Tiger Accuracy

[rexford]

Site at http://www.panzer-vi.fsnet.co.uk/talesmenu.html offers interviews with Tiger crewmen, and quite a bit is said about accuracy.

In what appears to be his first combat, Bobby Woll seems to knock out 22 T34 with 25 shots, including kills at 1500m.

In Joachim Scholl's case, the gunner can't hit much of anything despite about 40 shots at various real and semi-real targets. Eventually, the accuracy improves on long distance tries and hits become more regular.

Both sides of Tiger gunnery, absolute best and somewhat difficult. 88% accuracy at what appears to be 500m to 1500m range.

The good ones were really good, and may have exceeded the estimates provided by ballistics analysis.

[Michael Dorosh]

What did Bobby Woll have for breakfast that day?

Do you think I'm joking?

Did he just have 8 hours sleep and a full stomach?

Did the other gunner go 3 days without sleep and food?

There is a very real human equation in all of this that often gets forgotten since it is difficult to quantify.

[Jeff Duquette]

“What did Bobby Woll have for breakfast that day?”

He must have been eating nails if he KO’d 22 T34’s with 25 rounds.

Joachim Scholl on the other hand prolly didn’t have breakfast....maybe some hard tack.

Now we know why the USMC traditionally feeds their boys steak and eggs before a beach landing…so they can KO 22 T34’s with 25 rounds.

[ 10-16-2001: Message edited by: Jeff Duquette ]

[Michael Dorosh]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Jeff Duquette:

“What did Bobby Woll have for breakfast that day?”

He must have been eating nails if he KO’d 22 T34’s with 25 rounds.

Joachim Scholl on the other hand prolly didn’t have breakfast....maybe some hard tack.

Now we know why the USMC traditionally feeds their boys steak and eggs before a beach landing…so they can KO 22 T34’s with 25 rounds.

[ 10-16-2001: Message edited by: Jeff Duquette ]<HR></BLOCKQUOTE>

Not sure I see the point behind this. Are you saying the human factor is irrelevant to the equation?

[JasonC]

I have a conceptual statistics question, or more properly exercise, for Rexford. I assume your 88% figure is simply 22 divided by 25 = .88. And I wonder whether you've give that the thought it properly deserves, because multiple triers and multiple trials are a bit more complicated, mathematically, than an x / y mean.

Here is the question - what prior probability do you think a group of Tiger gunners would need for such ranges, in order for you to expect, by chance, 1 gun crew out of a population of say 450 (there were 3 times that many Tigers, but not all at once), to have achieved a 22 out of 25 "run", as the best in the sample?

450 crews line up and fire. Any tank that reaches its 4th miss, count the hits so far and drop it from continued firing. Imagine a "histogram" of the length of the "streaks".

You want only 1 of the 450 to reach 22 hits. Solve for the uniform prior probability needed per shot, to achieve that (what "die roll" does a shot need).

If the estimate is a little rough, that is no problem, in the ballpark is fine.

Notice, it won't gonna be 88% chance of hit per shot. Go ahead and try that as a hypothesis and see what you'd expect as a result, to see why.

I offer this, because I think you've got the kind of mind that will take to the analysis well, and can see the point clearly if you work through the problem. The basic subject matter is what outliers in distributions can tell us about prior probabilities.

I hope this is interesting, but if anyone else doesn't get it (yet), that's OK. Besides Rexford, that is - LOL. More is expected of him.

[JasonC]

Here are some related questions, to further explore the problem.

1. Imagine that B. Woll's 22 out of 25 performance was an -average- one. What prior probability per shot would he need for this to be the case? Hint - the answer is not 88%.

2. After solving the original problem (in the previous post) for the case of 450 shooters, solve it again with varying population sizes for the shooters. How much does the needed prior hit probability fall if there are 1350 shooters in the sample?

3. Like the previous, but this time with only 100 shooters in the sample - how much does the required prior hit probability rise?

4. From the answers to the previous two, and to the original question, how sensitive is the implied prior hit probability to various assumptions about whether B. Woll's performance on that occasion was a top 1% performance, or a best of all Tiger tanks performance? If the difference large?

