Tiger Accuracy

[Jeff Duquette]

The human element is obviously key…gee what a surprise…thanks for pointing out the obvious Dorosh. Obviously the system itself influences results just a tad. That’s why two crews of equal experience will consistently get different results on TTVIII depending on whether they are sitting in an M48A5 or an M1A1.

[Michael Dorosh]

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

The human element is obviously key…gee what a surprise…thanks for pointing out the obvious Dorosh. Obviously the system itself influences results just a tad. That’s why two crews of equal experience will consistently get different results on TTVIII depending on whether they are sitting in an M48A5 or an M1A1.<HR></BLOCKQUOTE>

Your contributions to this thread have sterling as well, Missy.

[Mannheim Tanker]

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

No need to lecture me on how statistics work, Jason - I use them all day long now that I have a job in the civvie world (in science no less). I'm a firm believer in using them to quantify results when possible.

I'm not disagreeing with the findings of your statistical analysis. The point I was making was that Franz may have hit 22 out 25 shots that day, but that doesn't mean the next 25 shots (that day or the next week...doesn't matter) will have the same results as most of the variables affecting his accuracy are constant (as most human variables are). I can't even begin to count the days where I did awesome in the UCOFT one day, only to completely eat dog poo the next. Fortunately, I was usually much more focused when it came to firing real bullets on the range.

Hehe...yeah, I know's it's obvious to some people, Jeff. However, there are also a lot of discussions on this board that tend to get bogged down in an effort to quantify every last element in a combat engagement. BTS has even stated that the outcomes of the battles in CM are much more predictable than anything in real life since you can never come really close to quantifying many of the intangible factors that affect the final outcome.

Edit: One point, Jason, that you are realling missing. The results that you cite aren't as predictable as you might first think. An example: I shoot 5 good shots in a row. On shot #6, I forgot to toggle the ammo selector switch when I switched from AP to HE...and the shot misses by a wide margin. Frustrated by this newbie error, I'm distracted on #7 and flub that shot as well.

This is exactly a scenario that I witnessed as a loader once (and learned a good lesson that I carried forth as a gunner later on). My point is that the numbers never tell the whole story. You can argue otherwise until you're blue in the face, but nearly any statistician will agree with me on this. With that said, there is still some value to stats...as long as you understand their limitations.

[ 10-18-2001: Message edited by: Mannheim Tanker ]

[JasonC]

Both of the effects you mentioned are perfect examples of things indistinguishable from luck. Luck is not a mystical additional force or a reflection of quantum uncertainty, it is simple the aggregate resultant of effects just like the ones you mentioned (good day, bad day, momentarily flustered, etc). You will get exactly the same effects from not modeling any such minutae and then making appropriately random "to hit" rolls. Which will streak or not, have momentary phantom correlations that then disappear, yada yada. Which is not something additional, it is the whole point of the random component of "stochastic" models.

[Mannheim Tanker]

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

Both of the effects you mentioned are perfect examples of things indistinguishable from luck. Luck is not a mystical additional force or a reflection of quantum uncertainty, it is simple the aggregate resultant of effects just like the ones you mentioned (good day, bad day, momentarily flustered, etc). You will get exactly the same effects from not modeling any such minutae and then making appropriately random "to hit" rolls. Which will streak or not, have momentary phantom correlations that then disappear, yada yada. Which is not something additional, it is the whole point of the random component of "stochastic" models.<HR></BLOCKQUOTE>

I disagree, as human factors are not necessarily stochastic. If I start to do badly in gunnery - and get frustrated about it - the probability that I'll flub the next shot suddenly increases.

Edit: I agree that in a sim (or game), however, that things like this should just be modeled as a random occurence. You're just beating your head against a wall to do otherwise LOL!

[ 10-18-2001: Message edited by: Mannheim Tanker ]

[JasonC]

Occasional short run correlations do not detract at all from the applicability of random models that get the mean and distribution shape right. There is no need for each successive trial to be literally independent in some metaphysical sense (a condition never fully fufilled in physical systems anyway). It is not just "in practice" or for games that such effects can be ignored, they can be ignored theoretically too, unless the correlations are both so common and so strong that one is really measuring one event rather than two. Then just shifting the "unit" that you "roll for" is enough. With small sets it is completely unimportant, because you will get "hot" and "cold" streaks that duplicate such effects anyway, by chance. 1/4 of the time two rolls in a row will be below average.

The whole subject is a distraction. It is being advanced (you weren't the first to bring it up, I know) to make it seem as though any range of numbers somebody wants may be appropriate. It is akin to general claims that because something is not known exhaustively (at a molecular level, say), therefore nothing can be known about it, so one can have any opinion about it. Which is the purest hand waving.

