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Damage Modifiers for Aliens


Zombie

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Are your tests for initial impact damage only, or have you included the universal fire damage caused by incendiary impact damage to units standing in fire? I think we're just expecting incendiary effects to behave like a normal area effect weapon.

The Quarterpod for my Incendiary test was standing in the air, thus negating the effect of it standing in fire. I shot at the Quarterpod with an Incendiary round once, then aborted. I didn't think we were after the additional damage inflicted to a unit if it was standing in fire. If you want, I could expand my tests somewhat to include these at a later date. And yes, Incendiary ammo is not really an area effect ammunition like high explosives are.

 

Thanks for modifying the Heavy Plasma to accept the Stun Bomb and the Incendiary Rocket. That was a good idea. I downloaded all your new Sectopod and Reaper test games. There are a couple of things I would like to see for later scenarios.

 

1) All the soldier's health modified to 200.

2) More space between the test aliens. (And equal space mind you). It's just easier with the area effect weapons. If the HE damage is modified to do 50, then 10 spaces between the test subjects is sufficient. 5 spaces to the edges of the map is also good.

-OR-

6 or so spaces between test subjects with 2 barriers (like a hedge, a fence, a stone wall) between them. I realize that these are just cosmetic changes and won't affect the trials much, except to give me piece of mind that extra damage isn't being inflicted from the units being spaced so close. (The barriers sop up the spillover damage).

3) A mind-controlled Sectopod (under X-COM control) with it's weapon damage modified to do 50.

4) A mind-controlled Cyberdisc (under X-COM control) with it's weapon damage modified to do 50.

5) A mind-controlled Celatid (under X-COM control) with it's weapon damage modified to do 50.

 

You might be able to combine the last three suggestions into a single scenario. A Sectopod, Cyberdisc and Celatid each shooting at a different Sectopod target. I would like to test out those terrorist weapons against the different aliens. Stupid? Maybe. But while we are at it, we might as well give it a go if it isn't too much trouble! :)

 

-----

 

Bomb Bloke: can you make another version of your program which just records the stun damage, or will it be a combo-logger? (Both health and stun)? It would just be easier with a separate stun logger, that's all. If it's too much trouble, don't bother. :)

 

-----

 

I am rapidly finishing the final HE test against the Quarterpod. (Q-L0, S-L1). I also formulated a working theory on why the HE tests are different from normal ammunition. Now it just has to pass the mathematical scrutiny test before I can offer it to everyone. I'll keep you informed! :P

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Actually, I was thinking of getting a few UFO walls put between the test subjects to block excess area effect damage. Wouldn't be too difficult to implement I'd imagine. I know they're next to impossible to blow to pieces unless they're on mountain terrain ground tiles, and I very frequently employ a strategy where I drop a high explosive on one side of the wall and take one step aside behind a UFO wall to escape its effects. However, fire and smoke may seep through.

 

As for the terror unit turrets, I can actually just install the turrets on a few X-Com controlled units if you want. However, the damage of the guns are stored in one of the executable files, and are therefore beyond my ability to edit. Of course, someone out there knows where it is.

 

Or, I can make the targes all have 100 armour. You won't be able to count the iterations of values under 100 that way though. But it will reduce the damage so that it doesn't kill the test subjects outright. So when guessing the damage done, don't forget to add 100 to it (or whatever the armour was before the shot, as armour can deteriorate). Would that work?

 

- NKF

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When it's done, it'll be a combo logger. Each stat will go into it's own file, though, so you can effectively treat it as a single logger.

 

The stats I will have it log are:

 

- Current armor on each side

- Amount of armor lost from each side

- Current amount of health that unit has

- Amount of health that unit has lost

- Amount of stun damage

- Amount of moral lost

- And maybe whether the unit has been set on fire.

 

Anything else I should add?

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NKF:

 

That is a very good idea using UFO walls to separate the test "subjects". They are pretty much impossible to destroy with the weapon damages we are using for the test scenarios anyway. Doesn't matter if they let smoke or fire "seep" through, as long as the distances remain roughly the same.

