Accuracy vs TU Efficiency

In almost every case (Rockets are the exception), Snap fire is a more efficient use of TUs than Aimed fire. This means Aimed fire is not useful apart from certain specialised activities.

Proposal

Would it be unreasonable to correct the TU and/or accuracy values of weapons, so that if we call the efficiency (hits per unit of time)

K = accuracy/TUs

and we have

Kai (K - Aimed) Ksn (K - Snap)

we correct the game tables to ensure that for any given weapon:

Kai > Ksn

In English, we are saying that extra time spent on aiming is no less useful than time spent snap firing. Or, if I spend twice as long on an aimed shot than on a snap shot, my chance of hitting should be doubled.

( In an unmodified game, this relationship does not hold, for all cases except Rockets. )

The purpose of this modification would be to ensure that, in terms of delivering hits to the target per unit of time, Aimed fire is more effective than Snap fire, which in turn is more effective than Auto fire.

Otherwise there are few reasons not always use the fastest available fire rate.

(3 reasons I can think of are:

• Conserving ammo - often of minor importance, except with single launcher rounds (Rockets etc), especially rare/expensive ones such as Blaster Bombs.
• Avoiding "collateral damage" to friendly troops, civilians, or valuable recoverable items
• "First shot kill" - killing the target before it can reaction-fire

But for general combat, there is often no reason to prefer Aimed fire over Snap, or Snap over Auto.

Discussion

Analysis of 20th century battles showed that ordinary soldiers were more effective at killing the enemy when they were given automatic weapons. Resistance to equipping troops with full auto small arms as standard was mainly on ammunition cost grounds (as well as conservatism). This was further refined by studies showing that a burst mode (as used in XCom) was optimum.

However, this was true only for the ordinary troops, who were found to be too unsettled by combat to fire in a controlled fashion. For the minority who had the presence of mind to fire under control, taking slow, carefully aimed shots was more effective and this is where the bulk of the overall effective firepower of an entire formation would come from.

Now, which group do we think XCom soldiers fall into?

Spike 13:28, 10 November 2008 (CST)

X-COM soldiers are selected as the best available volunteers from the various militaries of the funding nations, according to backstory. Thus they'd probably be more geared towards the latter class. However, given the...shall we say...less-than-ideal stats of some recruits, its clear that even then that's not going to hold. Bravery would probably be one of the main stats applicable to this argument. It should also be noted that X-COM soldiers are fighting a completely different war, one which could well make most regular soldiers break down from the stress alone. Think about it, for the first half of the game, at least, X-COM soldiers are out-equipped, fighting ALIENS, some 4 times thier own size, who can kill them in one glancing hit from a PLASMA weapon, while they themselves have trouble even hurting some of them, and whom are coming from OUTER SPACE in UFOs they can't scratch on the ground and which can VAPORIZE F-22s(or whatever the Interceptor is). That's not even mentioning the funding issues, terror attacks, or psychological scarring. And every time the Skyranger goes out, they can pretty much count on the fact that at least 2 or 3 of the people they're inside it with will be coming back to base in a body bag. This is liable to put ANYONE, even a battle-hardened combat vet of a normal earth military, off balance, at the very least. Which can be seen in how rapidly X-COM recruits tend to panic when things go bad. Overall troop morale would be one X-COM's (or any such organization's) greatest problems.

As for the use of aiming/snap/auto, it's basically been established that in UFO, auto reigns supreme. Whereas in TFTD, auto fire is only available on a handful of weapons, with horrendous accuracy for it, and usually with a fairly small clip. I don't know how many Aquanauts I've had run dry on ammo at a critical moment because I used the Jet Harpoon's Autofire too liberally(read: use at all) TFTD's weapons, however, have awesome Aimed accuracy stats, swinging it in the opposite direction of UFO; aimed is the prefered fire of choice. Also, perhaps use Scout/Sniper some more if you want to use Aimed mode; it increases overall safety. :) Arrow Quivershaft 13:50, 10 November 2008 (CST)

Good points there AQ. It's probably reasonable (for many reasons) to treat XCom's "elite" recruits as effectively rookies when tangling with aliens and alien weapons.