5. Compare a mean figure from the previous question to the answer for #1 above. What accounts for the difference? What is the difference between a "naive" mean as x hits over y shots, a mean -performance- in a distributional sense, and an outlier performance?

[Sgt Steiner]

Hi all

Ref the Tigers one factor that numerous accounts etc mention is that (at least initially) the Tiger units were given the cream of Panzer personnel and one would therefore expect (if such was indeed true) that their 'accuracy' would be better than average.

Bobby Woll appears to have been an exceptional gunner by all accounts (and big part of Wittmans fame) some note he had good ability to shoot on the move (something not practiced by most WWII crew).

In period of CMBO (ie 1944-45) this 'Elite' crew status may have been a lot harder to acheive due to losses ?

I believe similar 'Elite' crew status was claimed by the Stug units and indeed by British Tank Destroyer Regts as they had Royal Artillery crew who were rated above average (at least by themselves).

Cheers

[JasonC]

I'll give further help, to make it easier, but still encourage Rexford to work through the exercises given himself. Consider this the "back of the book" answers section.

You may use a mathematics or statistics software package to help with the analysis. I used Mathematica. If you use that, make use the standard add on package (should be included) called Statistics - Discrete Distributions.

Spoiler Alert - Answers Below - Spoiler Alert

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The answer to the original question in the first post is 60% hit probability.

The answer to #1 in the second section is 84.6%. With a hit chance that high, the mean of the resulting distribution of runs is 22 long.

The answer to #2 in the second section is 57%, only 3% lower than the 450 shooter case.

The answer to #3 in the second section is 66%, only 6% higher than the 450 shooter case.

The answer to #4 is that the difference is not large, plus or minus 5-10% in prior hit probability only. Most of the effect exists just going to a "top 1% performance". With larger and larger shooting populations, the implied prior hit probability continues to fall, but more and more slowly, "diminishing returns" style. A three-fold increase in shooting population only reduced the prior hit probability 3 percentage points in absolute terms, once up to a "best in 450" outlier.

For #5 in the second section, note that a hit probability in the range 57-66% is indicated by the outlier analysis, where a 85% hit probability was indicated by the assumption of an average performance (mean length of run = 22). The difference between them stems from the nature of outliers. Pure chance in a population of any significant size produces the change from 85 to 60-65.

The 85 figure is an average performance, which means a mean position in a set of multiple trials. Whereas the 88 naive mean makes no allowance for the role of chance in establishing run length. We can see this by assuming the 88 figure is the prior probability and seeing what happens.

If the prior probability of a hit were 88%, then the mean length of a run by the time of the 4th miss would be 29.33 hits, with a standard deviation of 15.6 hits. A top 1% performance with that prior probability would produce a streak 77 long. The best out of 1350 performance would be a streak 103 long by the time of the 4th miss.

Simple means are not sufficient for analysing streaks produced in multiple trials by large populations.

Extra credit human interest - people fooled by randomness. Imagine a group of 100 financiers guess the direction of the stock market. 20 right guesses and they can retire as millionaires. But just 4 misses and they go broke and have to find another line of work. Despite the fact that it takes 5 times as many correct guesses to win as wrong ones to lose, if they have just a 2/3rds chance of guessing right each time, 2 of them will retire as millionaires. The other 98 won't.

I hope this is interesting.

[rexford]

The original post shows that Tiger gunnery was not a constant high quality, but appears to have varied from one extreme to the other, just like everyone else.

However, the fellow who couldn't hit tanks on the fly had no problem dropping HE rounds close to trucks, guns and infantry. So Tiger gunnery against "soft" targets appears uniformly good from the few stories that are available.

Most readings of Tiger exploits show a remarkable ability to wipe out the soft targets, ending with a terrific count of knocked out guns, trucks and infantry. While Tiger HE muzzle velocity (810 m/s) is very high and increases ground dispersion of HE rounds, the great effectiveness against soft targets suggests that Tigers were consistently hitting near the soft targets, which infers great gunnery and range estimation.

Why the difference between T34 and truck/gun/infantry accuracy? Trucks and infantry don't fire big rounds at tanks, and artillery and 45mm anti-tank guns aren't much of a threat most of the time (they are aimed high in the air for artillery purposes).

So maybe it is psychological.

