Film of Stuka 87G in action

[pamak1970]

Originally posted by JasonC:

You haven't the slighest idea what "my theory" is, you are arguing against a straw man between your own ears. Nuance is wasted on you because you pay no attention to the exact logical meaning of careful statements, you just jump to imaginary generalizations you can quibble with.

Of course I have partitioned all losses among all causes of loss, necessarily crudely given the uncertainties, but using estimates and rankings of relative effectiveness. That is where statements like the average German vanilla AFV got no more than 1 kill come from, with figures no higher than 3 for Panthers and 5 for Tigers overwhelmingly likely. Everything from fausts to 88s is included in those estimates.

Enjoy your last words. You've never taught me a thing or mentioned a single point I hadn't long since considered, and won't take instruction. So you are useless to me.

You still refuse to give the "proper equation".

You say i make generalizations and used your equations wrong.

Where are the proper ones ?

Or give me the equation that calculates the average T-72 kill per a M1 Abraams and show me why my application does not follow the logic of your theory.

If you want to point or prove something related with numbers, then use math, not lectures

[pamak1970]

There is also another thing that Jason implies.

When average kills per weapon asset are so low and average lethality was not really so big in the battlefield,then all wargames including CM gross overestimate the efficiency of all weapons.

We are talking here about dozens-maybe hundred times of increased lethality.

recall that on average a single tank according to Jason would KO half up to four or five enemy tanks during the whole duration of its operational life which was many months (one year for Soviets according to jason)

So the question for other members that might follow this conversation is the following.

Do they beleive that game designers,during their effort to provide excitement and action to players,use models that are dozens or hundred times more lethal than real ones?

[NCOIC]

Do they beleive that game designers,during their effort to provide excitement and action to players,use models that are dozens or hundred times more lethal than real ones?

This has been discussed many times before, the answer is yes.

The models are good, its their usage that is inflated in games.

[JasonC]

It is a matter of inferences not equations. You can cancel many quantities or estimate them as unity, less than unity, etc readily without knowing all the details, and general enough inferences "run". Inequality reasoning, order of magnitude reasoning, in other words.

In the case of T-72 kills, you'd partition all the losses among the causes of loss to get a fraction to M-1s, divide by number of M-1s doing the killing. You would not however conclude that figure is the kills per M-1 over its service life, because it is still around. You would conclude the kill per M-1 during the war figure, was low. It was.

You would then ask what quantity as a per engagement amount, integrated, resulted in that average figure. You would find ammo consumption was very low - if dead APCs were also included, you'd find it within an order of magnitude of losses apportioned to M-1s. You would notice M-1 losses are non-existent. And you would conclude the M-1s ran out of targets, not own side tanks or ammo. Shot incidents and kills would not obviously be 2-3 orders of magnitude apart. Therefore, you could not tightly constrain per shot effectiveness, as you can with WW II losses, combat length, and ammo expenditure figures.

The same reasoning fails utterly if the hypothesis is made that the same thing happened in WW II (i.e high per shot effect, limited targets to use it on before all are gone). It predicts too few dead tanks on the winning side, expecting most of them to survive the war. It gets expected ammo expenditure wrong by two orders of magnitude. It predicts a very short war with lopsided losses. These predictions are all falsified. Ergo, the same thing did not happen in WW II. Which is obvious to every rational person.

[pamak1970]

Originally posted by NCOIC:

</font><blockquote>quote:</font><hr /> Do they beleive that game designers,during their effort to provide excitement and action to players,use models that are dozens or hundred times more lethal than real ones?

This has been discussed many times before, the answer is yes.

The models are good, its their usage that is inflated in games. </font>

[pamak1970]

You would not however conclude that figure is the kills per M-1 over its service life, because it is still around. You would conclude the kill per M-1 during the war figure, was low. It was.

So you admit that "average" kills per M1 during the war was low. No problem witht that.

The problem is that inspite the above the lethality of M1 in the battlefield was VERY HIGH.

