German-Allied loss ratios in aerial combat, Western theaters

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Sid Guttridge
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Sid Guttridge » 12 Mar 2021 12:33

Hi TMP.

You post, "Feel free not to comment in the thread if you find it uninteresting."

I wasn't commenting, I was asking a question: "What is the rationale for considering German-Allied loss ratios in aerial combat in splendid isolation?"

You are under no obligation to answer and we can leave it hanging if you wish.

I would just observe generally that casualties/losses are the currency expended to gain an advantage and their significance needs to be measured against the results achieved. Allied bombers were not over Germany to engage German fighters and so their results cannot be measured by their victory ratio over them. Likewise, part of the aim of the Allied fighters was to enable their bombers to reach their targets, so victory claims are not the only measure of their success.

Anyway, this is an interesting thread, so thank you for starting it. I shall continue to watch it.

Cheers,

Sid

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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Sheldrake » 12 Mar 2021 21:42

I don't think the Lanchester model works well for air to air battles. Lanchester is based on a set of duels. Once you have a furball - a true dogfight Lanchester works.

However, IRRC from Shaw's fighter combat that there are three situations under which a force initials air combat, with an altitude advantage, on the level or at an altitude disadvantage. Rule #1 is to avoid combat at a disadvantage...

In the Battle of Britain the RAF were committed to engage bombers, regardless of the tactical advantage. Lanchester applied.

German fighters for much of the war were outnumbered, but rarely forced to engage until the US daylight raids on Germany. Their experten had the latitude to engage only under favourable conditions and avoid combat without the numbers or altitude. Dogfights were to be avoided. The ideal was to take an enemy force by surprise make a couple of kills and evade - then repeat. Lanchester needs adaptation if one side only fights if they start in a superior position. Until mid to end of 1943 they had aircraft that could evade combat with allied fighters.

The Red Army lacked radar until quite late in the war so at Kursk they could not translate a numerical superiority to the air. A disproportionate amount of VVS air would be needed as standing patrols, which are also targets.

If you wanted to build a model of this set up one in an on line computer simulation. About 20 years ago I used to design and umpire these for iEN Total Sims. The Luftwaffle would always have an favourable loss ratio in a replay of the Circus operations, Kursk or over the western desert. .

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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by histan » 13 Mar 2021 16:33

Hi Sheldrake

You have reminded me that the 1941 air campaign over France is an interesting one to look at, because it is one of the very few where loss ratio is a meaningful measure of effectiveness rather than just an output measure of military activity.

It is well analysed by the Air Historic Branch, which had the benefit of both RAF and Lufwaffe aircraft loss records.

It is another example of how the defence used its limited resources well.

I will have a look to at the 1942 air campaign but it is known that the defence did well at Dieppe.

As an aside, the air battle over France in 1941 and 1942 show that any attempt at an invasion in 1942 was unlikely to succeed. The decisive condition of air superiority (as a minimum) and air supremacy (if at all possible) was simply unachievable. It took a lot of very hard work in late 1943 and early 1944 to create the conditions needed for a successful invasion.

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John

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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Richard Anderson » 13 Mar 2021 17:51

Sheldrake wrote:
12 Mar 2021 21:42
I don't think the Lanchester model works well for air to air battles. Lanchester is based on a set of duels. Once you have a furball - a true dogfight Lanchester works.
Well, exactly, since that is what Lanchester envisioned in his equations, months before the first air-to-air combat occurred. Is it any wonder that his theories did not precisely replicate reality? :D
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by TheMarcksPlan » 28 Oct 2021 04:19

TheMarcksPlan wrote:
12 Mar 2021 07:17
In their article, "Safety in Numbers: Ideas of Concentration in Royal Air Force Fighter Defence from Lanchester to the Battle of Britain," authors MacKay and Price write:
If one fits the generalized model to data from the Battle of Britain, one
finds that Lanchester’s insight is essentially correct for British (Blue)
losses, with dB/dt ~ -gG^1.2. However, German (Green) losses dG/dt ~
-bG^0.9, not at all as expected in the aimed-fire model,
Coming back to these ideas...
TheMarcksPlan wrote:The above insights have different implications for different analytical scenarios:
What I was getting at, but didn't quite articulate fully, is different implications for tactical vs. strategic analysis.

Mackay and Price's counterfactual tactical analysis of the BoB - should Dowding have kept up with Big Wing? Should Germany have concentrated on larger raids? - does not permit some counterfactual strategic analysis for obvious reasons: neither side could choose to have bigger overall air forces during the BoB.

Strategic counterfactual analysis is useful in other non-BoB WW2 settings, however: Should Germany have focused more on fighter defense (most say yes)? Would Germany have been able to defend its skies, had it defeated the Soviet Union?

The latter is, of course, the counterfactual to which I've devoted most thought. As I say here (and elsewhere), a German victory over the SU would enable 4x Germany's OTL aircraft production and (after accounting for no Eastern Front LW losses) at least 5x the flow of aircraft opposing the Wallies.

