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No they are not added together, and no there is no direct exponential effect. Each fires and inflicts what it does, probabilistically. Where you can see more than linear impact, though, is on the morale recovery side.

The deeper a unit is driven down the morale state ladder, the harder it is for that unit to snap back to "OK" rapidly. If the firepower of each shooter is tiny, this is a minor effect. But if it is substantial, enough to cause "cautious" to "pinned" results taken individually, then successive smacks like that will push the target unit down to "panic" or "broken". Because it won't have recovered back to "alerted" or "OK" before the next shot hits.

So, one unit firing 3 times in succession will generally have less impact than 3 units firing at once. Simply because rally is a function of time, and the unit being hit has less time to recover from the effects of the previous hits. So it gets driven deeper into the low morale states. And the lower you go there, the longer it takes to climb back out, even a single level. (e.g. alerted to OK takes just a few seconds, cautious to alerted can take about the length between typical shots, pinned can take a full minute to recover to cautious, etc).

Make sense?

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The only extra positive aspect is the impact angle. The target will usually turn its harder front to the shooter.

If you fire at it from 3 different angles in a short timeframe it cannot do that and gets a lot of firepower from the sides.

I am not sure how that plays with my findings that subsequent bursts are more casualty-effective than first hits.

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Jason, your post makes sense, but I disagree with the modelling. Redwolf, you made an interesting point, too.

If three squads are firing, each at firepower 100, there should be an exponential affect. That's a *lot* of incoming bullets. I think the cummulative affect would make it more devastating than taking each squad individually at 100.

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It isn't at all intuitively clear to me that the effect would be enhanced. It could also be subject to a saturation effect and thus increase sub-linearly rather than super-linearly.

It is known that the lethal radius of HE shells does not increase linearly with explosive weight, because a lot of the additional energy just goes to overkill near the impact point. So you will generally get more casualties from multiple, smaller shells. (So long as they are strong enough to penetate cover).

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Originally posted by Sanok:

Jason, your post makes sense, but I disagree with the modelling. Redwolf, you made an interesting point, too.

If three squads are firing, each at firepower 100, there should be an exponential affect. That's a *lot* of incoming bullets. I think the cummulative affect would make it more devastating than taking each squad individually at 100.

I'd say the effect of more bullets should be a lower effect per bullet.

Reason 1:

If ten shooters target ten targets, it is likely that several shooters target a single man. If that men is hit, it does not matter how much of the others hit him.

So I'd expect less killed by 3 squads shooting at one squad than by 3 squads shooting at 3 different squads. The easiest example is if you take a hit prob of 100%. Every shooter hits its target. Case one sees 5.5 kills on average. Case 2 sees 15.5 kills.

A more convenient example is 3 shooters shooting on 3 targets or shooting at one target... each with a hit prob of 100%. Case 1 sees one target hit three times = 1 causalty. Case 3 sees an average of 2 kills.

Decreasing the hit prob will decrease that effect, but it will always be there to some extent.

Reason 2:

Imagine a squad in a trench. It gets a little incoming. They shoot back - ie they are heads up. Now it gets an awful lot of incoming. They will cease firing and take cover, presenting no target.

Which case sees more casualties?

BTW: I assume that the shooters do not coordinate "I hit that one, you hit the next one etc." - this is a battle. So shots/hit probs are independently distributed.

Gruß

Joachim

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You are right about the theoretical effect of overkill, making for less than linear addition of FP. But there is a countervailing issue, which is crossfire's effect on cover. Fire from multiple points of origin encounters less effective cover than fire originating from a single point. Because the dead ground created by any given obstacle varies from point of origin A to point of origin B. Each casts a different "shadow". The set of locations in the shadow of all shooters shrinks as the number of shooters rises.

There is no obvious way to tell which effect will outweigh the other. The second, cross fire effect, is modeled to some degree already, in an independent fashion, but only for large angles of difference. I am referring to the greater vulnerability when shot from a side or rear facing. But that does not account for all of it, or perfectly. Overkill is also accounted for once it gets beyond a certain point, because it is somewhat easier to hit a man in a unit with many men remaining.

