don't matter:

• Having Line of sight (direct visualization) on the target
• Aliens use the same equation as soldiers
• Different X-COM editions (DOS 1.4 also WinCE Gold) also doesn't matter
• Differences in elevation have no effect; this doesn't add to distance. (Careful, though - this means you're at distance 0 when directly over or under aliens - see Aliens Vs. X-COM, below.)

The Attack Chance equation can be re-arranged to compute particular values:

Attack Strength

When re-arranged to have AS on the left, the equation becomes:

``` AS = DS + .56A% - Constant + Distance

AS for 100% MC  =  DS + 56 - 25 + Distance  =  DS + Distance + 31
AS for   0% MC  =  DS +  0 - 25 + Distance  =  DS + Distance - 25
```

For Panic percent success instead of MC, subtract 20 from the right-hand side of equation.

Defense Strength

``` DS = AS - .56A% + Constant - Distance

DS for   0% MC  =  AS -  0 + 25 - Distance =  AS - Distance + 25      - never MCed
DS for 100% MC  =  AS - 56 + 25 - Distance =  AS - Distance - 31      - always MCed
```

For Panic instead of MC, add 20.

Distance

The distance at which a particular effect can be accomplished can also be computed. Think of the attacker as surrounded by two concentric circles where anything within the inner circle (of distance a.k.a. radius R) will have 100% attack success, and anything outside the outer circle will have 0% success.

``` Distance = AS - DS - .56A% + Constant

Distance for 100% MC  =  AS - DS - 56 + 25  =  AS - DS - 31
Distance for   0% MC  =  AS - DS -  0 + 25  =  AS - DS + 25
```

For Panic instead of MC, add 20. (The "concentric rings" for Panic success are 20 tiles further from the attacker.)

As you may have guessed, the outer distance/radius is R+56. In other words, the outer, 0% circle is 56 tiles radius farther than the inner circle of 100%. Compare that a 5x5 tileset map is only 75 tiles across at its widest diagional... there's a huge area within the inner and outer circles!

Psi Stats versus Psi Strengths

As shown in the equation, psi strength (PST) and psi skill (PSK) do not contribute equally to Defense Strength (DS) and Attack Strength (AS).

DS is PST plus a fifth of your PSK. Basically, soldiers are born with most of their DS, and can only add 20 more points by maxxing their PSK.

AS is PST*PSK/50. Because PST doesn't change for soldiers, another way to consider the AS equation is a PST/50 "view". PST/50 can vary from 0 to 2 (for PST 0 to 100), which then multiplies your PSK. So if your soldier has a middling PST (e.g. 50), each new PSK point adds one more point to his AS. If she's a psi master (PST 100), each new PSK point adds 2 more to her AS. Because your PSK can increase up to 6 points per combat, a psi master's AS can increase up to 12 points per combat.

Tables for DS and AS, by PST and PSK:

```          Defense Strength

PSK
0   10   20   30   40   50   60   70   80   90  100
PST   0    0    2    4    6    8   10   12   14   16   18   20
10   10   12   14   16   18   20   22   24   26   28   30
20   20   22   24   26   28   30   32   34   36   38   40
30   30   32   34   36   38   40   42   44   46   48   50
40   40   42   44   46   48   50   52   54   56   58   60
50   50   52   54   56   58   60   62   64   66   68   70
60   60   62   64   66   68   70   72   74   76   78   80
70   70   72   74   76   78   80   82   84   86   88   90
80   80   82   84   86   88   90   92   94   96   98  100
90   90   92   94   96   98  100  102  104  106  108  110
100  100  102  104  106  108  110  112  114  116  118  120

Attack Strength

PSK
0   10   20   30   40   50   60   70   80   90  100
PST   0    0    0    0    0    0    0    0    0    0    0    0
10    0    2    4    6    8   10   12   14   16   18   20
20    0    4    8   12   16   20   24   28   32   36   40
30    0    6   12   18   24   30   36   42   48   54   60
40    0    8   16   24   32   40   48   56   64   72   80
50    0   10   20   30   40   50   60   70   80   90  100
60    0   12   24   36   48   60   72   84   96  108  120
70    0   14   28   42   56   70   84   98  112  126  140
80    0   16   32   48   64   80   96  112  128  144  160
90    0   18   36   54   72   90  108  126  144  162  180
100    0   20   40   60   80  100  120  140  160  180  200
```

Attack Strength is symmetrical, but Defense Strength is not.

Alien Psi Stats

Alien psi stats for all levels have been summarized here. For a spreadsheet of all psi stats (only) see this, or for ALL alien stats, see this.