 

A couple of additional things I would like to see added is:

1) The soldier's Time Units increased to 80. (As it stands now, it is tough to properly set the soldier up to start testing in the first round. Waiting till the second round makes some of the "quarterlings" recombine into their 2x2 counterparts. Everything takes TU, and dropping items in the hands to make room for the weapon(s) in the backpack, then loading the weapons leaves few TU to do much of anything, especially with their meager stats). :P

2) The soldiers equipped with the ability to fly. This helps when I have to move them around for the HE testing. It's just easier so I won't have to manually edit the soldiers to fly. Just strip off any armor of the Suit, and increase the Health of the soldiers to 200.

 

For the Terror units: Again, good idea to equip a soldier with the "turret". So you can't change the damage associated with the weapon. Hmmm. See, the max damages we are talking about is this:

Celaitd: 140*2 = 280

Cyberdisc: 130*2 = 260

Sectopod: 100*2 = 200

 

My question is this: Those damages are awefully close to 300. Is it possible to increase the health of the units to 300? I know that the "cap" is 255, but what would happen if you cranked it up to 300? Would the game crash, or would the health just go into the negatives once past 255? The Sectopod's weapon should deal a max damage of 200, which might be close enough so you wouldn't have to modify anything, but the other aliens have theoretical damages 80 points more (not to mention Sectoids and Floaters which are 1.6 times more susceptible to Acid Spit which could have damage as high as 480)!

 

Bomb Bloke:

 

Awesome! Splittin' the different stats up into a separate file is just as good! The only other things I see missing from your list is possibly current Time Units and current Stamina (Energy).

 

If you could, just start with the stun logger. I'm ready to begin the tests for stun, and the only thing preventing me from doing this is that your logger (which helps tremendously) only takes down the health stat. It's possible I can hold out for a little while as the full Sectopod tests for HE and IN need to be done yet. Other than that, I'll have to skip to the Reaper tests to keep busy. I'd just like to finish the Quarterpod tests first, so that I can sign off on the data and give a short conclusion, that's all. Then move to the Sectopod, the Reaper quarterlings, the full Reaper, etc. :)

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Ok, I wrote the new version just this morning. It's stashed in a rar file instead of a zip file, but I presume you have proper compression software on your system. :)

 

Installation is the same as before, but as you've already got the original setup, all you really need to do is extract the archive right into your game directory. Then run the reset program, so it can get it's bearings, and you're good to go. the old log file will be ignored by the program, as logs now go into a sub-directory, called '_logs'. Names and uses:

 

badamage.txt - Damage to back armor

barmor.txt - Current back armor

damage.txt - Total health lost

echarge.txt - The amount of energy a unit will recharge per turn

fadamage.txt - Damage to front armor

farmor.txt - Current front armor

health.txt - Current health

ladamage.txt - Damage to left armor

larmor.txt - Current left armor

morale.txt - Current morale

radamage.txt - Damage to right armor

rarmor.txt - Current right armor

stun.txt - Current stun levels

uadamage.txt - Damage to under armor

uarmor.txt - Current under armor

 

I thought of logging the TUs and current energy points, but couldn't think of a single use for them... :P I can add them if you like. Indeed, with a little more tinkering, I could add an ini file, which would allow you to easily add extra logs...

 

Concerning the energy recharge log. Each unit has a hidden stat which details how much energy it will recharge per turn. I'm interested to know if battle damage decreases this stat. If so, some of your tests might bring that to light, since any changes will show in the log as you go.

 

Keep in mind, though, that the quarterpods you're working with now have been set to have an energy recharge rate of nothing, so useful results won't be instant. :) (Your troops, on the other hand, will recharge 100 energy points per turn).

 

Concerning health. The value which holds that stat is a single byte. You can go up to 255 with that, and no higher.

 

Note that if it were a signed value (that is, a value which is capable of becoming negative, the highest value would be around 128, but you'd be able to go down to -128 as well, so the total amount of possible values would remain the same. (Those min/max values are not 100% accurate, but I'm not in the mood to work them out. It doesn't matter).

 

Simply put, you can't go higher then 255, because there's nowhere to put the extra data. Bigger numbers take more space.

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I'm very sure that the game can dish out well over 255 damage, but the programmers must have taken that into account and cast the resulting value to a byte before updating the unit data.

 

To reduce the values that go well over 200, I propose padding the aliens with some armour. Say something like 100. So if the target is damaged by 90 and you had 100 armour before the shot, the actual damage would then be 90 + 100 = 190. You wouldn't be able to take stats for all the values under 100 though.

 

I'd have to make a new savegame for this.