Given both factors, linear adds are a reasonable approximation.

In practice, there is a significant difference in the effect of fire delivered one to one for a long period, and many on one ("intense") shifting from target to target. The former tends to do little against units in heavy cover, and to suppress but not break otherwise. The latter tends to break units in succession - while allowing the last few targets (as yet unhit) some time to fire unsuppressed.

So, functionally, you spread fire to just keep their heads down and reduce your own fire received, but you concentrate to break units permanently. The morale system is the real driver here, but it is the driver that matters and the effect is real and large. Whole platoons break squads, single squads only pin them down.

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I agree that when there are three squads firing at one, some of the men are going to target the same person. However, when one squad is feeling the affect of 300 firepower, it seems logical to me, that feeling it as one large factor of 300 is more "realistic" than feeling it as three separate factors of 100. There should at least be some sort of cummulative affect. When thirty men are firing at you, the odds are greater that you'll be hit than when only ten are shooting.

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Err, um, of course 100 three times does a lot more than 100 once. Each rolls and does x. Three rolls will do on average 3 times the average done by x. Suppose the FP is enough to get 1 man 50% of the time. Then three shots will get 3 men 12.5% of the time, 2 men 37.5% of the time, 1 man 37.5% of the time, and nobody 12.5% of the time. Expected hits 1.5 men.

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Originally posted by JasonC:

Given both factors, linear adds are a reasonable approximation.

It is a convenient approximation and it might work. Anything more complex will probably be just as bad, so I can live with that.

Don't think we need to discuss the morale effects. Those are pretty obvious.

Gruß

Joachim

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One point that always concerns me is that if multiple people fire at a target then how do they know which way to adjust their aim.

This really pertains mainly to rifle fire as a machinegun can trace its effect .... unless another machine gun is firing similarly.

However I am convinced there is an effect and that accuracy will diminish as more fire and it is weight of fire and then luck that does the damage. I sthier any research on this?

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Well, rifle fire is aimed but not really adjusted by any visible fall of shot. But also, the average number of bullets fired to inflict one casualty was on the order of 10,000. So a lot of it was obviously spray and pray, or firing just to suppress without having a visible target. Clearly it also did suppress. Because even area fire would hit more people than that, unless they quickly got under complete cover, when under any significant weight of fire.

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Yes. I have heard this figure of 10,000 bullets but it does raise a question of calculation - It is probably derived from dividing total bullet production ( both sides ) by the total number of casualties ( on both sides ) - however a significant number of bullets were never fired - they were lost, stolen, destroyed, captured and those that were not fired due to the termination of the war. Regardless, the point is valid, the number of bullets fired greatly exceeds the number of casualties.

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No, it is not based on bullets produced, it is based on figures for bullets expended. Division resupply reports and the like.

For instance, a typical US division in the ETO run expenditures of 50,000 to 100,000 rounds of 30 cal ammo per day. Bullets inflicted only about a quarter of typical losses suffered; most were from shell fire. US alone, not counting Brits and French, had about 10000 (I count 9259 from a USCMH table) division-days in combat in the ETO, not counting the MTO (Italy etc). There were 405k German losses in the west from D-Day to the end of November, a portion of the campaign probably comparable to the US share of the fighting. (PWs are extra, about as large). Those US divisions lost 435k combat casualties.

Do the math and the average US division in a day of combat probably inflicted (and took) around 40-50 casualties, 10-12 of them by bullets. So 1/4000 is an upper bound on per bullet effectiveness. (Leaving out the air force etc). If you do the same sort of math for the Germans in Poland, you get around 1/8000. (395.5 million rounds of 7.92mm expended in the 1939 campaign, 200k Polish casualties, but most from artillery).

It might be off by a factor of 2. It isn't off by a factor of 10. As an order of magnitude observation, it is sound.

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