Firing tactics at long range


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#1 Hobbes

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Posted 20 September 2005 - 02:55 AM

I've been playing a new game but instead of using the recommendation at the Unofficial Strategy Guide I am mainly using Snap/Aimed for long range instead of auto.

This is what the USG says:

Quote

Auto shot fires three rounds, but is the least accurate of the
three shots.  On the other hand, when you use the laws of
probability, you actually come out ahead using an auto-shot,
since each shot is calculated independently.

For example, let's say chance of hitting in auto shot is 25%, and
snap shot is 30% (average).  The chance of getting at least one
hit out of three is 1-(chance of no hits).  So 25% hit prob AND
no hit in three tries is 0.75 * 0.75 * 0.75 = 0.42

Chance of getting at least one hit is then 1 - 0.42 = 0.56, or
56% which is much better than 30% (but no higher than the aimed
percentage).  When your accuracy improves, you increase your
chances of hitting the target multiple times, which ensures a
kill, and you use less TUs than ONE aimmed shot.

Now this assumes each shot being calculated independently but without considering full TU usage shooting, plus the difference in his weapon stats doesn't correspond to the stated values (in most cases snap has more 20% accuracy that auto).

Assuming this and using his math for a laser rifle (but with the UFOPedia stats, not game values), it would go:

0.54 * 0.54 * 0.54 = 0.15 or a 85% chance of hitting with at least 1 shot out of the 3

It beats the odds of snap with laser rifle (65%) right? But what if you consider the unit spending all of its TUs?

0.54 * 0.54 * 0.54 * 0.54 * 0.54 * 0.54 = 0.024 or a 99% chance of hitting with at least 1 shot out of the 6

but with 4 snaps from the laser rifle

0.35 * 0.35 * 0.35 * 0.35 = 0.01 or 99%, but on this case there is a bigger probability of hitting with more than 1 shot (my recent game observations show it).
Is there a way to prove this mathematically? I think the USG is right if you consider that the unit fires either snap or auto but its logic (advice) doesn't apply to when the unit fires several shots each turn.

PS - The firing of 2 auto bursts also allow for an extra snap shot for the laser rifle, which would make the odds more even related to firing 4 snaps.
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#2 Bomb Bloke

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Posted 20 September 2005 - 06:25 AM

I always use auto shot. It is HIGHELY uncommon that I use an aimed one, and I only use snap when I can't afford auto.

My logic is based my on instinct then logic here, but a lot of it comes down to distance. At point blank range, the accuracy modifiers don't mean much.

At point blank range I use auto, as I don't want a glancing shot to get me killed via return fire. That's where autoshot has a large advantage - three shots with no chance of interuption (and possibly death) by an enemy with high reactions. Dead aliens don't shoot back.

Sure, there are other ways to avoid reaction fire, but if you walk into a medium scout UFO, you can expect to find multiple aliens in there. Often a single autoshot can kill two of them, and if you're lucky, the third won't see your unit.

I also use it at long range - sometimes the extra shots can be used to clear out annoying obsticles between my unit and the target (like walls), allowing the followup blasts to kill the target.

My rule of thumb is treat every shot as though it's got the same chance to hit. Thus I aim to spit out as many shots as my TU will allow. Given that accuracy seems to be mostly dependant on the range between you and your target, as opposed to the type of shot you choose, it seems to work.

The only time I use aimed shots are when I'm using a soldier with GOOD accuracy, there's a very clear line of sight with no window sills or the like to clip by accident, and I'm sure that one shot will be enough to kill the enemy.
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#3 Pete

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Posted 20 September 2005 - 06:49 AM

BB - At point blank range, on full autoshot, my Commander missed a Floater standing right in front of him and wasted the floor either side (rather than the Floaters standing either side which would have been nice).

Puzzled by this, I did a littl reload test and he did it a furhter two times before finally hitting the Floater and getting wasted by his two escorts.