The bottom line of the two Tiger crewman stories is that a good Tiger could attain an accuracy well above what is normally considered to be possible, even assuming 10% or 5% average range estimation error. The best Tiger crews were heads above the average.

It is said that Sergeant York could shoot instinctively well, like he was born to shoot which gave him an advantage.

The best outdo the others by significant margins, and sometime don't miss much. Like Wittman in a StuG IIIA who knocked out T34's one after the other with single aimed shots: nerves of steel and an eye to match on his and the gunners part.

[Herr Oberst]

<BLOCKQUOTE>quote:</font><HR>Originally posted by JasonC:

I have a conceptual statistics question, or more properly exercise, for Rexford. I assume your 88% figure is simply 22 divided by 25 = .88. And I wonder whether you've give that the thought it properly deserves, because multiple triers and multiple trials are a bit more complicated, mathematically, than an x / y mean.

Here is the question - what prior probability do you think a group of Tiger gunners would need for such ranges, in order for you to expect, by chance, 1 gun crew out of a population of say 450 (there were 3 times that many Tigers, but not all at once), to have achieved a 22 out of 25 "run", as the best in the sample?

<HR></BLOCKQUOTE>

I'm a little confused by this notion of a "streak"... What we heard is that 22 of 25 hits/kills/whatever were achieved, roughly 1 miss for every 8 shots. I'm not disputing the uncanny accuracy that such a "win/loss" record would require.

Where the misses occur within the 25 trials is irrelevant to the outcome of concern, namely 22 out of 25. Is each shot treated independently in a probabilistic sense?

This would seem to devolve into a simple combinatorics question, depending on the assumptions made.

Feh! I had sworn off the field of Sadistics some years ago. Curse you for bringing it up again, and making me remember old training...

[Michael Dorosh]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Sgt Steiner:

Hi all

I believe similar 'Elite' crew status was claimed by the Stug units and indeed by British Tank Destroyer Regts as they had Royal Artillery crew who were rated above average (at least by themselves).

Cheers<HR></BLOCKQUOTE>

You're referring at self-propelled Anti-Tank regiments I presume? Doesn't every British regiment consider themselves the best?

Considering the crap THEY had to eat for breakfast, I would rate their skill much higher than the smelly old Germans.

[Michael Dorosh]

<BLOCKQUOTE>quote:</font><HR>Originally posted by rexford:

The original post shows that Tiger gunnery was not a constant high quality, but appears to have varied from one extreme to the other, just like everyone else.

<HR></BLOCKQUOTE>

Again, the question is "why"?

Training?

Inconsistent quality of their equipment?

Inferior enemy? Did the tanks that Wittman was firing at have radios, or did they mill about in confusion when they were attacked that day (or did they even know they were under fire - buttoned up and without a radio, how would they know?)

Individual skill - Alvin York was a born shot; was Bobby Woll a "born tank shot"? Is there such a thing?

May be useful to talk to a real living, breathing armour gunner about this issue.

Lots more to consider than made up numbers.

[Jeff Duquette]

“May be useful to talk to a real living, breathing armour gunner about this issue.”

I think the original post is based on interviews with real gunners.

[Michael Dorosh]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Jeff Duquette:

“May be useful to talk to a real living, breathing armour gunner about this issue.”

I think the original post is based on interviews with real gunners.<HR></BLOCKQUOTE>

Who seem not to have been asked "why"?

[Andreas]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Michael Dorosh:

Considering the crap THEY had to eat for breakfast, I would rate their skill much higher than the smelly old Germans.<HR></BLOCKQUOTE>

If you can stomach Sewer Trout and powdered egg for breakfast, you can take out a Kingtiger at 3,000 yards at the first shot. Hmmmm, M&V pie...

[Tuomas]

<BLOCKQUOTE>quote:</font><HR>Originally posted by JasonC:

The answer to #1 in the second section is 84.6%. With a hit chance that high, the mean of the resulting distribution of runs is 22 long.

<HR></BLOCKQUOTE>

While the answer you gave is right in a way it is no better than the original by rexford. Yet another answer is 91%. Actually any given hit propability between 85% and 91% will yeld 22 hits out of 25 shots. So the "right answer" would be .88 +/-.03. Another thing to note is that IRL every individual shot has a diffrent hit propability (as in CM) so this speculation is fruitless.