 

By the way, terror unit weapons deal plasma damage. surely they'd do the same amount of damage as your standard plasma guns?

 

- NKF

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He wants to test if they do deal the same type of damage as standard guns, I would think.

 

I'm guessing the health is stored in memory as a larger type then it is stored on disk, perhaps.

 

Say we tried this test... Give a unit 255 stun with a hex editor, then hit it with a stun rod (the unit should stay on it's feet until it takes another blow, as I doubt the game checks stun if they are not being hit).

 

Now, presuming the stun decreases at a set rate, we should be able to work out what the total amount of stun was by seeing how many turns it takes to wake up (and checking it's stun level when it does). If the result is over 255, then values are only stored on disk as single bytes, not in memory.

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By the way, terror unit weapons deal plasma damage. surely they'd do the same amount of damage as your standard plasma guns?

Are you absolutely positive that the Terror Units with turrets (Sectopod and Cyberdisc) have plasma weaponry? See, the shots do indeed look like plasma fire, and the UFOPaedia entries say these aliens are armed with a "powerful plasma beam". But the OSG (which is normally correct) says this about the Sectopod: "The weapon used by the Sectopod is a beam weapon, similar in function and power to terrestrial heavy-laser weapons". Now, if the Sectopod does use a laser-type weapon, it should do 1.5 times the listed damage against another Sectopod. If it only has a plasma-type weapon, it should do 0.8 times the listed damage against another Sectopod.

 

It's probably true that the Sectopod is equipped with a plasma weapon, but I'd like to find out for sure. The damage modifiers should help to narrow the weapon down to one type (160 max damage if plasma, and 300 if laser). Since our Sectopods are modified with no armor and 200 for health, there shouldn't be any insta-kills with a plasma-type weapon maxing out at 160, but there should be plenty with a laser. :P

 

----------

 

Well, back to the damage modifier tests I guess. Chalk up another 1000 trials for Zombie, this time for HE ammo fired from L1 by an X-COM soldier, at a Quarterpod standing on L0 (the ground). The results are mildly surprising, and I'll list them at the far right of the HE table I drew up a while back:

 

                           Quarterpod vs. HE ammo

           Q-L0, S-L0    Q-L1, S-L1    Q-L1, S-L0    Q-L0, S-L1
            Damage=50     Damage=50     Damage=50     Damage=50
Minimum:        16           20            20            20
Maximum:        48           60            60            60
Range:          33           41            41            41
Median:         32           39            40            40
Mode:           32           20            52            36
Ant. Ave:       32           40            40            40
Act. Ave:     31.59        39.23         39.53         39.92

As in all the previous tests, the probability of inflicting a certain damage number within the range is random. For some reason though, the game must consider the last three HE trials exactly the same. The only difference between these 3 was how far they deviated from the expected frequency. The last trial is by far, the most accurate among any of the scenarios I finished. (I'm not the one to blame for the inaccuracies, it's the game's random number generator). Doesn't matter really.

 

Figuring since those last three trials had the same Min, Max, Range and Anticipated Average, it might be a good idea to lump them all together. At the surface, it's actually the same trial with different orientations. I'll combine those trials and report back soon with an overall result from 3000 hits. That should give a definative answer! :)

 

I needed to finish off the IN trial where the Quarterpod was standing on the ground. In order to do so, I figured I might as well go back to the beginning and complete the Armor Piercing ammo trial with a 50 for damage (instead of 56 like I did). Three Quarterpods were shot with the AP-50 ammo, while the 4th was strictly for the Incendiary damage.

 

I made some serious progress this year in the damage modifier tests, so expect to see a few trials complete very soon. After the flurry of crunching all those numbers has subsided, I'll start work on the stun trials with help from Bomb Bloke's new logging program! :)

 

- Zombie

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Since I wanted to complete an Incendiary trial for the Quarterpod standing on the ground, I decided I might as well try and finish the trial for the Quarterpod vs. Armor Piercing rounds doing 50 for damage. I probably didn't need to actually redo this trial just because the first time I forgot to switch the obdata.dat file to do 50 (instead of 56) for damage. But it at least brought me one step closer to getting the answer for the Incendiary trial. Here are my results:

 

Quarterpod vs. Armor Piercing rounds (Damage = 50)

Minimum:

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Maybe it was me, but now I don't think so. It is in LSN, that the damage stat is the average value. Here in UFO it is the maximum, I think.