Further tests with snap showed accuracy vastly improved, though I didn't probably do enough tests to find out anything conclusive aside from autoshot probably isn't your best option at range, let alone at close quarters at the beginning of the game using a trusty rifle :D
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#4 Gimli

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Posted 20 September 2005 - 08:01 AM

I am not sure, but I think accuracy mostly depends on the type of shot, rather than distance. Like Pete said, sometimes soldiers miss three shots when at point blank range. I also noticed that, usually, if my chance to hit an alien with autoshot is 16% (roughly 1/6), he will indeed hit him once in 6 shots no matter the distance.

I was wondering something about the aimed shot, though. Does it inflict extra damage? Usually, when I hit an alien with the aimed shot he gets more damage/is more likely to die.

I'll try to keep track of this, although I'm playing TFTD, but I don't think there's a difference.

#5 Bomb Bloke

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Posted 20 September 2005 - 01:17 PM

In my experiance, point blank range shots don't miss. That is to say, if there are no tiles between your enemy and your soldier, then it'll hit.

But I may just be lucky.  :D
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#6 Hobbes

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Posted 20 September 2005 - 05:31 PM

Guys, this isn't about point blank shooting :D

I've been trying calculating the possibilities it but I am afraid I was never good at statistics plus I've forgotten most of it by now.

What I was looking is for a way to calculate the probability of 2 shots hitting out of 6 fired (with a 46% chance) and compare it with the figure of 2 shots hitting out of 4 fired (with a 65% chance).
Or, to make the TU usage more similar (since the laser rifle can still fire a snap after 2 autos) to use the plasma rifle's stats instead. There you have 6 auto shots fired (with a 55% probability) or 3 snaps (with a probability of 86% for each shot). What is the probability for Snap/Auto to hit twice?

I am inclined to wonder if Gimli isn't right. When I use conventional rifles with aimed shot against sectoids it seems that they achieve 1 shot kills more easily against sectoids. But this can be just a wrong impression.
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#7 Danial

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Posted 21 September 2005 - 12:02 AM

Hobbes, on 21st September 2005, 3:31am, said:

Or, to make the TU usage more similar (since the laser rifle can still fire a snap after 2 autos) to use the plasma rifle's stats instead. There you have 6 auto shots fired (with a 55% probability) or 3 snaps (with a probability of 86% for each shot). What is the probability for Snap/Auto to hit twice?
Shouldn't the probablity be 55% and 86% no matter how many shots are fired?? :D

I mean, 55% of 6 shots is 3.3, and 86% of 3 shots is 2.58, so the 55% auto-fire has the higher chance to hit, making it the better option.

#8 Knan

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Posted 21 September 2005 - 01:21 AM

Danial, on 21st September 2005, 2:02am, said:

Shouldn't the probablity be 55% and 86% no matter how many shots are fired?? :D

I mean, 55% of 6 shots is 3.3, and 86% of 3 shots is 2.58, so the 55% auto-fire has the higher chance to hit, making it the better option.

Let's see. Look up binominal distribution formulas, if you like, but you're right in some ways - average number of hits is better with auto shot.

As for Hobbes' question, though...

6 shots at 55%
Probability for no hits is straightforward, 0.45 ^ 6 = 0.8 %
Probability for one hit ... (720/5) * 0.55 * 0.45^5 = 6.1%
Probability for two hits ... (720/48) * 0.55^2 * 0.45^4 = 18.6%
Probability for more hits ... 100% - (0.8 + 6.1 + 18.6) = 74.5%
(ie 93.1% chance for 2+ hits)

3 shots at 86%
Probability for no hits is still straightforward, 0.14^3 = 0.3%
Probability for one hit, (6/2) * 0.86 * 0.14^2 = 5.1%
Probability for two hits, (6/2) * 0.86^2 * 0.14 = 31.1%
Probability for more hits ... 100% - (0.3 + 5.1 + 31.1) = 63.5%
(ie 94.6% chance for 2+ hits)

So the winner is ... snap shot! If you're sure that two hits will drop the Evil Alien Thing.