While statistics can be a great tool for analysis it can be used also to bash our opponents as earlier shown by tss.

-TNT-

[c3k]

JasonC,

Still at it I see. Good.

Now, you ask us to analyze a sample of 450 to come up with a single streak of 22 hits for 25 shots. This exercise is purely your own fiction. That day, there were NOT 450 Tigers shooting. How many were there? Not sure. 2, 4? (Maybe Rexford could answer that.) Okay, now run your little math exercise using that as a sample size. Changes things just a little.

[My tone seems a bit harsh as I re-read my post. Not meant that way at all. Statistics have their place, but the underlying assumptions in calculations MUST be thoroughly understood.]

[As a further exercise, JasonC, I ask you this: give me a Tiger with 1 shell, on a hill with good LOS. 2,000 meters away put a T-34. Now, would you climb into the T-34 and give me my one shot?? I'll let you quote any statistics you want as I line up the sights. ]

Ken

[ 10-17-2001: Message edited by: c3k ]

[RMC]

<BLOCKQUOTE>quote:</font><HR>Originally posted by JasonC:

I hope this is interesting, but if anyone else doesn't get it (yet), that's OK. Besides Rexford, that is - LOL. More is expected of him.<HR></BLOCKQUOTE>

As this topic moves into its third thread in recent weeks, I have discovered who JasonC really is:

And we are just poor pinkys unable to comprehend the master's teachings.

In a related note, I wonder if JasonC is interested in applying his statistical precision and his ideas about tiger tank accuracy to rifle accuracy.

It seems to me that most people would agree that the Garand, Enfield and Mauser were all accurate rifles. And yet what is the average amount of rifle ammunition expended per hit on enemy soldiers? I expect it is very large, but I do not doubt the inherent accuracy of the weapons themselves. The delta has to be found in soldier psychology and training. This brings us back to a post I made in one of the earlier threads. How do we do justice to the demonstrated capabilities of the equipment AND capture the influence of soldier mental states on the usage of that equipment?

[Sgt Steiner]

Hi Michael et al

<BLOCKQUOTE>quote:</font><HR>Originally posted by Michael Dorosh:

You're referring at self-propelled Anti-Tank regiments I presume? Doesn't every British regiment consider themselves the best?

<HR></BLOCKQUOTE>

Yes SPAT Regts, which as far as I know were all Royal Artillery Regts (at least in NW Europe as were the AA Units) note they are organized in Batteries not Squadrons.

Royal Artillery do consider themselves the best gunners bar none (I serve with a few ex-RA types) and nothing wrong with that I supposse (unless you have to listen to the claims firsthand !)

Here is little ditty ref 62nd AT Regt RA during fighting around Buron on 8th July 1944 quote is from their War Diary ( excerpt found in Osprey Vanguard 10 by Bryan Perrett)

"At about 0900 the Infantry (the Highland Light Inf Of Canada) had taken Buron though there were several Germans still holding out at the far end of the village. The Battery moved moved up and 'B' Troop were deployed on the SE side of the village and 'A' Troop at the S and W of the village. Shortly afterwards the Germans put down a very heavy shelling and mortar barrage and quickly followed this up by a counter-attack of some 20-30 Tanks. Two guns of 'B' Troop were able to engage and between them accounted for some 12-13 Panthers and Panzer IVs. The remaining tanks withdrew to the SE. The guns which accounted for the tanks were commanded by Sgt HW Bowden & Sgt GPJ Donovan'

A further note by Perrett states

'the Battery had not got off lightly and after the action only three of its Achilles were in a fit state to continue'

Also :

'During subsequent operations in Belgium, Holland and Germany the British TDs in addition to other duties often acted as heavy-weight snipers moving into posistion before the start of an attack to take out potential enemy observation posts in the church steeples and windmills that dominated the flat landscape'

Does anyone know if US Tank Destroyer units were allocated the cream of the crop as crewmen in their units ?