That is why i say from the beginning that average numbers do not point lethality in the battlefield.

[pamak1970]

You would then ask what quantity as a per engagement amount, integrated, resulted in that average figure. You would find ammo consumption was very low

Ammo consumsion?

The first time you talked about ammo consumsion during this long discussion was in the previous post(edit- try to quantify it)

Until now you were using numerators and demoninators only.

The other thing is that you do not address the problem of how to calculate ammo fired against a target .

As i said earlier ,ammo consumsion can be generated in many ways .

If ammo convoys or depots are destroyed, this will generate a new ammo supply.

Still noone of the previous rounds were actually used against a target.

This type of ammo "consumsion" was not used to try to kill enemy targets

[ August 24, 2005, 10:01 AM: Message edited by: pamak1970 ]

[JasonC]

Yes all wargames dramatically overmodel weapon effectiveness. They also dramatically overmodel actual firing. They predict loss rates as a result that have no connection with historical reality.

I showed some AARs of tank fighting in Korea at the Pusan perimeter recently. They showed (1) no armor engagements at all took place during the day. The Americans had good tank support in place and complete control of the air, and the NKs respected both enough to only send their tanks forward at night in small probes.

The principle here is denial of battle. One side or the other generally has an incentive to do so. It is difficult to bring them to bay and force a fight when they can see the terms are unfavorable. It is rare that both sides tactically seek battle. The side that seeks it generally gets advantages from its willingess to do so. But typically when battle actually occurs, the seeking side has had to give something up in terms of location, terrain, force mixes present etc, compared to their overall strength.

(2) Tanks on the losing side turned around and left, successfully. Night helped this, a WP smoke round probably played a role in another incident.

The principle here is limits of LOS and its interaction with the previous. Only portions of forces enter the lethal areas of effective enemy weapons. Most are outside of LOS, and most of the rest are barely inside LOS, when engagement occurs. This is particularly true of things like tanks which are relatively hard to conceal, and essentially impossible to conceal while moving or firing.

The result is the distance to break contact is typically short. Only green formations or doctrinal errors typically result in a weaker formation pressing deep into the lethal fire zone of a superior one, to be destroyed entirely. Only very small units are exceptions to this. That is, lead elements or small units manage to brush closely, most do not, and many get back out of effective range while the forward elements exchange fire.

(3) Shots were made in complete darkness, blind. Shots were made at sound. One shot missed at a range of less than 100 yards, probably because it was a newly acquired target, and the gunner probably pulled the trigger as soon as the loader yelled "ready", without waiting to make sure his barrel was actually aligned with the target by then. Whole platoons fired without result, while a lead shooter did all the actual hitting. Lead shooters ran through their ready-rack ammo engaging only a few vehicles.

Moreover, these were excerpts from a battle that lasted three weeks. There were less than half a dozen incidents in that entire period when armor of the two sides saw each other at all. Mostly, armor supported by shelling hills occupied by enemy infantry. The typical result of that fire was that the enemy infantry moved back to a reverse slope, or otherwise broke contact. The losing side does not stand to be shot to rags on a parade ground.

In a typical CM engagement, the losing side losses virtually its entire force and the winning side loses up to a third of those engaged, sometimes higher. Operations research indicates instead that most units that suffer 15% losses break off whatever military action they are currently performing. Higher losses, 30-50%, do happen, but are rare. They are typically bloody fiascos that befall only the losing side. Occasionally, attackers press home with losses as high as 30%, usually because some objective is particularly important, sometimes because the troops are particularly green (green units take higher losses).

In absolute terms, the average losses per US infantry division per combat day in western Europe were about 25. Russian figures might have been 2-3 times higher but are the same order of magnitude. In active attrition combat, attacking daily, losses can reach 25 men per battalion rather than per division, per combat day. CM players lose that much in half an hour from each company without batting an eye.