- Knan

#9 Danial

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Posted 21 September 2005 - 02:25 AM

Knan, on 21st September 2005, 11:21am, said:

So the winner is ... snap shot! If you're sure that two hits will drop the Evil Alien Thing.
Lol... Barely :D

#10 Bomb Bloke

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Posted 21 September 2005 - 03:01 AM

You forgot to throw in the probablity of the alien shooting your unit dead with reaction fire, thus giving a 0% accuracy for all subsequent shots.  :D

(What can I say - I just like auto shots!  ;) )

Concerning aimed shots doing more damage... The game calculates shots more or less in 3D. A unit can get hit in one of six locations - arms, legs, body and head.

I'd assume a head or body shot would do more damage then a shot to a limb. An aimed shot is more likely to hit the center of seen mass.
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#11 NKF

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Posted 21 September 2005 - 07:43 AM

The fact that an aimed is more likely to actually hit a target means a lot more than not hitting a target at all.

All ranged attacks behave the same way, with the main difference lying in how accurate the launching angle is and how fast the individual shots can be fired. I doubt the hit point of the target matters much, because I've had soldiers get hit in the head only to get leg wounds.

It doesn't matter what shot you use, if the game rolls a good damage number, and you hit a weak side of the target (like the back), you get a good result. I see this all the time with pistol snapshots against sectoids...

With the faster snaps and autos, your chances of hitting the targets based on individual shots are even worse, but you still get many more tries. With the slower aimed attacks, you do get a better launching angle, but because the attack is more expensive, misses are quite costly, so you don't get so many attempts.

Think of the individual shots. The laser rifle actually costs 25%, 11.33..% and 50% and provides 65%, 46%, 100% accuracy modifiers for each bullet (snap, auto and aimed modes respectively).

I'd also like to point out that the type of weapon you use also influences what sort of attacks work better over great distances. The rocket launcher for example works best with aimed attacks, while the laser pistol was built for continuous automatic fire over any range.  

Apart from the situation, just remember to play to the strengths of your weapons, or reconsider your strategy, and you'll do fine. There's no silver bullet, unless of course you've got a 125 accuracy soldier and there's no longer any difference between aimed and snap shot (heavy plasma and plasma rifle)...

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#12 Hobbes

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Posted 21 September 2005 - 01:49 PM

Knan, on 21st September 2005, 1:21am, said:

Let's see. Look up binominal distribution formulas, if you like, but you're right in some ways - average number of hits is better with auto shot.

As for Hobbes' question, though...

6 shots at 55%
Probability for no hits is straightforward, 0.45 ^ 6 = 0.8 %
Probability for one hit ... (720/5) * 0.55 * 0.45^5 = 6.1%
Probability for two hits ... (720/48) * 0.55^2 * 0.45^4 = 18.6%
Probability for more hits ... 100% - (0.8 + 6.1 + 18.6) = 74.5%
(ie 93.1% chance for 2+ hits)

3 shots at 86%
Probability for no hits is still straightforward, 0.14^3 = 0.3%
Probability for one hit, (6/2) * 0.86 * 0.14^2 = 5.1%
Probability for two hits, (6/2) * 0.86^2 * 0.14 = 31.1%
Probability for more hits ... 100% - (0.3 + 5.1 + 31.1) = 63.5%
(ie 94.6% chance for 2+ hits)

So the winner is ... snap shot! If you're sure that two hits will drop the Evil Alien Thing.

- Knan

<{POST_SNAPBACK}>



Thank you very much. :D

It was this type of calculations that I was looking for. I think i got the formula. Here's my calculations for the Laser Rifle.