Cheers

[PJungnitsch]

<BLOCKQUOTE>quote:</font><HR>Originally posted by rexford:

So maybe it is psychological.<HR></BLOCKQUOTE>

No doubt it is another important factor. Once a tanker 'got the hang' of a Tiger after transferring up from a Stug or PZIV, he would realize that 1) He's got a gun at his disposal that shoots very flat and pretty much destroys whatever it hits 2)He's got the optics to match the gun 3)There is enough armour around him that under most conditions he can calm down and concentrate on knocking out the other guy. The resulting confidence no doubt enhanced the training and equipment advantages.

Note -by mid '44 some of these advantages were gone, to the point that warnings were circulated, ie:

<BLOCKQUOTE>quote:</font><HR>Now the Tiger, for long time regarded as a 'Life Insurance Policy', is relegated to the ranks of simply a 'heavy tank'<HR></BLOCKQUOTE>

But by then many crews were probably through the learning curve far enough they could still be extremely dangerous. Many of those 1350 or so Tigers produced seemed to last an extremely long time considering the odds against them, some ending up in the French army after the war.

[Mannheim Tanker]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Michael Dorosh:

May be useful to talk to a real living, breathing armour gunner about this issue.

Lots more to consider than made up numbers.<HR></BLOCKQUOTE>

Exactly. As a real, living gunner (former anyway) I can attest to the huge effect that the human element has on the results of any gunnery exercise. You can run stats all day long on the results, but it misses the key issue - everything is dependent on the human elements affecting the gunner during the exercise (or battle) being examined. The fact that this is so overlooked in many of the arguments on this board just makes me chuckle - I'm glad you pointed it out in this one, Michael.

Did I eat breakfast that morning? Was I recovering from a cold? Was I distracted because of something that happened earlier? The list is endless...

The bottom line, is that IMO any cold, fact-based statistical analysis or what-have-you is only answering a piece of the question, and that piece might not even be a large one! I won't put any confidence limits on it, though. My $.02...

[JasonC]

No Rexford, it is not that simple. If we want to isolate the effect of crew qualities on prior probabilities, we first have to estimate the effect from randomness alone, and remove it. Only the "skew" that remains can be attributed to skill differences.

To see this, consider my 100 financiers example again. The worst one will get his first 4 calls in a row wrong. The best one will retire with his millions after 20 correct calls out of 23 or 24 tries. You can be sure all the wags will say the first had no head for business, and the synchophants around the second will flatter his great market calling skill. But by construction, the only difference between them is pure chance.

To discover the effect of differences in skill, we have to remove the distribution created by chance alone, and look at what is left over. Suppose 900 out of 1000 attempted financiers only have a 50-50 chance on their market calls, while 100 have the 2/3-1/3 chance. Then we'd still see 2 outliers that make it the distance, because the odds against the 50-50 people are quite steep to achieve such a long run. The best out of 900 of them by pure chance will only get 17 "hits" before his 4th "miss".

Seeing 2 outliers that long out of 1000, it would be consistent with either all of them having a 58% chance of being right each time, or with 1/10 of them having a 2/3 chance of being right, and the other 9/10 having only a 50-50 chance. But what you can't conclude is that the pair who got 20 out of 23 had an 87% chance with every guess. The real skill effect could easily be "2/3 rather than 1/2 each time, for the best 1/10 attempters".

It is very easy to fool oneself with the effects of randomness. It is very easy to put down all distribution effects seen to skill alone, even though one knows that cannot possibly be correct, just from the mechanisms involved. A financier trying to estimate whether his own skill is 1/2-1/2, 2/3-1/3, or 7/8-1/8 can easily err on the upper side by ignoring the pool he is a part of, and ascribing everything that happens to him to skill rather than chance.

When they happens, he lets out his horns, takes bigger risks out of confidence, and blows out. This is not mere theory nor is it easy to fully grasp. It happens every day. The same thing happens to gamblers, especially in cases where some skill is involved, like poker.

To the guy who said "what if only 2 or 4 were shooting that day?", the answer is simple enough. If that were average performance out of 2 or 4, it would be close to average performance for everybody, and you'd hear not about one 22 out of 25 streak, but about 10s of them per day once Tiger battalions were in action. Which would have only the Tiger outliers - not the rest of the Tigers or all the other tanks or the PAK or the other weapons - accounting for about twice as many dead Russian tanks as the Russian had tanks.