Average Tiger accuracy at medium ranges is not 88%, and we know it. The idea that prior accuracy can be anything because it varies infinitely from case to case is false, and we know it. Varying results from case to case are what one expects from the notion of a prior probability in the first place. "Look, so and so hit a lot, while such and such missed a lot" is not evidence against a model with limited variations in prior probability and random resolution of each trial, because such distributed outcomes are exactly what such models are meant to reproduce, and do reproduce.

The evidence presented is consistent with prior hit probabilities between 1/2 and 2/3 for average crews at medium ranges, depending on how large the skill effect is, as opposed to luck, associated with the cited incident. The higher that skill effect was, the closer you get to 1/2 rather than 2/3 for an average Tiger accuracy at such ranges. Nothing anybody has said since supports otherwise.

But more important, I do hope that rexford looks at these modeling prior probability effects and explores the whole subject of expected distributions, beyond averages and variation from one incident to the next. Because I know he has a head for such things, and his thinking on similar subjects can be honed by examining these aspects of the question.

I don't expect everyone else to get into the numbers, though I certainly encourage it for anyone interested. Abstract pronouncements on the modeling process are sterile compared to looking at real random models, numerically.

[Andrew H.]

I'm not going to get into the numbers.

I am interested in the human aspect part of gunnery, though, esp. wrt things that can be accounted for in the game. It might be interesting, and it might be realistic, if tank gunners got some sort of accuracy bonus for shooting, when, due to range or unawareness of the enemy (maybe), the enemy would not be able to hit the shooting tank. Like, say, T-26's at 2000 meters. There may be some sort of de minimus rule, so that tanks with a very low chance to hit don't invalidate the bonus.

At first I was going to try to make up some number realistic sounding bonus (like 10% of the actual chance to hit added as a bonus, so a 50% chance becomes a 55%; 90 becomes 99, and 5% becomes 5.5%). But then a simpler solution suggested itself: have a crew, for shooting purposes, act as the next higher quality level. So regulars would shoot as veterans, veterans as crack, etc. Elites can't get any better; that's what elite means .

I think that the bonus should be temporarily lost if enemy units come within firing range, and permanently lost (for the rest of the qb/scenario) if the tank is hit by enemy fire, regardless of whether it is AP, HE, arty, or small arms fire.

I am assuming, of course, that there is some firing benefit that more experienced crews get. There must be, since order delays and morale don't apply to vehicles, but more experienced vehicles cost substantially more.

Anyway, does anyone have any thoughts on this system?

[Jeff Duquette]

<BLOCKQUOTE>quote:</font><HR>I shoot 5 good shots in a row. On shot #6, I forgot to toggle the ammo selector switch when I switched from AP to HE...and the shot misses by a wide margin.<HR></BLOCKQUOTE>

I recall a somewhat similar training incident in which we are firing an engagement against a BMP. TC calls out GUNNER HEAT BMP. I’m the loader and grab HEAT give the gunner his UP. He fires two rounds and puts a hole through the plywood target on the second round. Well before the TC announces cease-fire I have a third round of HEAT up. Next engagement TC announces Gunner SABOT TANK…well HEAT is still UP so I yell at the top of my lungs “FIRE HEAT”. Whether the gunner indexed HEAT or SABOT into the ballistic computer I have no idea. I know we fired several more rounds of SABOT during the same engagement.

It’s like baseball. One week you can bat .400 and the next week you might bat .180 that’s part of the game. But the good hitters typically have much more consistency and have the ability to dig down deeper when their suffering from head colds or didn’t get their Wheaties this morning. That’s why you get German tank aces that run up scores of 100+ kills and other gunners that are lucky to hit the broad side of the moon at 200meters. Some folks suck…Some folks have lucky streaks…some folks are just plain good.

[Mannheim Tanker]

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

Occasional short run correlations do not detract at all from the applicability of random models that get the mean and distribution shape right<HR></BLOCKQUOTE>

Actually, this isn't exactly correct (you can have a certain amount of "drift" or bias in your distribution), but I'm not going to argue with you about it Jason since I know I'm right. There is a often distinct difference between the classroom answer and the real world answer. I've seen this in other problems as well (one I'm working on right now for that matter).

Excellent point, Jeff, about the good gunners being able to adapt more quickly and bounce back from setbacks. One of my COs preached PT like the Holy Word, and it certainly paid off. Our company consistently did better in night engagements and maneuvers as a result of being more fit (and thereby having greater stamina).

[Dan Robertson]

One factor which is not brought into gunnery equations is situation and phsycology.

Imagine two situations.

1. 88mm Flak gun verses Sherman range 500m, the tank has been visable for 3 minutes now is firing at an infantry trench to the right of you. Your gun is seen by the tank and you have had plenty of time to assertain the range.