Thinking about auto modes, actually it does make sense that they have better firepower than the other modes. Otherwise why would they be used at all? Auto should be more effective per unit of time, less effective per unit of ammo - which it is.

That being the case, a more moderate proposal would be to tweak the game to ensure that Kai > Ksn, i.e. Aimed fire is more effective than Snap, per unit of time. Surely that is just common sense? Otherwise there is very little reason ever to Aim.

By the way, could you expand on your thoughts about Scout/Sniper? I'm not sure I understand how this tactic gives greater weight to Aimed Fire. Are there any considerations apart from reducing friendly fire and enemy reaction fire?

Spike 09:32, 11 November 2008 (CST)

One additional benefit I can see for using the scout/sniper strategy other than the benefits already mentioned would be the fact that the sniper will not have to move as much, if at all. Therefore the sniper will have more TUs available to make aimed shots. Obviously this means nothing for some weapons that can only be fired once per turn on aimed, but for weapons that can be aimed several times, then every extra TU helps. Just as snaps and auto shots bank on extra attempts to improve their odds of success, the same can apply to aimed shots too. -NKF 22:38, 12 November 2008 (CST)

In real combat, both quick and carefully aimed shots are useful depending on the situation, for at least two reasons. In situations such as an ambush, when the target is unaware of the firer, it is beneficial to hit it with the first shot, regardless or how long it may take to aim precisely, because after that the firer's position, if only approximately, will be made known to the enemy, who will then be prepared for fire from the same quarter and will seek cover and possibly fire back. This consideration can hardly be accounted for in the classic X-COM (but must be in the games it inspired).

The second reason is that snap shots are more effective at close range and aimed ones at long range. It happens because at short range the dispersion cone is much smaller than the target's angular area and aiming consists of pointing the weapon roughly at the target without the use of sights. The hit change is near 100% so the one who shorts first is the winner. At long range, however, the situation is reversed. The weapon must be aligned carefully to point at the small target and stabilized to narrow down the dispersion cone. The effect of distance is not uniform across all ranges but follows the behavior of the quantiles of the normal distribution:

where Φ is the cumulative normal distribution function, d the distance to the target, and r the target's characteristic radius as projected in the firer's direction. The standard deviation σ determines the opening angle of the dispersion cone and thus the accuracy of the shot. Here are the graphs for three different accuracies:

Precise aiming takes a certain time determined by the weapon and the firer, after which accuracy reaches a plateau and then starts to degrade due to fatigue. During the effective aiming stage the rate of accuracy increase is highest at the beginning and becomes lower at it approaches the plateau, but in the end the probability of defeating a remote target is improved out of all proportion with regard to the time spent aiming.

That being said, I don't think serious improvement is possible unless someone can change the hit-chance formula so that it will approximate, if loosely, the varying effect of distance at different ranges described above. As distance increases the effectiveness of auto- and snap shots should become lower compared to that of an aimed shot. Ant 222 (talk) 15:28, 1 September 2016 (UTC)

UFO:EU does actually use dispersion cones, FYI. The displayed accuracy of the shot is the chance that it will use the narrower "hit" dispersion cone instead of the wider "miss" dispersion cone, but "hits" can miss (usually due to cover, such as trying to hit an alien in a building through a window, but at long ranges true misses are possible against small targets) and "misses" can hit (most obviously at point-blank range). The size of the cones is also adjusted based on that accuracy, so the dispersion of a "miss" from a shot with 10% displayed accuracy is much larger than that of a "miss" from a shot with 99% displayed accuracy. So the "improvement" you want is already there to some extent. Magic9mushroom (talk) 00:58, 2 September 2016 (UTC)

I fear that we disagree about the term dispersion cone. I understand it as the normally distributed direction of the projectile, so that each shot is modeled by a single dispersion cone, which describes all the possible outcomes with their corresponding probabilities. This interpretation leaves no place for two dispersion cones. If UFO:EU chooses the wider or the narrower of some two dispersion cones depending on accuracy, then it largely defeats the cause of the normal model with respect to the non-linear dependency on distance, for the choice of either the hit or the miss dispersion cone is the definitive factor, whereas the subsequent modeling with the chosen cone is only secondary, because the hit cone almost always results in a hit and the miss one in a miss.