 

For example (it is from TFTD, though, since now I'm experimenting much with it, so have more info and, since the two are almost identical, this doesn't matter) we will look at my favourite Loby man. The Lobsterman Soldier has 90 health and 12 under armour. Suppose we fired large torpedo at him (and what is most important hit right at him). Large torpedo has the damage of 90. This value is halved for Lobsterman.

 

So, we got 45 minus 12 for armour: it is 33. Personally, I've never seen more damage caused to Lobsterman by torpedoes or even high explosives, even when it's armour was already damaged.

 

That indicates, that the this damage value is a maximum possible and, since the values are distributed according to the normal distribution (if I'm right), the probability of the maximum values (as well, as the minimum ones) is not very big.

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I've actualy achieved a number that was very close to 30 against a lobsterman with the Gas Cannon and AP shells (60AP). -24 for the armour, of course, so I got a number that was very close to 8 damage.

 

Damage listed is very close to the average. It's just multiplied by 2, and then multiplied by the amount that the unit resists that damage type. Say we're using a rifle (30ap) and the unit takes 80% from AP and has 12 armour.

 

The maximum damage this unit would take would be 30 * 2 * 0.8 = 48. Subtract the armour and we end up with 34. I imagine you'd more likely get a value of 17 or so points in general.

 

- NKF

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Hmm, if it is multiplied by 2, then in my example the max damage would be 90 * 2 * 0.5 - 12 = 78 points. Never seen such values, nothing close. The max was, as I said, around 30. Well, I don't have such patience as Zombie to try it for say 1000 times :), so maybe I hadn't ever seen max values.
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I'm assuming here that a Large Torpedo is equivalent to a Large Rocket, and the damage type is High Explosive, right? I'm also assuming that the Lobby man is 100% susceptible to HE. If so, read on.

 

Since the average damage for the Large Torpedo is 90, the max should be 180. Therefore the range should be between 0 and 180, right? NO! My results for HE ammo shot at a target in the air shows a constant +20 damage plus an additional random amount from 0 to 140. This gives a range of 20 to 160. Assuming that you are lucky and roll the perfect 140 the total damage comes to 160. Subtract the armor of 12, and you are left with 148 points of damage maximum, applied to the Lobby man's health of 90. That's an overkill of 58 points.

 

Assuming you shot the Lobby man while he is standing on the ground, you have to modify the numbers a little. The min is now a constant 16. The max should theoretically be 128. Subtract the armor and you are left with 116 max damage to be applied to the health. That's an overkill of 26 points.

 

But as I said before, because the range is so large (141 for air and 113 on ground), the probability of seeing the max happen is 0.71% for the air and 0.88% on the ground. That means you need to run at least 141 or 113 trials to see the max damage happen once! Most people do not have the patience to run this many trials (let alone 1000) so they make an invalid conclusion from a too small sample size.

 

Even so, because the probability of any damage number happening is random, it might take 282 trials, or it might never happen. It's how the game rolls the dice that allows the max to happen! :)

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Actually, I'd like to know how much a damage HE does to lobstermen. Anyone with the TFTD Official Strategy Guide by Dave Ellis care to offer this information?

 

Because if the lobsterman literally takes 50% of your damage, then it would have to have a HE damage susceptability rating of 25%.

 

2 * 0.25 = 0.5, see?

 

- NKF

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First of all. Zombie, I hadn't run any special tests on damage, my information is what I've acquired during the play. But I've killed or at least damaged more than 70 lobsters so it's about half of the amount needed (not to say that every one of them needed at least three shots to take down - and that was a very good roll). So it's not that small sample size. :) And damage was never greater than the amount I've indicated. Still, if I'll have some free time and strong inclination to do so, I run this test to be sure I'm right.

 

Second. The OSG will really come handy, since the USG only indicates that Lobstermen are resistant to most types of attack, including HE, but without actual values. Maybe it is not 50%, as I supposed, but 25, so the damage values indicated in Ufopaedia are the average ones indeed.