2. You cresh a small hill in your Tiger and 500 meters away is a Firefly Sherman pointing it gun directly at you. You have seen the tank for all of 2 seconds, the tank is still rocking on its suspension. You can only guess the range.

At the moment as far as I know the gunnery equations simply take into account target exposure, range weapon and an experiance modifier.

In later CM I would like every tank to be given a "personallity" at random.

You may have a new crew man with exelent eye sight and training, who can accurate estimate range and aim with a steady hand, in occasions where the unit is not under fire he shoots execptionally accuratly. Where under fire he comes to pieces and rarely hits the target.

One the other hand you may have an experianced shooter who is not technically brilliant but performs in a similar manner whether under fire or not.

At the moment the random aspect of gunnery is a bit odd, the same gunner is randomly good or bad.

[Mannheim Tanker]

<BLOCKQUOTE>quote:</font><HR>Originally posted by Dan Robertson:

At the moment the random aspect of gunnery is a bit odd, the same gunner is randomly good or bad.<HR></BLOCKQUOTE>

I agree, and this is the point I was trying to make to Jason. He's assuming some normal distribution to the shots fired, but that distribution may change over time (if viewed as a time series).

[JasonC]

Actually, those are two different points, not the same one. Whether the distribution is "stationary" for one shooter is different from the other poster's expectation that randomness in accuracy should only reflect crew skill, and thus once a good shot, always a good shot, and once a piker always a piker. Which is not a matter of whether one shooter's distribution is stationary, it confuses the distribution of shooters with the distribution of shots by each - or expects the second of those to be nearly deterministic, rather than random.

On non stationary distributions for a single shooter, my point is that it is going to (1) wash out in the long run when not a systemic shift (e.g. random variations in situation are effectively ergodic) and (2) it is going to be lost in the noise of the randomness of each shot in small samples anyway.

On the suggestion of a bonus for "invunerability" (or for time in LOS), I have no problem with either. They won't make much difference either way compared to tactical factors like exposure time and luck of the random to hit rolls, but they are plausible effects and in some extreme range cases might matter.

I have a somewhat different diagnosis of the general issue in these discussions, however. I think that many people are not comfortable or familiar enough with varied distributions of random elements and many trials, while they do know accurately several tactically relevant facts about critical factors in engagements, common engagement lengths, anecdotes of accuracy or runs achieved, etc. And they try to deduce simple means or "typical" situations out of those, and expect things to more or less always be that way. And then they notice that there is lots of variation left, and want to bring in other variables - hidden ones, or crew quality as the catch all leftover - to explain the fact that all engagements do not fit their picture of what is typical.

Whereas thinking about the whole subject as a matter of distributions of random outcomes explains things much more simply, and also accounts for a lot of the different aspects that often cause confusion or unrealistic expectation. It is an Occam's razor solution. Certainly effects from things like crew quality remain, but they are smaller than some probably think they have to be. And "hidden" extra variables besides these are not really necessary at all, to explain what is known.

To help at least some see this, I offer a sample random model of tank shooting. Assume engagements are broken up into 4 different range brackets, with prior hit probabilities of 50%, 25%, 10%, and 4% for each of the four. Say 1/4 of all engagements fall into each category. To see what this will mean for overall engagement averages, ammo expenditures, it is a matter of weighting results from 4 random distributions added to each other. What results does the above model predict?

~1/4 of all engagements are first shot hits. 1/2 are decided in 3 rounds or less.

2/3rds are decided in 6 rounds or less, thus probably within one minute. High prior hit probabilities are not needed to create those results - chance will provide some of them, and a portion of short range engagements.

Does this mean the average rounds to get a kill is only 3? No, it is a bit over 10. Only 1/6th of the rounds fired, get 2/3rds of the kills. The unluckier and longer range engagements use up more ammo. The median engagement is decided fast, but the long outliers take quite a few shots.

Half of all fights decided in 3 rounds creates an impression of high prior accuracy, which seems incompatible with 10 rounds per kill overall. But they actually fit perfectly. The rapid engagements do not require high prior hit probability to show up - the distribution produces some of them anyway. The luckier long range shots add to the relatively high hit probability, short range ones. While the long range cases have a "tail" of combined poor luck and poor initial probability, which occurs only in a modest number of engagements, but accounts for lots of rounds fired.

For what it is worth.

[ 10-19-2001: Message edited by: JasonC ]

[Slapdragon]

I think Jason et. al. you need to move one step higher in your use of statistics to considering mean and variance to the mean between any two gunners and a series of gunners.