Most players (these days!) are playing at Superhuman difficulty level. Here's a table of all Superhuman psi stats, sorted by decreasing Defense Strength:

``` Alien/Rank             DS   AS    PST  PSK    N
Cyberdisc             116    -    116    -    1
Sectopod              116    -    116    -    1
Silacoid               92    -     92    -    1
Ethereal Commander     86   87     75   58    1
Zombie                 80    -     80    -    1
Ethereal Leader        79   71     69   52    1
Sectoid Commander      71   80     58   69    1
Sectoid Leader         69   67     58   58    1
Celatid                69    -     69    -    1
Ethereal Soldier       67   53     58   46    1
Chryssalid             58    -     58    -    1
Snakeman Commander     58    -     58    -    1
Floater Commander      52    -     52    -    1
Snakeman Leader        52    -     52    -    1
Floater Leader         46    -     46    -    1
Sectoid (Common)       46    -     46    -    4
Snakeman (Common)      46    -     46    -    3
Floater (Common)       40    -     40    -    4
Reaper                 40    -     40    -    1
Muton (Common)         29    -     29    -    3
Civilian (Common)       5    -      5    -    2
```

As for Defense Strength:

• The strongest defenders are robots (DS 116), then exotics (silacoid 92, zombie 80) and psi-active aliens (86-67).
• Squarely in the middle are celatids (69), chryssalids (58), and psi-inactive leaders (58-46 for Snakeman and Floater LDRs and CDRs).
• Reapers (40) are by far the most susceptible terrorist.
• Common ranks (navigators, engineers, medics, and soldiers except Ethereals) are at the low end (46, 40).
• All mutons are the lowest of any enemy (all 29; mutons do not have leaders).
• Civilians basically have no defense at all. Ironically, this might mean they'll survive the worst attackers of all better (Ethereals), since many might be MCed! Has anybody seen this?

Here are Superhuman psi stats for psi-active aliens, sorted by descending Attack Strength:

```  Alien/Rank            DS    AS   PST   PSK
Ethereal Commander    86    87    75    58
Sectoid Commander     71    80    58    69
Ethereal Leader       79    71    69    52
Sectoid Leader        69    67    58    58
Ethereal Soldier      67    53    58    46
```

Notice that four out of five have a DS approx. equal to or greater than their AS, but the Sectoid Commander has a lower Defense than Attack strength.

X-COM Vs. Aliens

Surface chart of X-COM PST and PSK for chance of MC on a muton (DS 25) at distance 25. If PST and PSK are both low, there's no chance (the red in the spreadsheet). If they're both high, then it's guaranteed (blue).

For every alien at a given distance, a surface (3D) graph of the PST and PSK needed to psionically attack can be made (see inset). But due to the fact that Psi Strength never changes for a given soldier, it's probably easier to consider PST as fixed, in which case only Psi Skill varies - which makes for a simple line equation (Psi Skill vs. Attack Strength, where AS equals percent Panic or MC success).

Along these lines, a table can be made that shows the Psi Skill that a soldier with high Psi Strength (PST 90) needs for a guaranteed (100% AS) chance to Mind Control an alien. Because Psi Strength is randomly determined for recruits, 10% of your soldiers will have PST 90 or higher.

I've shown Superhuman in the table because many of you are probably playing at that level, but the lowest target (Mutons) at Beginner difficulty level is also shown for comparison. If anybody wants to see numbers for other difficulty levels, let me know - MTR.

Some observations can be made, which reflect how the equation operates:

• Distance is always a simple additive. Your Attack Strength must be +15 if a target is at distance 25 instead of 10.
• The difference between 0% chance and 100% chance is always +56 AS. This is due to the slope of the equation (100/56). Here, the equation is re-arranged for an inverted 56/100, which is then multiplied by 100 for the 100% chance.
• Related to this, the Psi Skill needed by the PST 90 soldier in the last column of the table does not rise as fast as defense strength. This is because, at PST 90, every 1 point of PSK increase is worth a 1.8 point increase in Attack Strength (AS= 90/50*PSK= 1.8*PSK). A difference of 56 AS for a PST 90 soldier equals a PSK difference of 31, not 56 (31= 56/1.8= 56/90/50).
• Notice that the psi equation Constant disappears at distance 25 (Constant +25, Distance -25). This shows up as the Defense Strength being equal to the 0% Attack Strength. Maybe the programmers used this "average" distance of 25 as a benchmark to design their equation around.
• Also notice that the weakest possible target - a Beginner Muton at distance 1 - pins down the lower end of where Attack Strength begins to have an effect. If, in theory, you could have a 0 PSK soldier who could psi attack, he would just barely not be able to affect the weakest possible target. Interestingly, if you hack a target to a Defense Strength less than 25, soldiers with the weakest possible Attack Strength (1) can successfully Mind Control them.
• Rookies with a maxxed PST (100) won't quite have the 32 Attack Strength needed to 100% MC an adjacent Beginner Muton right out of the Psi Lab, but they'll be close. 24 is the highest PSK one can have coming out of the lab; 100*24/50 is an AS of 48, which is close to the 57 needed for a 100% MC chance. But then few soldiers will be both 100 PST and 24 PSK right out of the lab (only 1 in 909 - 0.11% - will be), nor is a Beginner Muton always right next to you. :) For a more likely scenario - a 90/20 psi newbie (AS 36), and a Superhuman Muton (DS 29) at distance 25 - you have a 12.5% chance of MC right out of the gate. And you can't touch any of the tougher aliens, not yet - but you can gain 3 to 6 PSK, and 5 to 12 AS (at high PST), each combat.
• The game is well-designed inasmuch as soldiers grow from just barely being entirely psi worthless (unable to affect an adjacent Muton; see above) to being able to MC the toughest targets over long distances, at very high Psi Skill. And you do need high Psi Skill for even high PST soldiers to be certain of MC on the toughest targets. But due to the fact that you may have a number of mid-range PSK soldiers with high PST, each of whom can make 2 or 3 MC attempts, even tough targets are rarely a problem for high PST but mid-range PSK soldiers.
``` Level        Target                 PST     PSK      DS    0% AS  100% AS  =PSK*  Notes

Weakest possible alien target, directly adjacent (distance 1)

Beginner     Muton                   25       0      25       1      57      32   The weakest possible alien target, directly adjacent

Short range (distance 10)

Beginner     Muton                   25       0      25      10      66      37   Beginner Mutons
Superhuman   Muton                   29       0      29      14      70      39   Superhuman Mutons
"        Common                  46       0      46      31      87      49   Gets all sub-LDR Floaters, Snakes, Sectoids, & Reaper
"        Sectoid CDR             58      69      71      56     112      63   Gets all but Ethereal LDR+, Zombie, Silacoid, Robots
"        Ethereal LDR            69      52      79      64     120      67   The Zombie is 1 DS higher (DS 80)
"        Ethereal CDR            75      58      86      71     127      71
"        Silacoid                92       0      92      77     133      74
"        Cyberdisc & Sectopod   116       0     116     101     157      88   Robots have the highest DS

All the above, at medium range (distance 25)

Beginner     Muton                   25       0      25      25      81      45
Superhuman   Muton                   29       0      29      29      85      48
"        Common                  46       0      46      46     102      57
"        Sectoid CDR             58      69      71      71     127      71
"        Ethereal LDR            69      52      79      79     135      75
"        Ethereal CDR            75      58      86      86     142      79
"        Silacoid                92       0      92      92     148      83
"        Cyberdisc & Sectopod   116       0     116     116     172      96

All the above, at long range (distance 50)

Beginner     Muton                   25       0      25      50     106      59
Superhuman   Muton                   29       0      29      54     110      62
"        Common                  46       0      46      71     127      71
"        Sectoid CDR             58      69      71      96     152      85
"        Ethereal LDR            69      52      79     104     160      89
"        Ethereal CDR            75      58      86     111     167      93
"        Silacoid                92       0      92     117     173      97
"        Cyberdisc & Sectopod   116       0     116     141     197     110

Worst cases at extreme distance (opposite corners of 5x5 map; distance 75)

Superhuman   Ethereal CDR            75      58      86     136     192     107
"        Cyberdisc & Sectopod   116       0     116     166     222     124
```

* "=PSK" is the Psi Skill needed for 100% MC, for a soldier with PST 90.