Moreover, we fire far more than the real participants did. The average US rifleman got a new basic load of ammunition every week, sometimes twice a week in active combat. That meant 120-240 rounds per week. We run out of ammo supplies modeled as about that size in 20 minutes.

The limiting factor is clearly how often occasions arise in which a mere riflemen can see any point in firing at the enemy. They are much rarer in real combat than in games. Morever, we know from loss apportionment that few riflemen hit anyone, ever. It is not like the firing opportunities they held out for were picture perfect shots. No, they could go through a day of battle without ever seeing the enemy. They might or might not area fire at places they heard or suspected enemy. If they saw enemy, they saw them very briefly as poor, fleeting targets.

Armies approached each other closely, much less often and much less aggressively than we do in games. Limited forces probed. Most of the time, the enemy's dominance of particular areas was simple accepted as an accomplished fact. The areas so owned shifted according to maneuvering, intervention of superior arms, achievements of local tactical advantages etc, all of which persuaded one side to give ground, long before being ejected from their positions. Often with modest losses in the process, from forward elements, patrol actions, shelling, etc.

There was a lot more cat and mouse seeking small advantages, and a lot less mindless mashing into each other until one side bled to death. Even armies notorious for the latter, did it far less often than we do in CM.

It is not limited to WW II, the point is general throughout military history. We can tell from expenditures, for example, that the average musket ball in the Napoleonic wars was fired under conditions that yielded only 1/200 accuracy at best, with 1/1000 much more likely.

Direct tests show the weapons themselves readily achieve 25-40% accuracy against the large formations regularly used, at relatively long ranges by contemporary accounts. If they averaged that, no one would have walked off Napoleonic battlefields alive, and the battles could have been decided in half an hour.

Instead they took 4 hours minimum and sometimes 2 days, a third of the losing side were sometimes hit but rarely more than a quarter of all those engaged on both sides combined. Despite carrying 60 ball (which could be shot off in 30 minutes at sustained ROF), and being resupplied with more from artillery trains.

No, they did not all walk to within 100 paces and let fly. They'd all be dead, and they aren't. Such brushes did happen, and could wound a third of those involved in less than five minutes when they occurred. But they happened rarely, among subunits, at critical points. Not along entire frontages for hours.

What a Napoleonic battle actually was, for most of its length, was what we would call skirmishing. Meaning the opposing frontages lined with open order screens shooting at other open order screens - often at ranges as far as 1000 yards (I am not kidding - no Napoleonic wargame lets muskets fire beyond about 200 yards, but we know to a demonstration the average ball was fired under less favorable conditions than that).

And there was an excellent reason for this. You could not increase the other guy's loss rate by packing more men into a given frontage than a skirmish line gave, without driving up your own losses to his replies in direct proportion. Because it was all area fire. A thicker front meant more of your own men hit. The only efficient use of numbers was to outlast the enemy. You could use them to push him aside and take ground instead, only by locally driving the loss rate higher, and the loss ratio against what you could achieve by skirmising.

Moreover, one side or the other frequently had an edge in such skirmishing due to terrain or whatever. The other side then let them be, tried elsewhere, or made only a limited demostration in that area to keep losses low. Again the forces are not mashed together nearly as forcefully as they are in games. They act much more tenatively, paying much greater heed to small advantages. They blaze away at ranges where hits are quite unlikely, but they still inflict losses that way, because ammo is not scarce nor men's willingness to take losses very high.

As for Napoleonic artillery, we are frequently treated to the stories of the best ball that took out 25 men, or the batteries firing case that tore a hole in an enemy line. But the prosaic fact of the matter is the average cannonball, fired at massed infantry targets at 1000 yards or less, flat missed. How or why? Smoke is a large reason in this case. After the first few volleys, they could not see their targets. The targets moved. Artillery fire denied ground, as men got out of the beaten zone, much more than it killed. A few rounds might have had high effect, but the bulk of them had no real chance of hurting anyone.