Outliers tell us quite a bit about the distribution they are drawn from. Making outliers into supposed means results in absurd predictions, which the facts will always falsify. Any model of prior probabilities drawn exclusively from them, will always lead to nonsense outcomes at higher scales. While models of prior probabilities that are consistent with outcomes at higher scales, will still let the outliers show up properly, in the distribution of results per item.

Going back to what the outlier told us, B. Woll's run told us that some Tiger commanders had hit probabilities as good as 60-65% for average shots at 500-1500 meters. That is definite information. It didn't tell us some had 88% hit probabilities at those ranges. It didn't tell us how much B. Woll's run was luck among a population with 60-65% chances, and how much was higher chances for him personally - along with chances below 60-65% for the rest of the Tiger population, who do not report lots of such runs. Undoubtedly some of the effect was skill. Which tells us B. Wolls hit chances were probably north of 2/3rds, and that other Tiger crews chances were probably south of 3/5ths.

Next another fellow remarked that actually, the prior hit probability is varying for each shot. That is true, and mathematically the way one deals with that is to add a weighting function called a measure to the prior probability, and then integrate over the measure, instead of using an average prior hit probability. In B. Wolls run of 22 out of 25 shots, for instance, some were at 500m and some at 1500m. The nearer ones will have a higher hit probability than the calculated implied prior probability (~60%), the farther ones will be lower.

But only systemic effects like range need to be included in such a measure. Random effects, like random variations in the sighting picture, or in crew readiness state from one shot to the next, can be ignored, because their effect is indistinguishable from just different "die rolls" at each trial. An uncorrelated random effect added to systemic variables will disappear on integration - a few are +3%, a few are -2%, etc, and the net effect is nada.

The interchangeable nature of uncorrelated random effects is one of the secrets of the power of statistical methods in the first place. It is why e.g. a statistical description of a gas is quite good enough, without needing to know the position and velocity of each atom. The mean is not moved by the shot-to-shot variations. Thus a model that uses a mean prior probability and a random determination for each trial, can faithfully reproduce the right mean and distribution effects (variance, skew, etc), without needing to vary the probability of each shot. Different "die rolls" will model the small shot to shot differences.

This the the reason modeling techniques like random walks, Markov chains, and stochastic processes theory generally, work as models even of processes whose minutae we can't track exhaustively. In physics or in econ, as well as in cases like this.

Of course we don't know all the outliers and the whole shape of the curve of accuracy, the distribution of shots fired by range (exactly, anyway - we can make better and worse models of that) so we can only estimate effects like crew quality (skewness), and the fall off of accuracy with range will have more certain aspects and less certain ones. If the fall off of accuracy with range is close enough, though, random rolls will do the rest, on the second question.

As for the fellow's question about small arms and the obvious difference between firing range and combat performance, I am perfectly willing to see the same sort of analysis applied. I think you will find that CM today gives a rifle only about 1/100 of the accuracy that basic rifle marksmenship tries to teach every soldier.

A rifle has an average firepower of about 5 over the ranges BRM covers (Army - Marines shoot farther). It takes about 250 fp times exposure to generate 1 CM casualty (more against a ducking target sometimes). Open ground cover is typically 70% exposure, so about 72 CM shots are needed for 1 rifleman to generate 1 casualty. The number of rounds in a CM rifle shot is uncertain, but between 2 and 4.

So 1/144 to 1/288 is the average accuracy of a CM rifle firing at a target in open ground, as at BRM. On the real world firing range, a soldier can typically hit 3/4. So the difference for combat conditions modeled in CM is a factor of 80-160, or call it around 100. Cover beyond open ground then reduces the accuracy actually achieved by 2/3 to 4/5ths (15-25% exposure), so that 240-750 rifle bullets fired cause 1 casualty. Some recon by fire, some additional long range fire in static situations not covered by CM, would presumable reduce it further, but 1/500 is probably a reasonable figure.

With machineguns, the ammo expenditure is even higher, and of course they do most of the shooting by bullet count, and shoot at longer ranges where the accuracy is decidedly less. Under the best conditions CM allows for about 1 hit in 300 rounds fired, and against typical cover more like 1 in 1000, or about half the accuracy per round of rifles, but a much larger portion of the rounds fired. There is more recon by fire here than in the case of rifles, too, and far more long range fire at uncertain targets, mostly beyond the scope of CM scenarios.