6 shots at 46%
Probability for 0 hits: 0.54 ^ 6 = 2%
Probability for 1 hit:  (720/120) * 0.46 * 0.54 ^ 5 = 7%
Probability for 2 hits: (720/48) * 0.46 ^ 2 * 0.54 ^ 4 = 21%
Probability for more hits: 100% - (2% + 7% + 21%) = 70%
(i.e. 91% chance for 2+ hits)

4 shots at 65%
Probability for 0 hits: 0.35 ^ 4 = 1,5%
Probability for 1 hit:  (24/6) * 0.65 * 0.35 ^ 3 = 11%
Probability for 2 hits: (24/4) * 0.65 ^ 2 * 0.35 ^ 2 = 20%
Probability for more hits: 100% - (2% + 7% + 21%) = 67.5%
(i.e. 87,5%chance for 2+ hits)

Auto shot wins for the Laser Rifle ;)

And the Heavy Plasma?

6 shots at 50%
Probability for no hits: 0.50 ^ 6 = 1.6 %
Probability for one hit: (720/120) * 0.50 ^ 6 = 9.3%
Probability for two hits: (720/48) * 0.55 ^ 6 = 23.4%
Probability for more hits: 100% - (0.8 + 6.1 + 18.6) = 65.7%
(ie 89.1% chance for 2+ hits)

3 shots at 75%
Probability for no hits: 0.25^3 = 1.6%
Probability for one hit: (6/2) * 0.75 * 0.25^2 = 14%
Probability for two hits: (6/2) * 0.75^2 * 0.25 = 42.1%
Probability for more hits: 100% - (42.1 + 14 + 1.6 ) = 42.3%
(ie 84.4% chance for 2+ hits)

And the Rifle

6 shots at 35%
Probability for 0 hits: 0.65 ^ 6 = 7.6%
Probability for 1 hit:  (720/120) * 0.35 * 0.65 ^ 5 = 24%
Probability for 2 hits: (720/48) * 0.35 ^ 2 * 0.65 ^ 4 = 33%
Probability for more hits: 100% - (2% + 7% + 21%) = 35,4%
(i.e. 68,4% chance for 2+ hits)

4 shots at 60%
Probability for 0 hits: 0.40 ^ 4 = 2.6%
Probability for 1 hit:  (24/6) * 0.60 * 0.40 ^ 3 = 15.4%
Probability for 2 hits: (24/4) * 0.60 ^ 2 * 0.40 ^ 2 = 34.6%
Probability for more hits: 100% - (34.6 + 15.4 + 2-6) = 47.4%
(i.e. 82%chance for 2+ hits)

Wow! Now this is a clear win for Snap.

Assuming all this calculations are correct, at long range use Auto with the Laser Rifle and Heavy Plasma, and with the other rifles one should use Snap, especially in the case of the conventional Rifle. Of course, this doesn't take into factor the fact that Auto fire usually allows for an extra Snap shot, if all TUs are used for firing (which is the case in the number of Snap shots considered).

And, like Bomb Bloke said, you might not be able to fire the second snap because of the alien's reaction fire...
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#13 Knan

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Posted 21 September 2005 - 04:58 PM

Hobbes, on 21st September 2005, 3:49pm, said:

Thank you very much. :D

It was this type of calculations that I was looking for. I think i got the formula. Here's my calculations for the Laser Rifle.

6 shots at 46%
Probability for 0 hits: 0.54 ^ 6 = 2%
Probability for 1 hit:  (720/120) * 0.46 * 0.54 ^ 5 = 7%
Probability for 2 hits: (720/48) * 0.46 ^ 2 * 0.54 ^ 4 = 21%
Probability for more hits: 100% - (2% + 7% + 21%) = 70%
(i.e. 91% chance for 2+ hits)

4 shots at 65%
Probability for 0 hits: 0.35 ^ 4 = 1,5%
Probability for 1 hit:  (24/6) * 0.65 * 0.35 ^ 3 = 11%
Probability for 2 hits: (24/4) * 0.65 ^ 2 * 0.35 ^ 2 = 20%
Probability for more hits: 100% - (2% + 7% + 21%) = 67.5%
(i.e. 87,5%chance for 2+ hits)

Auto shot wins for the Laser Rifle ;)

Yep. Somewhat interesting looking at the results with more typical (<100 firing accuracy) rookies.