Firing chances >> ammo available >> men present >> men hit. Universally true, from the dawn of gunpowder until the advent of precision guided munitions. For that matter, it is equally true of arrows before gunpowder.

[JasonC]

I've included ammo in all my analyses on this board for two years, you are just late getting to school. Consumption of ammo other than firing it at the enemy cannot explain order of magnitude differences between shots and hits. The most generous allowances for it might give you a factor of two, but the numbers to be spanned differ by two to three orders of magnitude. Making a distinction without putting an order on it is not an argument. The same is true of overkill theories. The huge discrepancy can only be spanned by the average shot flat missing.

[pamak1970]

Originally posted by JasonC:

I've included ammo in all my analyses on this board for two years, you are just late getting to school. Consumption of ammo other than firing it at the enemy cannot explain order of magnitude differences between shots and hits. The most generous allowances for it might give you a factor of two, but the numbers to be spanned differ by two to three orders of magnitude. Making a distinction without putting an order on it is not an argument. The same is true of overkill theories. The huge discrepancy can only be spanned by the average shot flat missing.

I do not know why you give numbers like that saying that most generous allowances give a factor of two.

I say it is much more.

Counting ammo "consumed" when it was destroyed by any source,from aircrafts attacking convoys and depots to submarines attacking merchant ships.

Ammo "consumed" when it was abandoned during retreats,

Ammo "consumed" during training.

ammo-AP rounds used in other than tank targets,

ammo "

ammo "consumed" as part of a stock inside a tank which was KOed and cought fire,

even ammo "consumed" when the gunner fired away the AP round inside the barrel juct because he wanted to free the barrel to load HE round to engage a non tank- target ( you do not attempt to replace a shell already inside the barrel).

It is a mystery why you think that all the above and more that i failed to mention give a factor of two .

Counting also that during a battle a tank is going to fire a good portion of its stock which is dozens of rounds not counting possible resupply and real estimations about lethality during battles are more complicated.

I agree however with your previous posts about the fact that battles are rare and very often combatants avoid it

I said the same thing from the beginning.

This is different than claiming that WHEN battles take place , there is not so much lethality

[Guest Mike]

I think "average" lethality is definitely less than that represented in almost any wargame you care to mention.

that's because wargames need to be interesting - therefore we cut straight to the interesting bits.

A good example is the figure gaming that I mostly do - I play a set of rules called "DBM" for ancient era (mostly pre-gunpowder), and hte games we play are invariably representations of "fair and open battle" because that's about the only thing that can hold our attention/inmterest.

Think of, say, the Pelopopnesian war - from 425-403 BC - 22 years give or take a bit, and IIRC <big><big>3</big></big> "fair and open" battles large enough to be represented as wargames (Delium, 1st Mantinea & a 3rd that escapes my memory). Famous actions like the surrender of the Spartans at Pylos were "skirmishes", which can certainly be wargamed if you have apparopriate rules, but were also not that common. Plus there weer a handful of other actions such as surprise attacks, ambushes, etc.

So average lethality of the Greek armies over this period was very small. But we ignore the 99.99% of the time when no-one was getting killed and concentrate on the interesting bits to make it worthwhile.

IMO it is the same with CM - of course we're ignoring the 99% of times and places when nothing much happened - precisely BECAUSE nothing much happened.

[Battlefront.com]

IMO it is the same with CM - of course we're ignoring the 99% of times and places when nothing much happened - precisely BECAUSE nothing much happened.

Exactly. I remember doing some research on a big, critical battle in the Bulge. Great TO&E info, fantastic descriptions of locations, etc. The ramifications were immense too. But the battles themselves at the CM scale... rather booring. Tons of artillery, entire German force getting stuck in the mud (then pounded by artillery), skirmishes from great distances with the Germans pulling back instead of pressing on, etc. etc. In the end both sides lost quite a bit of material and manpower, but for the most part it was just chipped away over the space of a couple of days. Rather dull to play that battle out, so I scratched it from the scenario list IIRC.