Well, the western Allies lost about 1 million KIA between them and about 3 times as many WIA. The Russians lost up to 10 times as many KIA but probably only 2 WIA per KIA. All told, perhaps 34 million Allied casualties. The causes of wounds usually put bullets at 25-33% of the total, which would mean 8.5-11.3 million hits. The Germans produced around 10 billion 7.92mm, far and away the dominant type, which works out to 1 hit per 1000 fired, plus or minus 15%.

Notice, if you believed just firing range data, you'd set the combat accuracies too high by a factor of several hundred, and at CM ranges everybody who came into LOS would be hit practically immediately. Blown up to strategic scales, one would predict absurd loss totals, like everyone on earth shot several times over by the Germans alone.

The wonderful thing about having data - about outliers or means - is that we don't have to make these things up. The numbers check each other. Purely willful fantasy numbers about the average effectiveness of weapons do not withstand scrutiny. The range of reasonable assumptions consistent with even the spotty data we have is not very wide.

Now let's consider one simplified crew quality model and see what it would suggest about hit probabilities with the outlier info we have. Suppose we imagine there are 500 Tiger crews over the war, using up 2.7 tanks each as some are KOed or break down, etc. Then lets assume there are 1/6 of them 1 standard deviations (SD) or better above the mean, 1/6 of 1/6 2 SDs above, and 1/6 of that 3 SDs above. We have 2 crews +3 SD (super elite presumably), 12 +2 SD (elite), 70 +1 SD (crack), and 416 also rans (vet or regular - say the 250 below average crews regular and the other 166 veteran).

The average accuracy of the pool would be about 1 standard deviation above the regular accuracy. From a statistical standpoint, there isn't a big difference between those luckier by a few SDs and those better by a few SDs. "Lucky" and "good" both give similar results in practice. The overall effect of the skill mix is to bump the mean up about 1 SD, reflecting the skew toward the top end of performance. If the average performance is 55% hit probability at those ranges, the outlier result would be consistent with that model of crew skill. The modest reduction in mean hit probability (55% vs. 60% without accounting for crew quality effects) will be made up on the top end by a few crews shooting better than that average.

Then we can add a model of the distribution of ranges fired at, and average regular accuracy at the various ranges. Suppose the 500-1500 range shots are distributed roughly 1 at 500, 2 at 1000, 2 at 1500. The 75% at 500m, 60% at 1000m, and 40% at 1500m would be one approximate "fit". If more of the shots involved were in close, say distributed 2-2-1, then the implied hit probabilities would be lower, like 70% at 500m, 50% at 1000m, 35% at 1500m.

In plainer English, some of B. Woll's best streak can certainly be accounted for by luck, which alone is going to pull the average accuracy figure down into the 3/5 - 2/3rd area. The more of it you subscribe to his exceptional quality, the lower the accuracy of an average Tiger crew goes, but in the range of 50% up to the previous figures. We needn't and can't distinguish completely between his skill and his luck (from one outlier report, that is - in principle with enough reports we could model the skew and seperate chance from skill completely), but that is the scale of effect one expects from their combination. And the more of it you assign to particularly close range shooting on that occasion, the lower the average accuracy of a Tiger at 1500m will go, to remain consistent with the outlier, with a reasonable range of 1/3 to 2/5 for the average Tiger crew at 1500m. Incidentally, I submit those are also plausible figures on their face, which would fit with quite a few first shot kills, and many more 2-3 shot kills at that range, from typical Tiger crews.

[ 10-17-2001: Message edited by: JasonC ]

[JasonC]

"it misses the key issue - everything is dependent on the human elements"

This is a basic misunderstanding about the nature of statistics and why they work. The motions of each molecule of a gas are fully determined by its position and velocity and that of all the other molecules - an enourmous mass of varying and unknowable minutae. But we can nevertheless know the mean behavior of the whole gas even if we ignore these unknown factors completely. A life insurer does not need to know every factor effecting health, he just takes an average, and that deals adequately with uncorrelated causes neither he nor his policy holders can forsee.