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Listen cyrus, I'm not doubting you. You probably did get some good rolls for the damage inflicted by the Large Torpedo. However, through all the test I've run so far, I usually don't get the Min or the Max until I reach about 200. That's just a generalization, but normally this holds. 200 seems to be the magic number in X-COM, as I've found poor statistical results with anything less, hence why I'm doing 1000 trials. I don't know, maybe you did hit the Max, but with only 70 or so trials to draw upon, I seriously doubt it. 70 trials is actually a small sample size in X-COM, sorry to say. The Max is probably going to be a multiple of 5 or 10, so if the highest damage you've got so far is not, its safe bet you haven't hit it yet. That's what my experience tells me, though I've been wrong before. :)

 

Damn! I wish I had the Official Strategy Guide for TFTD right now. Then I could make a prediction based off the damage modifier table. Anyone got it? If so, post the info asap. Thanks!

 

----------

 

Ah well, back to my tests. I've just completed another 1000 trials for the Quarterpod vs. Plasma. I ran some extra trials for the Plasma since I am concurrently working on the Quarterpod on the ground vs. Incendiary. I'll just slap those plasma results down here, right next to the first 1000:

 

             Quarterpod/Sectopod vs. Plasma
            First 1000       Second 1000
            Damage=50        Damage = 50
Minimum:         0                0
Maximum:        80               80
Range:          81               81
Median:         39               41
Mode:           36               12
Ant. Ave:       40               40
Act. Ave:     38.87            39.56

As you may see, my second trial is much closer to the Anticipated Average than the first one was. That's good. Hmmm..... I'll have to combine those two for an overall 2000 result. Can't believe I forgot to do that! Oh, well.

 

Ok, right now I'm working on the Quarterpod vs. HE, which should bring my ground Incendiary trials up to 1000. I'll post those results soon. In addition, I got Bomb Blokes new logging program up-and-running so I can start work on the stun trials. Those shouldn't take too long, so expect a post on them soon.

 

- Zombie

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Ho there my comrades in the land of Number Crunchery! I almost forgot but I have made a few updates to the save files that might just come in handy.

 

1. A little trick I realised that would allow you squeeze multiple uses of the mind probe rather than 2 per soldier. Works only on the first round then it reverts back to two per turn. The cost is 50% of the max, not the current, see? So by dropping max TUs down to 50 and current up to 250, you'll get plenty of uses out of this.

 

2. Separators.

 

3. A little walkway for no apparent reason apart from raising your elevation by walking rather than flying.

 

4. Toggled the 'can fly' flag for all X-Com soldiers. You end up with the soldiers cutting themselves in half in mid air, but it's just a cosmetic issue.

 

5. I've deleted the natural armour sectopod. It just got in the way.

 

6. I might have update the obdata file, but I can't remember. Doesn't really matter. I wouldn't have changed much, if at all.

 

7. Testers now have 250 TUs and Stamina to enable cross country jogging goodness.

 

8. Testers have been beefed up to 200 health.

 

I might have forgotten a few other bits and pieces, but that's about it.

 

As usual, it's on:

 

https://www.geocities.com/nkfarma/fun/testgames.html

 

- NKF

 

P. S: While making the edits, I came upon a shocking realisation. The Skyranger walls are not solid. No, no, sorry, that didn't come off right. Let's put it this way. A rocket fired directly 'into' a Skyranger wall (note how you are able to actually select them), will have the same effect as shooting a rocket into a UFO corner. It's a GOOD thing the AI don't fire their blasters willy nilly at the Skyranger in general, eh? Truly nasty!

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Thanks for those modifications NKF! And just when I was starting to get good at hacking my own files. You da man!!! Hmmm... I can't find an Emoticon in the list to fit my thanks. *bows down to NKF* I'm not worthy! :)

 

Well, as promised, I combined the two Plasma trials into one. I'll list it at the far right of the other Plasma trials:

             Quarterpod/Sectopod vs. Plasma
            First 1000       Second 1000          Combined
            Damage=50        Damage = 50        Damage = 50
Minimum:         0                0                  0
Maximum:        80               80                 80
Range:          81               81                 81
Median:         39               41                 40
Mode:           36               12                 12
Ant. Ave:       40               40                 40
Act. Ave:     38.87            39.56              39.21

 

I'm almost finished with the HE and IN trials. Give me a couple of days to finish them and crunch the numbers. :)

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Today I just finished with my final High Explosive test for the Quarterpod. Hurray! Nothing really new to report, except the Actual Average is a little closer to the Anticipated Average. I had already completed 1000 trials for the Quarterpod and the soldier standing on Level 1. However, because I wanted to get some Incendiary tests in for the Quarterpod standing on the ground, I decided I might as well get a few more shots in for that HE trial! :)