That being said, the fact remains that wargames tend to overmodel the possibility of force destruction. This is the fault of players and player expectations, not wargmes themeselves for the most part.

Steve

[jeffsmith]

A corrollary is that Strictly Historical Battle Scenarios

are often not as interesting as Fictional ones

[Michael Emrys]

Originally posted by Battlefront.com:

That being said, the fact remains that wargames tend to overmodel the possibility of force destruction. This is the fault of players and player expectations, not wargmes themeselves for the most part.

I should think it is both. The wargames are definitely overmodeling the destruction. But they do so because the designers perceive (probably correctly—at least to a degree) that that is what the players want. Nobody sets out to deliberately make a game that won't sell more than a few hundred copies...if that many.

Michael

[ozi_digger]

I tend to avoid these threads because they degenerate into emotional arguments so quickly.

WRT earlier pages - from my experience, pilots definitely overclaim, even in this day-and-age with advanced technology.

For the probability guys - have any of you read Morris Driels, Weaponeering: Conventional Weapon System Effectiveness ???

IIRC he goes into some of this stuff. Have ordered a copy so will have another look and see if there is anything worth posting. (By that stage, this thread will be closed, so will open a new thread only if his work is worth reading).

[Andreas]

Originally posted by jeffsmith:

A corrollary is that Strictly Historical Battle Scenarios

are often not as interesting as Fictional ones

I agree with you on that, but I think it depends on what you play/design them for.

[ozi_digger]

*Puts flak jacket and helmet on*

Well, I said I'd post but I didn't wait for the text, I decided to go ahead with what I know and add to the air power debate, specifically this thread and Thorn in the Tiger's Side. Apologies in advance to those who thought they'd seen the back of this debate and were gonna let it die a natural death.

If you want a realistic model for CAS, you may as well use accurate data. Statistics as a percentile of armour kills, due to air power, for specific campaigns can be an inaccurate measure of their efficacy because of environmental factors. Therefore, IMHO, the best method to employ is to extrapolate weaponeering data. WW2 weaponeering data probably exists but will take longer to research, so modern weaponeering data is used here as an example. The data is taken from this link: General Air Munitions Data

The example I work through here is a single bomb dropped against a tank. Other weapon types such as FFAR rockets and 20mm cannon are also included in the link.

Given the defined release parameters (see link) the 500lb bomb has a Circular Error Probable (CEP) of 300ft. This means that 50% of bombs will fall within a 300ft radius of the aimpoint.

At this juncture, lets define the kill radius (Krad) of the 500lb bomb. As outlined before, our target is hard - a tank. Krad will be greater for softer targets. From the table, the crater diameter for a 500lb bomb in medium soil is 19ft. This sounds about right to achieve a tank kill.

This is where we extrapolate our data. Our CEP = 300ft, which represents an area of pi.r.r = 282857 sqft. Our Krad = 9.5ft, which represents an area of 284 sqft. The area covered by our bomb for a kill (Akill) = 284/282857 = 1/996th of the total CEP area.

Remember CEP is 50% of impacts. Therefore SSPK = Pcep.Akill = 0.5 x 1/996 = 1/1992.

The crater diameter of a 500lb bomb can be massaged to represent a firpower kill or mobility kill on a tank. Say 2 x diameter represents area that gives us a 70% chance of achieving an M-kill or F-kill. Thats a radius of 19ft, which is an area of 1135 sqft.

P (M or F-kill) = Akill x Pcep x Peffective

= 1135/282857 x 0.5 x 0.7

= 1/711

As mentioned before, the relevant data can be extrapolated to represent kills against soft targets, which will dramatically increase SSPK.

Similar methods can be utilised to represent gun and rocket runs, artillery and small arms fire.

All of the above is for academic purposes only - since BFdotcom plans to keep the same CAS model.