All that is necessary is that there be a lot of those factors and that they vary randomly, in ways not closely correlated with each other or some other macro characteristic of the gas. Or, in our gunnery cases, as long as what the gunner ate and the way a bead of sweat rolled down his brow are uncorrelated with the range to the enemy tank. All such varied and random effects disappear in the mean - because their difference from trial to trial is random - and leave only a random distribution or "fuzz" around that mean.

That "fuzz" is exactly what is captured by the random to-hit roll. There is no measurable difference between 33%, 30%, 34%, 35%, 33%, 32%, 32%, 34%, 33%, 34% over ten trials, and 33% each of ten times. There is only a 1/65846 chance of missing all ten the first way, and 1/65292 chance of missing all ten the second, and the mean hits are the same. Minor uncorrelated random differences from trial to trial are simply irrelevant - the mean and the random roll (with the right distribution, naturally - 2d6 or 1d10, etc) capture their effects entirely.

There is no need to know the underlying human variables affecting one shot compared to the next. One on shot, the shooter will roll 1d100 and get a 14, and on another he will roll 1d100 and get a 67. If the mean and distribution of hits over a large number of trials by a large number of shooters is correct, the whole process will be accurately modeled.

The reason range needs to be modeled is because it is not like such uncorrelated random variables. It is a systemic variable - the number of hits in a given number of trials will closely correlate with the range the shots were fired at. Similarly, crew skill shows up as a consistent correlation between previous "good rolls" and later ones, by the same crew, and as a skew in the overall distribution of results from many trials by many crews.

[Michael Dorosh]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Mannheim Tanker:

Exactly. As a real, living gunner (former anyway) I can attest to the huge effect that the human element has on the results of any gunnery exercise. You can run stats all day long on the results, but it misses the key issue - everything is dependent on the human elements affecting the gunner during the exercise (or battle) being examined. The fact that this is so overlooked in many of the arguments on this board just makes me chuckle - I'm glad you pointed it out in this one, Michael.

Did I eat breakfast that morning? Was I recovering from a cold? Was I distracted because of something that happened earlier? The list is endless...

The bottom line, is that IMO any cold, fact-based statistical analysis or what-have-you is only answering a piece of the question, and that piece might not even be a large one! I won't put any confidence limits on it, though. My $.02...<HR></BLOCKQUOTE>

I knew we had an armour gunner on here but couldn't remember who...thanks for the insights. Dear Johns count for something in the grand statistical scheme of things, too...

[Michael Dorosh]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Sgt Steiner:

Hi Michael et al

Yes SPAT Regts, which as far as I know were all Royal Artillery Regts (at least in NW Europe as were the AA Units) note they are organized in Batteries not Squadrons.

Royal Artillery do consider themselves the best gunners bar none (I serve with a few ex-RA types) and nothing wrong with that I supposse (unless you have to listen to the claims firsthand !)

Here is little ditty ref 62nd AT Regt RA during fighting around Buron on 8th July 1944 quote is from their War Diary ( excerpt found in Osprey Vanguard 10 by Bryan Perrett)

"At about 0900 the Infantry (the Highland Light Inf Of Canada) had taken Buron though there were several Germans still holding out at the far end of the village. The Battery moved moved up and 'B' Troop were deployed on the SE side of the village and 'A' Troop at the S and W of the village. Shortly afterwards the Germans put down a very heavy shelling and mortar barrage and quickly followed this up by a counter-attack of some 20-30 Tanks. Two guns of 'B' Troop were able to engage and between them accounted for some 12-13 Panthers and Panzer IVs. The remaining tanks withdrew to the SE. The guns which accounted for the tanks were commanded by Sgt HW Bowden & Sgt GPJ Donovan'

A further note by Perrett states

'the Battery had not got off lightly and after the action only three of its Achilles were in a fit state to continue'

Also :

'During subsequent operations in Belgium, Holland and Germany the British TDs in addition to other duties often acted as heavy-weight snipers moving into posistion before the start of an attack to take out potential enemy observation posts in the church steeples and windmills that dominated the flat landscape'

Does anyone know if US Tank Destroyer units were allocated the cream of the crop as crewmen in their units ?

Cheers<HR></BLOCKQUOTE>

Buron (the second battle in July, not in June) has always been of interest to me - I have done a scenario on it, and the HLI put out an excellent history on just that one day of fighting. Thanks very much for the info - outstanding!