 

Here are my results:

 

Quarterpod - Level 1, Soldier - Level 1 High Explosive trials

             1st 1000      2nd 1000      Combined
Minimum:         20            20            20
Maximum:         60            60            60
Range:           41            41            41
Median:          39            40            39
Mode:            20            36            20
Ant. Ave:        40            40            40
Act. Ave:      39.23         39.35         39.29

 

With this final He trial out of the way, I can cook some numbers up for the Incendiary trials on the ground. I'll try to get that up before the new week starts. By the looks of things, Incendiary ammunition is unaffected by the ground. This means I can combine the two In trials. I also got a very good start on the stun trials: both the Stun Rod and the Stun Bomb. From my preliminary trials, the stun from a Stun Bomb is unaffected by the ground too. Therefore, I can skip one of those trials to save some time. No sense in beating a dead horse, right? :)

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Today I took a short break from the various other tests I was concentrating on and decided to combine all the similar HE trials I ran into one gigantic file. That's 4000 trials! Combining all the HE trials into one table was my ultimate goal so here it is:

 

               Quarterpod vs. HE ammo

           Q-L0, S-L0    All other HE Trials
            Damage=50         Damage=50
Minimum:        16               20 
Maximum:        48               60
Range:          33               41
Median:         32               40
Mode:           32               36
Ant. Ave:       32               40
Act. Ave:     31.589           39.507
Trials:        1000             4000

 

And that, my friends, completes the High Explosive trials for the Quarterpod! It was a long time in the making, but doing all these trials was not a waste of time. See, it gave me a deeper understanding of the mechanics behind a HE explosion. This allowed me to compare other potential "area effect" ammunition and decide if further testing was warranted on orientation.

 

Case in point: Incendiary ammunition is really not an area effect weapon, neither is the Stun Bomb. The ground plays no factor whatsoever on overall damage inflicted. If anything, I would go so far in saying that Incendiary ammunition and Stun Bombs are in the same family. Because I know how explosives work, I was able to determine rather quickly if more tests were needed on orientation for Incendiary and Stun. Orientation of the Quarterpod was meaningless so I saved myself from doing unnecessary tests there.

 

I think my theory on High Explosives stood up pretty well to my "mathematical scrutiny test". I threw everything at it I could think of (including the kitchen sink), and it still could explain why the ground plays a role. All I need to do now is to "cut the fat" from my theory. Right now, my proof is a little over six pages of equations, tables, graphs and dead-ends. Once I have the "meat" of the theory condensed into one neat package, I'll post it here. :)

 

Progress report for the Quarterpod (as of today):

Armor Piercing: Finished - 2000 Trials, Reported 11-09-2004, 1-16-2005

Plasma: Finished - 2000 Trials, Reported 11-14-2004, 1-25-2005

Laser: Finished - 1000 Trials, Reported 11-18-2004

HE Ground: Finished - 1000 Trials, Reported 11-22-2004

HE Orientation: Finished - 4000 Trials, Reported 12-02-2004, 12-11-2004, 1-09-2005, 1-29-2005

Incendiary Air: Finished - 1000 Trials, Reported 12-30-2004

Incendiary Ground: Finished - 1000 Trials, Not Reported Yet

Stun Rod: Finished - 1000 Trials, Not Reported Yet

Stun Bomb: Finished - 1000 Trials, Not Reported Yet

 

That should be everything for the Quarterpod. I'll get those unreported results up as soon as I can. As you can imagine, I was pretty busy doing spawn point scenarios for the past month, as well as various other on-going test projects of mine. That's just my free time, as the rest is spent in college. Hopefully, things will slow down somewhat to allow me to start work on the Sectopod tests soon! :)

 

- Zombie

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Thanks soooo much for the compliment, OmegaTwo! This is kinda a thankless (and menial) job, so getting any sort of praise is always a welcomed change.

 

People that know me always say that I have the patience of a saint. Honestly, I think I beat out those saints a long time ago. These damage tests not only require plenty of patience, but also some creative thinking. A strong understanding of mathematics doesn't hurt either. These tests have hopefully proved that beyond a reasonable doubt.

 

It's not just collecting a bunch of numbers to me. Numbers are meaningless unless you can do something with them. That's the trick. :)

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