*Takes helmet and flak jacket off*

[JasonC]

ozi-digger - the problem is that we know to a demonstration that every calculation of weapon effectiveness performed in that manner is too high for the actual results in real combat, typically by several orders of magnitude. For instance, following the same process and literally believing the results, for the case of Napoleonic era weapons, predicts that everyone on a Napoleonic battlefield was killed or wounded ten times over. Which is false, empirically. Weaponeering calcs are systematically false in the direction "too high".

[ozi_digger]

Originally posted by JasonC:

the problem is that we know to a demonstration that every calculation of weapon effectiveness performed in that manner is too high for the actual results in real combat, typically by several orders of magnitude.

(snip)

Which is false, empirically. Weaponeering calcs are systematically false in the direction "too high".

I've heard this argument before from a number of quarters and with no disrespect intended, I'll rebut.

First, if you look at the probabilities I arrived at above you'll find that the SSPKs are very low and not an inflation of what you'd realistically expect.

Second, don't tar all data with the same brush. Sure weaponeering stats are usually a game of averages which don't take all anomolies into account. That's also the beauty of it - you can lower your probabilities for weather, high stress, training, AAA fire etc. A lot of weaponeering modelling out there is gumf, especially the stuff that is not derived from real-world data. But when it is taken from real-world data, who am I to argue? The same goes for your example. Accurate weaponeering data for the Napoleonic era doesn't exist. Protagonists at the time didn't keep it and since then all we have is the SWAG of a grog with an interest in the subject matter. Which brings me to my third and final point.

Third. Since the formation of the US Army's Air Corps Tactical School a lot of this statistical data was collated and kept. Its not just pre-1943 'we can get a bomb in a pickle barrel from 10000ft' stuff that was refuted once the peacetime tests gave way to Real War experience. That 300ft CEP from the link is derived from a number of sources - low stress practice, mid stress exercises and high stress combat flying - its not a pluck. Its what real-world weaponeers use to compute the number of sorties they need to generate to guarantee a reasonable chance of mission success. No, the SSPK is not always too high, its not always 100% accurate, but it does give a ball-park figure. That same 'falsity of weaponeering' argument even comes from the pilots. I.e. "I've been in this game for 25 years and dropped more bombs than this equation of yours and I'm telling you you're wrong and my intuitive guess is right!"

Well, sometimes he is right, but 9/10 he's wrong and the equation comes up with a figure closer to the truth. Especially so when that equation is based on real-world data.

*dons flak jacket and helmet again* :cool:

[JasonC]

"all we have is the SWAG of a grog"

False. We have the actual weapons themselves, we have firing trials, we have representative targets, elaborate reconstructions and reenactments, the works. Telling us things like the average accuracy of a Brown Bess at 140 yards against a column sized target was 25%, and at 70 yards was 40%. And if you assume the actual numbers are anything remotely like those test results, you predict not something off by 20% or even by a factor of 3, but 50-100 times the casualties actually inflicted.

And a 500 lb bomb dropped under realistic combat conditions rarely landed within 300 feet of its intended target. The USAAF dropped 3.1 million 500 lb bombs and 560,000 1000 lb bombs over Europe. Estimated causalties, mostly wounded and mostly civilians, came to about 1.1 million. When all types are included, on average it took 6 HE, 1 fragmentation, and 1 incendiary bomb to wound each person. (Losses to the aircrews were about 1/10th as large as the losses to those they were bombing).

Pound for pound thrown or dollar for dollar invested or man for man wounded, 105mm and 155mm howitzers beat the air force, hands down.

[ August 28, 2005, 10:08 PM: Message edited by: JasonC ]

[Michael Dorosh]

Originally posted by NCOIC:

</font><blockquote>quote:</font><hr /> Do they beleive that game designers,during their effort to provide excitement and action to players,use models that are dozens or hundred times more lethal than real ones?

This has been discussed many times before, the answer is yes.

The models are good, its their usage that is inflated in games. </font>

[ozi_digger]

Originally posted by JasonC:

"all we have is the SWAG of a grog"

False.