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Strategic vs. Tactical Analysis, using Mackay and Price's findings

To repeat, neither side in the BoB could choose to have bigger air forces. In the Battle of Germany ("BoG"), aka basically the Combined Bomber Offensive ("CBO"), however, either side could have had different forces: Germany could have devoted more resources to fighter production or could have freed/obtained more resources by defeating the Soviet Union. Britain and America could have spent more on air forces and/or could have sent less to the Pacific.

These are strategic choices that have implications for tactical attrition ratios: A larger ATL tactical attacking force (B for Allies) would inflict kill percentages of enemy forces in proportion to (size delta)^1.2 * (OTL kills); same for a smaller tactical attacking force. A larger ATL defending force (G for Germany) would inflict kill percentages in proportion to (size delta)^.9 * (OTL kills). Mathematically we have:

dB/dt ~ [(size delta)*(OTL G)]^.9

dG/dt ~ [(size delta)*(OTL B)]^1.2

Note: dB/dt and dG/dt represent percentage loss of each force

This gives us a defender kill percentage that is sublinear with tactical strength and an attacker kill percentage that is supralinear with its tactical strength.

Now let's put some numbers to it, using my "defeated Soviet Union" counterfactual wherein opposing LW strength is 5x OTL.

OTL Allied losses = X ATL Allied losses = X * 5^.9 = 4.26X

OTL German losses = Y ATL German losses = 5Y

ATL attrition ratio = (4.26/5)*X/Y

note: X and Y represent absolute, not percentage, values

At the tactical level, this actually contradicts my working assumption that ATL attrition ratios would be at least as favorable to LW as OTL. ATL attrition ratio moves against Germany by 15% (Germany loses 5x the fighters, Allies lose 4.26x OTL).

That's not the whole story, however, as we move from tactical to strategic level of the entire BoG or CBO. Holding Allied European air resources constant, for now, the size and/or number of Allied air raids - their size in tactical engagements - would have to decline. If tactical strength declines, we can solve for when OTL attrition ratios by solving for Z in the below equation:

Z = (OTL Allied tactical strength) / (ATL Allied tactical strength)

( (5^.9) / 5) = Z ^ 1.2

Z = .875

...this is the crossover point where, on the Mackay/Price BoB model/data, the attrition ratio effect of smaller attackers (Allies) equals the effect of larger defenders (Germans).

Would Allied losses in this counterfactual environment (i.e. 5x initial LW strength) imply at least 12.5% smaller Allied tactical strength as the campaign wore on? Pretty clearly yes. To see why (if it's not intuitive already), let's look at OTL 8th/15th bomber strength:

Image

Then let's look at OTL AAF heavy bomber losses (to fighters) in Europe:

Image
source for both: AAF Statistical Digest

Let's now assume that from, say, June-September 1943, LW strength and losses are 5x OTL (covered by 5x ATL production) while AAF losses (370 HB's to fighters OTL) are 4.26x OTL (=1,576 HB's). Attrition ratio is worse for LW but AAF's 1,206 additional HB losses leave it only 348 bombers on hand to start October 1943.

In that strategic environment, AAF raids have to be radically smaller, radically rare, and/or AAF needs a massive uptick over OTL aircraft/crew replacement flows. Unless AAF husbands its resources for only a few large raids per month, its tactical size will shrink by at least 12.5% and - per Mackay/Price's BoB data/model - ATL attrition ratios will already be better than OTL for the LW.

-------------------------------

Note, btw, that even a 15% short-term swing against the LW in attrition ratios comes nowhere close to making aerial attrition even for the Allies. As discussed in OP, OTL aerial cost to Allies was ~3.8x higher than cost to LW.

------------------------------

Why the Mackay/Price BoB data model understates things for ATL LW

So far I've applied this model because it's one of the few quantitative, well-documented models I have. As regards fighter vs. bomber combat, however, it likely far underrepresents the attacker's tactical advantage from numerical concentration in the BoG. Why?

In BoB, German bombers didn't emphasize formations with interlocking fields of defensive bomber firepower. In BoG, AAF obviously did. AAF's bomber boxes declined in effectiveness as they were broken up by losses - thus AAF HB losses were often concentrated in a few bomber boxes per raid. A stronger ATL LW would break up more boxes, leading to kills supralinear with LW strength.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by rcocean » 31 Oct 2021 04:11

Fascinating thread. Just as an aside, I was surprised at the significant number of USA HB's shot down in April-Sept 1944. I'd gottten the impression from various books that "Big week" and air battles in early 1944 had "broken the back" of the GAF fighter force.