Is the algorithm that you have described documented anywhere? Accuracy_formula does not mention it and seems to imply a single dispersion cone per shot...Ant 222 (talk) 17:08, 2 September 2016 (UTC)

Here. And as I said, "misses" actually hit fairly often at close range, and "hits" failing to hit isn't unheard of. Magic9mushroom (talk) 22:20, 2 September 2016 (UTC)

Thanks for the link. The problem with the algorithm is that two of its three stages are physically meaningless. First—the random choice of the equation for the divergence factor, and second—its high dependency on an another random number within the chosen equation. For any given combination of the firer's stats, the weapon's stats, and shot type divergence should be strictly constant, and the very generation of a single angle distributed normally with the aforesaid divergence (which I take to be a measure of dispersion) should be the only source of randomness, whereas that algorithm severely diminishes the role of the normal-distribution model by introducing way too much randomness in the determination of its parameters.

Nobody seems to have understood that what User:Bomb Bloke so painstakingly logged is actually direct samplings of the cumulative distribution function of angular deviation. He need only plot his data correctly to see that.Ant 222 (talk) 01:08, 18 September 2016 (UTC)

Data Analysis

OK I did some quantitative analysis and the results are not good. The only weapons for which Aimed Fire has better efficiency of Accuracy::TU compared to Snap Fire, are Rockets and the Rocket Tank. In the notation above, there are only 3 weapons for which Kai > Ksn. In most cases, Snap fire is considerably more efficient - typically around 70% more efficient. Even for the Rocket weapons, Aimed Fire is only 25% (i.e. one-quarter) more effective. For all other weapons, including HWP and alien built-in attacks, snap fire is more efficient (in terms of generating hits on the target per unit of time). Obviously it is not good to have a game mechanic that is barely used because it has no real usefulness. I guess the proposal would be to raise the efficiency level of Aimed fire, and leave Snap fire where it is now. This would be the least unbalancing change, since Aimed fire is rarely used now, and even if it was more effective, it is tactically problematic to use because of the high TU cost. Even if you adjusted all weapons so that Aimed fire was 25% more efficient than Snap fire, I doubt that would be much incentive to use Aimed fire. 50% efficiency gain would be more likely to actually create real tactical alternatives that would get used by players in the game. By way of example, this would mean increasing the based Aimed accuracy of a Laser Rifle to around 200% (for 50% TU cost; vs Snap at 65% Accuracy for 25% TU cost). Spike 18:17, 6 December 2008 (CST)

There's other measures of efficiency, as well. For example, with any explosive munition, Aimed fire gets a second chance because as a general rule, you don't want an explosive going off in the wrong place. Particularly true with the Large Rocket and HC-HE. (Also somewhat of an issue with the Small Launcher, but it's mitigated because affected units are only stunned, not killed.) On a similar note, aimed is nice in Scout-Sniper so you don't shoot the spotter(The aimed guy doesn't have to move much so has lots of TUs for aimed fire.) Arrow Quivershaft 18:27, 6 December 2008 (CST)

Yes I definitely agree there are non-firepower benefits of Aimed fire, that are already present in the game. As you say these include control of collateral damage (with HE or with exposed scouts), and ammo-efficient (also "opportunity-efficient") use of single-shot weapons. Fair point! Can we list out all of the non-firepower benefits? I'm really trying hard to see if it's possible to make the case that Aimed fire is not pointless, from a game design / game balance point of view. Spike 19:21, 6 December 2008 (CST)

Well, one big thing is that reloading a weapon takes 15 TUs flat. This is actually a fair bit. For a rookie, it can be anywhere from 1/4th to almost 1/3rd of his full TU allotment, whereas its just below 1/5th for a top-level veteran. Any weapon with a small clip is going to require reloading on a regular basis if repeated snap fire is used. Anything with a 1-round clip counts, any arguably, so does the Heavy Cannon. (Though the Blaster Launcher has no mode other than Aimed, so is only included for example). The more ammo you use, the more you need to carry, thus the more space you need in the transport.