Let us rate gunners by how often they hit an enemy tank at x range. X can be what we are going to consider a good utility range, and is the range which we will be assuming the "norm" to which modifications will later be applied by a ballistics model, a weather model, and other models balanced to make a realistic simulation of a shoot.

The human factor is obviously the most random and the least able to be simply controlled by testing or evidence from range data. Our two humans will thus have an ability rating expressed as a percentage. Lets call our gunners Hans and Fritz.

If we were testing them in the real world, we would take Hans and Fritz out, reduce all variables, and have them both shoot at a hit / miss target (in pistol shooting we fire at a spray painted metal plate and count dings). Hans fires 10 shots and hits 8, Fritz fires 10 shots and hits 7, giving Hans and Fritz a rating of 80% and 70% respectively. Hans at this point is not better than Fritz though because, at 95% confidence (1 chance in 20 we have screwed everything up) we have a margin of error near 20% (I am guessing so I don't have to crank SPSS), making both numbers functionally similar. So to really rate the gunners we need to make them shoot 500, throwing are margin down to 5%, and assuring us of a practical difference in gunner skill.

In CM, the gunner skill is effected by crew rating (regular, veteran, etc.). To test how much this effects shots take a regular, a veteran, an elite, and a crack crew out to the CM test range and give them 1 target each (the same target) at the same range in the same weather etc. etc. and have them shoot 1 round and record the results as hit / miss. Do this 500 times (do not do multiple shots because you have a higher chance to hit with each shot and this acts as a variable between crew ability) and record the results. This is the real difference CM currently builds into tank firing as the "human factor".

Now the Tiger tank operator who had such a good record was likely statistically way out in the outer edges of his kind. This is the reason why quoting extraordinary circumstances to prove how good a force was is not useful, since you are not quoting the mean but the outer edge. A better measure of battlefield Tiger accuracy is to get the shooting record of 100 tanks and see what that is, hits and misses all told.

[Mannheim Tanker]

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

On non stationary distributions for a single shooter, my point is that it is going to (1) wash out in the long run when not a systemic shift (e.g. random variations in situation are effectively ergodic) and (2) it is going to be lost in the noise of the randomness of each shot in small samples anyway.<HR></BLOCKQUOTE>

No doubt. This isn't what I was arguing against. My point was simply that just because Hans shot 22/25 in one battle it probably doesn't mean that he'll always do that well. There are factors that might crop up in the next engagement that had zero effects in the first engagement of 22/25.

In short, I agree that people often infer too much from these extraordinary accounts and apply what they've read in a few accounts to most ordinary engagements. Hans may have simply had a really great day - and he might have had a particularly crappy day the next day due to factors not factored into the simple statistics.

<BLOCKQUOTE>quote:</font><HR>

I have a somewhat different diagnosis of the general issue in these discussions, however.

Whereas thinking about the whole subject as a matter of distributions of random outcomes explains things much more simply, and also accounts for a lot of the different aspects that often cause confusion or unrealistic expectation.<HR></BLOCKQUOTE>

I fully understand what your point is here, Jason. I'm comfortable with the theory behind the statistics. Your argument is valid in an abstract sense, but conversely, I think many people that are "statistically inclined" (you know, the egg heads like us!) tend to try to simplify a complex model to the point where important components are simply brushed aside as "random" elements or noise. The fact is, this "noise" can periodically outweigh everything else in the model! If Hans suddenly hears over the radio that his buddy Fritz just got whacked by an M-18, Hans' gunnery skills might suddenly go down the drain.

I agree that if you have a large enough sample size, you'll eventually encompass most of these "random" factors (they're not all random, BTW, as there is a cause-and-effect relationship in many of the human factors). I'm not arguing that. I am arguing against trying to estimate the skill of a gunner and wrap it up in a neat little mathematical model based on the results of a single engagment - and that's what this debate started out as.

[rexford]

There is a neat little example of the difference between firing trials and real combat in the movie GLORY.

One of the recruits is on the firing range and is hitting the target bullseye just about every time, claims he was a top squirrel shooter or something back in Alabama.

The officer gets really upset and demands that the troops be trained under combat conditions, so he has the great shot try to load his gun and fire while the officer is yelling and screaming and firing his pistol into the air.

The recruit who blasted squirrels and targets can't even load the gun with all the commotion, let alone get out os many shots per minute or even hope to hit a non-threatening target.

The CM model catches the guys who melt when the rubber hits the road, from green to elite.

But maybe it underestimates the Michael Wittmann's and Bobby Woll's and the Canadian who could hit a tiny area on the Panther mantlet and send a round down on the hull crew. These guys performed BETTER under fire than the others did on the training grounds.

This is the point of the thread, a few really good shooters and commanders do much of the killing, the others are along for the ride or do some flank protection.