MTR Psi Testing

This is a "lab notes" page for my (MikeTheRed) Psi Testing, if anybody wants all the gory details.

Conventions: Numbers such as 95/16 always mean, e.g., psi strength 95, psi skill 16. MC = psionic mind control.

Background

The equations governing psionic success have long been a subject of mystery and debate. If they were better understood, players could compare versus alien stats and know exactly how much Psi Strength and Psi Skill is needed, both as a minimum, and where one is maxxed out versus all aliens.

The Official Strategy Guide supplies psionic equations, but while they are very intriguing, they make no mathematical sense, as if the math operators are typo'd or something.

As part of my previous Experience testing ca. October 2005, I found that a 95/16 soldier directly next to a 25/0 muton had a MC success rate of 49% (1192/2420=49.26%), and that a 95/44 never failed. But I soon began to directly edit UNITREF.DAT experience counters for my tests, and thus didn't pursue in-game psi tests any more.

Ethereal Cereal performed the first true testing in May 2006, arriving at the equations:

Attack Strength (AS) = psi str * psi skill / 50
Defense Strength (DS) = psi str + (psi skill / 5)

Panic Attack chance = 44% + AS - DS
Mind Control Attack chance = 24% + AS - DS

For these equations, one is using the attack strength of one party versus the defense strength of the target.

He had a good number of data points, and the results appeared solid. However, they didn't agree with my one highly-tested point. His equation equals 29% for my 95/16 versus 25/0 situation, whereas I got 49% success.

One potentially important difference is that he had an alien MCing his soldiers, whereas I have my soldiers MCing aliens. Anyway, the results remained puzzling to me, but I didn't have time to do psi testing then. (EC, what version of X-COM are you using?)

Another reason it'd be good to know psi equations, is because effectiveness clearly decreases with distance. Again, how much strength and skill is needed to "totally rule", even across a large map? No one can say until the equations are deduced.

Test 1: Basics

Graph of Ethereal Cereal's equation results - click to see more details

For my test setup, I made a map with 16 mutons, and had 16 soldiers with psi amps that were directly next to and facing the mutons (zip file of it here).

For this first test, I wanted to keep it simple. I made all aliens 25/0, to compare with my earlier finding. Based on Ethereal Cereal's equations (see inset), if one attribute (Strength or Skill) is 100, the other can be up to 50% before the MC success rate is clipped at 100%. To simplify, half my 16 guys had Strength=100, half had Skill=100, then I chose eight equally spaced points within the range that would be applied to Strength or Skill (whichever was not 100 for those 8 soldiers). I chose this "alternating 100" approach because it would test the symmetry and, if it did look symmetrical, the results could be combined to give them more power (a better correlation coefficient on a regression line).

When choosing the eight points from 0 to 50, I also took into consideration how my finding was different from EC's, by 20 points. But I screwed up here and aimed for 0 to 70+... actually my finding was lower than his, so 0 to 50 would've encompassed all concerns. Anyway, I made my soldiers be 9 to 72 in the non-100 attribute.

Very quickly I saw that the higher half of each stick of eight was MCing 100%. So I limited my testing to the lower half of each stick (one attribute = 9, 18, 27, or 36; other attribute 100). I aimed for 50 trials, but went over by one, so N=51 per soldier. Each soldier only made one MC attempt per game turn (otherwise, it's problematical to have the target right next to them). I used the psi experience counter UNITREF.DAT[84] to determine success, because it's much less error prone than counting manually (this work is SO tedious!). But it counts by 1 for a failed attempt and 3 for a successful attempt, so this shows the success rate:

Successes = (UR[84] - Attempts)/2 = ([84]-51)/2
Success rate = Successes/Attempts = Successes/51

Given 51 attempts per soldier, the results were:

          UNITREF.DAT                                               Pooled
          [57]    [37]     MC    success        Pooled    Pooled   success  
 Soldier   Str     Skl  success    rate         attrib.   success    rate
    01       9     100     20      39.2%            9        39      38.2%
    02      18     100     29      56.9%           18        62      60.8%
    03      27     100     48      94.1%           27        96      94.1%
    04      36     100     51     100.0%           36       102     100.0%
    09     100       9     19      37.3%               
    10     100      18     33      64.7%               
    11     100      27     48      94.1%               
    12     100      36     51     100.0%

Although I suspected that the soldiers with an attribute level of 36 were maxed, I kept testing them, both to be entirely sure they were maxed, and as a check that I counted the number of attempts correctly, my UNITREF approach was working, etc.

The results do appear to be symmetrical, so they can be combined as shown in the pooled results above. N=102 for each of the four points, but the attribute=36 point is probably clipped (above the maximum) so it should be dropped from regression analysis. A regression line then drawn for success rate versus attribute level for the three points above (with the other attribute fixed at 100) gives the following for y=mx+b equations, where y is percent MC success, x is attribute level, and m is slope of line:

Int=0?     m         b         R2     100% Intercept
  no     3.10%     8.50%     0.9877     29.5
 yes     3.51%     0.00%     0.9682     28.5

In other words, when one attribute (psi strength or skill) is held to 100, every point of increase of the other skill increases MC success by 3.1% (if the regression line is not forced to go through success=0 at attribute=0) or 3.5% if the y intercept is set to 0. The 100% success ceiling is reached when the non-100 attribute equals ~29. Correlation rates are high.

Clearly, MC is more effective for me (i.e., lower attributes needed) than predicted by EC's equations. Until such time as it can be further understood, then, it appears that aliens are different somehow versus X-COM soldiers, such that they are less effective for a given psi strength and skill.

More to come --MikeTheRed 10:24, 2 September 2006 (PDT)