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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Richard Anderson » 31 Oct 2021 04:30

rcocean wrote:
31 Oct 2021 04:11
Fascinating thread. Just as an aside, I was surprised at the significant number of USA HB's shot down in April-Sept 1944. I'd gottten the impression from various books that "Big week" and air battles in early 1944 had "broken the back" of the GAF fighter force.
Yep, 2,173 of them in the ETO alone. Of which 915 were shot down by enemy aircraft and 1,035 by Flak. By May, Flak had replaced the Jagdwaffe as the greatest threat to the bombers.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by TheMarcksPlan » 31 Oct 2021 04:32

rcocean wrote:
31 Oct 2021 04:11
Fascinating thread. Just as an aside, I was surprised at the significant number of USA HB's shot down in April-Sept 1944. I'd gottten the impression from various books that "Big week" and air battles in early 1944 had "broken the back" of the GAF fighter force.
Yeah Big Week was a PR campaign that has stuck in many bad histories. A lot of decent historians point out that it didn't destroy the GAF though. Between April and June is when we really see LW's ability to contest German airspace tail off.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by AriX » 10 Dec 2021 02:21

"Other losses" in AAF stat digest should be configured out. I bet it was when the loss couldn't be determinated. In soviet aviation such thing was called "didn't return from combat sortie".

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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Richard Anderson » 10 Dec 2021 02:46

AriX wrote:
10 Dec 2021 02:21
"Other losses" in AAF stat digest should be configured out. I bet it was when the loss couldn't be determinated. In soviet aviation such thing was called "didn't return from combat sortie".
Sure. You can either ignore them, which would be silly, or assume that the pattern of loss for the DNR was similar to those that could be determined.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by TheMarcksPlan » 10 Dec 2021 18:31

Richard Anderson wrote:
10 Dec 2021 02:46
AriX wrote:
10 Dec 2021 02:21
"Other losses" in AAF stat digest should be configured out. I bet it was when the loss couldn't be determinated. In soviet aviation such thing was called "didn't return from combat sortie".
Sure. You can either ignore them, which would be silly, or assume that the pattern of loss for the DNR was similar to those that could be determined.
I'm sure some of the DNR were losses to Flak/fighters distributed in ratio similarly to the known losses. I didn't make that move, however, because surely many of the losses were to technical faults (engine problems, fueling oopsies, etc.). Another category is probably landings in neutrals, which reached worrying levels in Spring 1944 as morale strained under heavy losses.

For my ATL purposes it's hard to see which way the missing data skews. Non-combat "other" losses would scale with sorties and therefore would be lower in ATL. Combat "other" losses are hiding LW defensive success and therefore imply higher ATL LW success.

It would be interesting to know what percentage of previously, heavily damaged bombers later became "other" losses. HB's are complicated machines and it's easy to see overstrained crews imperfectly addressing a severed electrical/hydraulic line here or there, or imperfectly patching structural damage.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Richard Anderson » 11 Dec 2021 02:14

As best I can tell, four B17/B24 were interned in Sweden in 1943, one of which I believe crashed on landing and was wrecked. Also in 1943, 12 B17/B24 were interned in Switzerland. Of those, one was destroyed by its crew, two landed with battle damage, and two were shot down by Swiss AA and destroyed.

The notion that cause of loss of these aircraft would be unknown is somewhat odd, but certainly they were likely included in "other".

So then, in 1943, of 1,036 heavy bombers lost on combat missions in the ETOUSA, we know that 700 were recorded as due to enemy aircraft, 228 to AA, and 108 were to "Other Causes" of which we can account for 16...assuming the two shot down by Swiss AA were not counted as AA. We also know that in the Z/I in 1943, 422 B17 and B24 were lost to accidents, and that the chance of an accident of some type was about 0.03% for every hour flown. In 1943, there were 155,107 hours flown by HB in the ETOUSA, so we would expect that about 46 to 47 aircraft would have been lost to accidents.

Thus, we can estimate that of the 108 lost to other causes, perhaps 46 or 47 were to accidents, which might include some of those 12 interned in Sweden and Switzerland that were not battle damaged or shot down by Swiss AA. For the rest you might assume that the pattern of loss for the DNR was similar to those that could be determined.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by TheMarcksPlan » 11 Dec 2021 03:24

Richard Anderson wrote:
11 Dec 2021 02:14
We also know that in the Z/I in 1943, 422 B17 and B24 were lost to accidents, and that the chance of an accident of some type was about 0.03% for every hour flown. In 1943, there were 155,107 hours flown by HB in the ETOUSA, so we would expect that about 46 to 47 aircraft would have been lost to accidents.
Thanks, Richard. Where's the info coming from?

I would guess we shouldn't assume equal Z/I and ETO loss rates. ETO probably saw a lot more flying/tinkering by exhausted crews and probably under significantly worse average weather conditions.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by Richard Anderson » 11 Dec 2021 08:42

I always find it fascinating when someone natters on about how "we" shouldn't make assumptions and then proceeds to make blanket assumptions.
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Re: German-Allied loss ratios in aerial combat, Western theaters

Post by TheMarcksPlan » 11 Dec 2021 10:05

Richard Anderson wrote:
11 Dec 2021 08:42
I always find it fascinating when someone natters on about how "we" shouldn't make assumptions and then proceeds to make blanket assumptions.
Thanks, Richard.
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