For a minute I don't dispute what you're arguing. But wait - the tests you mentioned are by their very nature 'groggy' (is there such a word?). No actual data from the period exists, so what do we do? Conduct controlled firing tests at a variety of ranges versus static targets. Now make the targets moving. Add stress, smoke and anything else you can think of and the data may reduce your chances of hitting 100 fold. Thats a given. I wouldn't wanna refute it.

My point is that actual real-world, modern weaponeering data exists from high-stress situations that we can use as a baseline to model effectiveness. We could do a lot worse than accept some of their figures with a dose of healthy critique.

Going back to the link I posted, I found a minor error in my calcs - the crater diameter I used was for a 250lb bomb. I therefore ran another quick calculation. If I use more realistic stats, I get a SSPK = 1/567. The US 1st Tactical Air Force claims 407 tanks destroyed in the ETO Nov44-May45. By dead reckoning (taking no other factors into account), this alone represents over 230000 sorties where an AFV was the intended aim point - and you're saying my figures are too high?

Again, please don't tar all data with the same brush. A bit of healthy massaging of real data can produce a realistic baseline.

[ozi_digger]

And a 500 lb bomb dropped under realistic combat conditions rarely landed within 300 feet of its intended target.

Wolud ya wanna back that up with some evidence? CEP gives us 50% within 300ft. Which I re-figured above to 160ft BTW.

The USAAF dropped 3.1 million 500 lb bombs and 560,000 1000 lb bombs over Europe.

As a whole? Lets stick to tactical CAS.

Pound for pound thrown or dollar for dollar invested or man for man wounded, 105mm and 155mm howitzers beat the air force, hands down.

Thats not even part of my argument - because you're right. I'm arguing we can generate a realistic model instead of putting it in the too hard basket.

I'm going to try and get some accurate WW2 CEPs tomorrow.

[Michael Emrys]

Originally posted by Michael Dorosh:

</font><blockquote>quote:</font><hr />Originally posted by NCOIC:

</font><blockquote>quote:</font><hr /> Do they beleive that game designers,during their effort to provide excitement and action to players,use models that are dozens or hundred times more lethal than real ones?

This has been discussed many times before, the answer is yes.

The models are good, its their usage that is inflated in games. </font>

[JasonC]

USAAF claims 4500 AFVs destroyed and 3500 AFVs damaged for the war as a whole. But we know these figures are ridiculously inflated - awarding nothing to Brits, it has air wiping out the entire German AFV fleet in the west without the ground forces accounting for any. Twice.

That's how we got started - no air force estimate of the damage they inflicted can be taken as accurate or even as getting the order of magnitude right. So your numerator has no basis.

US tac air - fighters only, no light bombers -dropped around 350,000 500 lb bombs. The Brits flew Tiffies with rockets and much better cannon for strafing. And they might have accounted for the low 3 digits of tanks between them - while losing about 40 times that number of fighters. (5200 US fighter types alone).

How do I arrive at the low 3 digits score? German AFVs sent west only come to around 5000. (4k is more likely but I am being generous). Ground combat got the largest portion, mechanical losses and abandonments for tactical or fuel reasons most of the rest.

In the periods of heaviest air focused on armor, we occasionally see 11% caused by air attack. So 5-10% is a reasonable portion of the total, for the campaign as a whole. If the US with 500s got half that, we are talking about 100-200 KOs by direct hit over the course of the war.

Of course they were not always attacking tanks, quite the contrary. Most of the targets were truck columns and trains. USAAF claims for those are more than an order of magnitude higher than for tanks. While not an adequate indication of actual effect, those reports may well reflect how common the target types were, along with some allowance of easier KO of the softer targets.

1 in 500 to 1 in 750 are believable scale for those results, if we allow in addition for most attacks not being directed at armor, capped at 15-20% being so directed. (Probably lower; that is an upper bound).