Let's take a sharpshooter rookie, with 70 accuracy.

6 shots at 46x70=32%
Probability for 0 hits: 0.68 ^ 6 = 9.9%
Probability for 1 hit:  (720/120) * 0.32 * 0.68 ^ 5 = 27.9%
Probability for 2 hits: (720/48) * 0.32 ^ 2 * 0.68 ^ 4 = 32.8%
Probability for more hits: 100% - (9.9% + 27.9% + 32.8%) = 29.4%
(i.e. 62.2% chance for 2+ hits)

4 shots at 65x70=45%
Probability for 0 hits: 0.55 ^ 4 = 9.1%
Probability for 1 hit:  (24/6) * 0.45 * 0.55 ^ 3 = 29.9%
Probability for 2 hits: (24/4) * 0.45 ^ 2 * 0.55 ^ 2 = 36.7%
Probability for more hits: 100% - (9.1% + 29.9% + 36.7%) = 24.3%
(i.e. 61%chance for 2+ hits)

Well, the odds is nine to one you actually hit once or more.


And let us take a can't-hit-the-skyranger-from-the-ramp rookie, with 40 accuracy.

6 shots at 46x40=18%
Probability for 0 hits: 0.82 ^ 6 = 30.4%
Probability for 1 hit:  (720/120) * 0.18 * 0.82 ^ 5 = 40.0%
Probability for 2 hits: (720/48) * 0.18 ^ 2 * 0.82 ^ 4 = 22.0%
Probability for more hits: 100% - (30.4% + 40.0% + 22.0%) = 7.6%
(i.e. 29.6% chance for 2+ hits)

4 shots at 65x40=26%
Probability for 0 hits: 0.74 ^ 4 = 30.0%
Probability for 1 hit:  (24/6) * 0.26 * 0.74 ^ 3 = 42.1%
Probability for 2 hits: (24/4) * 0.26 ^ 2 * 0.74 ^ 2 = 22.2%
Probability for more hits: 100% - (30.0% + 42.1% + 22.2%) = 5.7%
(i.e. 27.9%chance for 2+ hits)

This useless rookie will actually hit the alien more often than not, even with 40% firing accuracy. And yes, auto shot is recommended with the laser rifle.

Though I am fond of aimed shot when there is a chance of shooting the spotter in the back instead.

- Knan

#14 JellyfishGreen

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Posted 23 September 2005 - 10:51 AM

I like what Hobbes is saying about accuracy at range, in addition if your support shooter is out of range of the alien then:

a) you don't have to worry about return fire, whereas in BB's point blank situation auto-fire obviously gives a benefit here

b) you may have to fire past your spotter or other friendlies, so you don't want stray shots

thus making an excellent case for snap shots at long range. With multiple support snipers I would go with the occasional aimed shot too, to see how my luck is going.

Good discussion, although I'm surprised we're still having it in 2005. It's points like this that will subtly influence my play style in my next game.
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#15 Hobbes

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Posted 23 September 2005 - 11:13 AM

JFG,

Those long range sniping tactics are very common on UFO2000 and when I started a new X-COM:UFO game the past week I've decided to use them (with a few alterations coming from the differences between both games).

Like Knan showed with his last calculations, the choice between Auto/Snap depends also on the accuracy of the shooter. With 40 accuracy seems to be more of a choice (but then again soldiers with that accuracy are usually a last resort for long range sniping).

Btw, I am already on August of my game and on the last terror site my commander (78 accuracy) fired 3 plasma rifle shots from the roof of a warehouse and killed the same number of Snakemen on a single turn. He was lucky but it was also very gratifying :D
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#16 Bomb Bloke

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Posted 24 September 2005 - 01:01 AM

Did your commander use an autoshot?  :D
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#17 Hobbes

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Posted 24 September 2005 - 02:15 AM

Bomb Bloke, on 24th September 2005, 1:01am, said:

Did your commander use an autoshot?  :D

<{POST_SNAPBACK}>


3 snaps. That's what made it remarkable ;)
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