207 Psi Attack Strength is the upper critical value. Psi Strength x Psi Skill = 10350, so 100 psi strength and 104 psi skill, or some similiar combinations will do it. This figure will give a soldier 100% chance to mind control a Superhuman Sectopod/Cyberdisk from 90 tiles away... which is the maximum in the game (from 1 base corner tile to the opposite corner tile)
Hi Jasonred, sorry for delay in responding. The farthest distance is 75 using the Walking TUs method, which needs a 222 Attack Strength for a 100% MC chance on the Cyberdisk or Sectopod. Unless I am missing something about XCOM distances or the Psi formula... in which case, please let me know! Otherwise we might remove these two comments. I like your next paragraph, though... I never thought of that, but it's true (and interesting). "Psi retard"... hehehe -MikeTheRed 20:34, 2 July 2009 (EDT)

Even a soldier with theoretical 0 AS aka ZERO psi skill/strength/attack has a 29% chance to panic a Muton from a distance of zero (directly above or below). He can't activate a Psi-Amp without at least 1 Psi Skill; assuming 1 Psi Strength and 1 Psi Skill (impossible under normal gameplay since the first month of psi training gives more than 10 skill - but the difference is negligible in this example), even this Psi retarded individual has a 1.8% chance of panicking a Muton at 15 distance for superhuman, and 19 distance on beginner.

Aliens Vs. X-COM

This table shows the 0% MC success distance for X-COM soldiers versus the five psi-active aliens:

```                                       Distance for 0% MC success chance,
for X-COM soldier of Defense Strength ...

Alien/Rank           PST   PSK   AS      0    25    50    75   100  Invulnerable DS
Ethereal Commander    75    58   87    112    87    62    37    12    111
Sectoid Commander     58    69   80    105    80    55    30     5    104
Ethereal Leader       69    52   71     96    71    46    21     -     95
Sectoid Leader        58    58   67     92    67    42    17     -     91
Ethereal Soldier      58    46   53     78    53    28     3     -     77
```

This is the distance at which you are safe from MC. At any closer distance, you're not safe, at a rate of ~2% MC success per tile closer (1.78% per tile; 100/56).

At 56 tiles closer than the distances shown, you are 100% vulnerable. Thus a total wimp DS 0 soldier can always be MCed by an Ethereal Commander at distance of 56 or less (112-56), that is, over the majority of the map. And of course a 5x5 map is 75 tiles wide at the diagonal, meaning an Ethereal Commander has a good chance of MCing a psi wimp anywhere on any map - as we've all learned to our chagrin.

The Invulnerable column shows the Defense Strength a soldier needs to be entirely safe from MC for each type of alien (a.k.a., 0% MC at distance 1). A DS 100 soldier only just barely has a chance of being MCed even when adjacent to psi active Commanders, and a DS 120 soldier (100/100) is entirely safe from MC, even right next to an Ethereal Commander.

For 0% Panic success distances, add 20 to the distances shown, and also to the Invulnerable column. So a 100/100 (DS 120) soldier can still be panicked by an Ethereal Commander when very near, although the chance is low. You'd have to be DS 131 to be entirely safe from Panic when directly next to an Ethereal Commander, but that would require, e.g., 100/155!

• The DS 0 to DS 100 columns reflect the distribution of Defense Strength for psi-locked soldiers.
• Elevation does not affect psionics. On a number of UFOs (Abductor, Harvester, and Supply Ship), you are very "close" to aliens on the bridge as you enter the ship. Indeed, if you are directly under them, you are at distance 0, even if they're on the third floor. None of the information on this page directly addresses distances of 0... you'd actually need a DS of 112 to be invulnerable to MC if directly under (or over) an Ethereal Commander.
• In the early days - before you get psi - only about 10% of your crew will be invulnerable to MC by Sectoid Leaders. So if you have 20 soldiers, only about 2 will never lose their wits. Still, it takes a DS 40 to be 100% vulnerable... over half your crew will be better than this. Furthermore...
• Psi-active aliens like to waste their TUs on your wimpiest soldiers, leaving the others free to act.
• But do remember that this changes as a function of distance... that's why things can get really crazy when, e.g., entering a Sectoid Abductor... your Panicked and MCed soldiers may be far afield right at the point that you're higher-DS soldiers enter the ship under its bridge, and need to clear that inner, lower room that's often packed with aliens. Now they may be the "best" targets! (Try keep your weaponless psi wimps close to psi-active aliens, so that the wimps will remain the best targets.)

While all of this is true, don't forget that you typically have many decent psi-unlocked soldiers pretty soon after getting psi, each of whom will get 2 or 3 psi attempts. Combined with the fact that aliens will be going for your wimpiest dudes, chances are very good that you can successfully psi attack even Ethereal Commanders before they successfully attack all of your guys, as we've all seen.

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 -30 and -10 versus actual values of 25 and 45) are 55 points low.

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.

Note

This is all the work I plan to do for the time being; I think I've covered all the pertinent details. I hope you've enjoyed it. If you'd like something shown in more depth, or think of something else entirely, just let me know! --MTR