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Subject: [Game Theory] Hit Probability - FRP vs AV vs Range rss

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Nex
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Have you ever wondered in the middle of a tense battle, when trying to pick a target for your brave anti-tank squad - "Should I engage that Tiger sitting at normal range, or do I have better odds against that Stug at long range?"
...No? Just me?

In either case, I ended up calculating hit probabilities for a given FPR versus AV's at the three different ranges, and I figured I might as well post it for your viewing pleasure.

I stuck with the core game and the "base" FPR and AV values - i.e. a single unsupported undamaged unobscured vehicle attacking a target in the open. However if anyone would like to see a specific FPR-vs-AV, I can certainly do that - just a matter of punching it into Excel.

First up - an FPR 2 unit (i.e. a Half-track) attacking a 0 AV (Truck), 1 AV (HT), 4 AV (PzIV, Stug, Sherm, M10), and 6+ AV (Tiger):


Needless to say, not much use against armor, and even against other HT's it's still a 50-50 gamble to only cause light damage.

FPR 4 (Inf w/o AT) unit attacking the same targets:


Worth noting that a Tiger at point-blank range still has an 84% chance to take zero damage. Otherwise pretty decent chances to cause light damage or finish off a damaged veh, even at range.

FPR 7 (Inf w/ AT):


34% to down-right blow up or heavily damage a Half-track at norm range. A 4 AV tank at point-blank is at 21% dead and 22% heavy damage odds; however tanks at long range are pretty much immune.

To answer the question I posed at the beginning of the post - the AT squad has a 30% chance to score at least a single hit on a Stug at long range, and a 24.5% chance to score a hit on a Tiger at normal range. And now you know

FPR 8 (Sherman):


Hard-pressed to do much damage to a Tiger, except for point-blank range, or to 4 AV tanks at long range. However a nice 9% to blow-up a 4 AV tank at normal range devil

FPR 10 (PzIV, Stug, M10):


Extremely dangerous for truck and half-tracks at normal range, and very good odds of causing significant damage to 4 AV at normal range.
Best case scenario for Allies to cause any damage to a Tiger at long range (with an M10) is 4% ... yep. wow

FPR 13 (Tiger):

(did not do a FPR 13 vs 6+ AV, since allies have nothing that powerful or armoured )

Numbers speak for themselves - 39% to blow-up a 4 AV at normal range and an overall 57% to cause damage at long range.


Also as an added bonus, here's a hit probability graph vs a 4 AV unit at normal range as a function of FRP:


Points of note:
* FPR 5 has a 55% chance of causing no damage
* FPR 8 is twice as likely to cause some damage than none at all
* FPR 10 has nearly equal odds of causing 0-1-2-3-4 hits - ~20% a piece
* FPR 13 has "4+ hits" as the most likely outcome wow
* The least likely outcome of all is "4+ hits" at long range from FPR 4 - has a chance of 0.015% - i.e. rolling four attack '6s' and not rolling a single 5 or 6 of the four defence dice.

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Michael McFall
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Having been a qualified Dragon Gunner and Javelin Gunner and knowing quite a few Soldiers from other Countries, I know what that anti-tank squad would do.

You will always engage the closest target, "ALWAYS".

The further out the Tank is the harder it is to hit. Also a rocket takes flight time to get to the target. If you engage a Tank head on you will probably die. He can see where you are by the smoke made by the launch and his direct fire will get to you long before your rocket does.

Also, he can perform what is called a sager drill. The Tank immediately goes into reverse and increases the range.

By the way, all this was done in WW2 and well as today. The only difference is, the missiles today track better. The Javelin has a top down kill ability.

So:

#1 Close before far.
#2 No head on engagements with a Tank.

These rules still apply today as the did back then.
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Nex
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Very valid points Michael, indeed.
However I was looking the AT squad question purely from the perspective of calculating the odds and the math involved, as opposed to real-life tactics

One thing to note, which I completely forgot about in my graph-making-frenzy, is that an infantry squad without any AT weapons has a range 1 versus armour. Which of course means they can only engage at two ranges - close (range 1) and long (range 2) - making the "normal" range part of the "FPR 2" graph unnecessary. (...the math and the numbers should still all be correct )
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Michael McFall
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Excellent job on the graphs Joe. While tactics may differ, it's always good to know what is possible.
 
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Nathaniel Beck
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nexprime wrote:
Very valid points Michael, indeed.
However I was looking the AT squad question purely from the perspective of calculating the odds and the math involved, as opposed to real-life tactics :p

One thing to note, which I completely forgot about in my graph-making-frenzy, is that an infantry squad without any AT weapons has a range 1 versus armour. Which of course means they can only engage at two ranges - close (range 1) and long (range 2) - making the "normal" range part of the "FPR 2" graph unnecessary. (...the math and the numbers should still all be correct :D)


Great analysis, Joe. There's been many times where I've had to contemplate the questions that you discussed. For instance, do you run your AT squad up to close range to try and knock out a tank threat (and possibly sacrifice them) or leave them put and try to do some damage from normal range instead of close range.

There's also been times where I've had to ignore the closer tank to fire at a tank that was further away in instances where the further tank was threatening to take an objective hex. This is especially true closer to the end of a scenario.

Another tactic to increase AT range is to put the squad onto a higher elevation (on a hill) or in an elevated house (Stalingrad, etc) to give the squad +1 to the their range for being at a higher elevation than their target. For a normal (non AT) infantry squad this can make a big difference in defending some positions as their threat range is increased to (normal) 2 and (long range) 4 for vehicle attacks.
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