A single soldier can carry, at most, 5 rockets, 7 Blaster Bombs, 66 Heavy Cannon shots(11 clips), or 25 Small Launcher rounds. (These numbers do not take into account Strength limitations, or use of the Item Stacking bug. Also note that there's no reason you should need that many Small Launcher rounds.) Consider how many spaces this is on the transport, for one. Then multiply this across the number of associated weapons...you hit 80 pretty fast. Using lots of ammo means less room on the transport for other gear. Also consider how weighted down the soldier is. A soldier hauling around a rocket launcher and 4 reloads is carrying 50 units of weight, leaving not much room for other gear.

The collateral damage is an issue that needs to be watched for, of course. Snap-firing a Large Rocket can kill large portions of your team if not done properly. Even if none of your soldiers are killed, you may destroy valuable equipment if not careful. (Especially true near UFO power sources!) And at range, snap fire's path can intersect the position of a soldier.

Cost is yet another. In particular, in the case of the Small Launcher, ammunition requires Elerium to manufacture. And Large Rockets don't come too cheap if you're firing them off willy-nilly.

And finally, when dealing with the tanks, the Ammo problem is even worse...you CAN'T reload in the middle of battle; you get one magazine and that's it. (This is only truly relevant for the Rocket Tank and Fusion Hovertank.) Plus ammo is even more expensive!

There was another idea I had, but it escapes me currently. Still, I think this is a fairly comprehensive list. Arrow Quivershaft 20:18, 6 December 2008 (CST)

TU Efficiency Table

The table below shows the extent to which Aimed fire is less efficient than Snap fire. A value of 50% would mean Aimed fire is half as efficient (in terms of accuracy:TU) as Snap fire. The table also shows what the required value of Aimed Accuracy % would need to be increased to, in order to make Aimed fire as efficient (100%) as Snap fire, or 125% as efficient, or 150% as efficient.

See also the Firepower Tables which show how ineffective Aimed fire is in terms of damage-on-target. The root cause of the damage-on-target inefficiency, is this TU inefficiency.

Aimed vs Snap fire - Accuracy::TU Efficiency
with corrective values for Aimed Accuracy

Weapon	Aim Acc%	Aim:Snap	100%	125%	150%
Pistol	78	78%	100	125	150
Rifle	110	57%	192	240	288
HC - AP	90	62%	145	182	218
HC - HE	90	62%	145	182	218
AC - AP	82	60%	136	170	204
AC - HE	82	60%	136	170	204
RocketSm	115	125%	92	115	138
RocketLg	115	125%	92	115	138
LaserP	68	62%	110	138	165
LaserR	100	77%	130	163	195
HvyLas	84	74%	114	142	170
HvyLas (XCU)	110	81%	136	170	205
PlasmaP	85	65%	130	163	195
PlasmaR	100	58%	172	215	258
HvyPlas	110	73%	150	188	225
Blast Bmb	N/A	N/A	N/A	N/A	N/A
Stun Bmb	110	90%	122	152	183
Tk Cannon	90	62%	145	182	218
Tk Rocket	115	125%	92	115	138
Tk Laser	85	75%	114	142	170
Tk Plasma	100	59%	170	213	255
Tk Fusion	100	N/A	N/A	N/A	N/A
Cyberdisc	110	73%	150	188	225
Celatid	110	73%	150	188	225
Sectopod	110	73%	150	188	225

TU Efficiency Mods

The following replacement OBDATA.DAT files implement the principle that Aimed fire should not be less efficient than Snap fire. To use these, make a safe copy of your original OBDATA.DAT in the GEODATA folder, then replace it with one of these files. You should see the new improved base accuracies (and in some cases reduced TU costs) in the in-game UFOPaedia.

• Media:OBDTU100.DAT fixes Aimed fire so it is exactly as efficient as Snap fire.
• Media:OBDTU125.DAT fixes Aimed fire so it is 125% more efficient then Snap fire. This is the same ratio between Snap and Aimed fire that exists for Rockets.
• Media:OBDTU150.DAT fixes Aimed fire so it is 150% more efficient then Snap fire. This is probably over-powerful, and too unbalancing in the other direction. Also, in some cases (Rifle and Plasma Rifle) it is necessary to reduce the TU cost of Aimed fire slightly, as otherwise Accuracy would need to be raised above 255% (not possible as it is held in a single unsigned byte).