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Monday, January 14, 2013

Mathnalysis! British Armour VS Panthers


With all the buzz about the new fangled 17pdr APDS ammo and the increasing cries of "Down with Panthers, Up with Fireflies!", I began to wonder if all the intuition floating around was actually correct.

So before anyone just 'says' Panthers are dead vs the new Fireflies, shouldn't someone actually run the numbers?
I LOVE Bullets with Shoes!
Oh right, that's my job.

SO:

3x Panthers = 560 points
2x Shermans + 2x Fireflies = 435 points

In order to make our mathematical comparison, we need to turn oranges (Brits) into apples (Germans). 1 Panther platoon is = 1.2873 Armoured Platoons when looking solely at points. This brings us to:

3x Panthers = 560 points
2.575x Shermans + 2.575x Fireflies = 560 points

In this "straight up" comparison, we will take full advantage of SIF and have both platoons standing and firing at each other at long range. No morale check will be done and bails will be ignored (this is easier to assume as neither platoon has an advantage when attempting to remount and both have FP 3+).

Since the Shermans in the Armoured platoon cannot harm the Panthers, we will have 2.575 AT 15 weapons firing when the platoon is at full strength (5.15 tanks). The weapon systems will then be destroyed in a 1:2 ratio, simulating the effect of the gun tank rule - 1 Firefly weapon system will be destroyed for every 2 Shermans destroyed.

Every hit generated by a Panther round results in .667 dead British Tanks (.444 dead Shermans and .222 dead Fireflies). Every hit generated by an Armoured Platoon results in .333 dead Panthers.

At long range, a Panther has a .333 chance to hit a British Tank at long range. At long range with SIF, a Firefly has a .556 chance to hit a Panther at long range.

Thus, every Panther shot will result in .222 dead British Tanks (.074 dead Fireflies and .148 dead Shermans) and every Firefly shot will result in 20/108 (.185) dead Panthers.

2 platoons enter! 1 platoon leaves!

IF, the Panthers engage first, moving to take first shots in the fight, then remain stationary to exchange fire until one platoon is dead.

THEN, the Panthers will be dead at the end of 4 rounds of shooting. 2.6 Tanks will remain in our hypothetical Armoured Platoon: .87 Shermans and 1.73 Fireflies.

IF, the Brits engage first, moving to take first shots in the fight, then remain stationary to exchange fire until one platoon is dead (no SIF on the first round).

THEN, the Panthers will be dead at the end of 4 rounds of shooting. 2.59 Tanks will remain in our hypothetical Armoured Platoon: .87 Shermans and 1.72 Fireflies.

THUS, the British Armoured platoon wins in terms of cost effectiveness in a straight up fight vs a Panther platoon.

So let's then take a look at what happens if an actual Armoured Platoon (2x Shermans, 2x Fireflies) runs into a 3x Panther platoon. The Brits are fighting from a points disadvantage, but the numbers above imply they still might be able to handle themselves.

2 platoons enter! 1 platoon leaves!

IF, the Panthers engage first, moving to take first shots in the fight, then remain stationary to exchange fire until one platoon is dead.

THEN, the Brits will be dead at the end of 5 rounds of shooting. .908 Panthers will remain in the 3x Panther platoon.


IF, the Brits engage first, moving to take first shots in the fight, then remain stationary to exchange fire until one platoon is dead (no SIF on the first round).

THEN, the Brits will be dead at the end of 5 rounds of shooting. 1.19 Panthers will remain in the 3x Panther platoon.


THUS, the Panther platoon win in terms of actual effectiveness in a straight up fight vs a British Armoured platoon.
Yay! I won something!
Now I'd like to take into consideration one last ability the Panther platoon has over the Brit Armoured platoon in this fight: Stormtrooper. People always say "Well what about Stormtrooper?" and the response always seems to be "Well you can't always lean on Stormtrooper."

But wait! Stormtrooper moves have a die roll involved, so let's throw it into our model! Stormtrooper moves have a .667 chance of success with our CV Panther platoons. Now, even with a successful stormtrooper, you won't always be able to get yourself out of harms way. Let's assume 50% of the time, when you successfully Stormtrooper, you are able to duck out of LoF from the Brit Armoured platoon, forcing the Brits to move and chase to engage. This reduces their RoF and removes SIF from the mix.

We can include this in our model by adjusting the number of shots that result in effective hits. 33.3% of the time (.667*50%), the Panthers are able to get out of the line of fire. We then model our effective hits as .666 * SIF shots and .333 * "On the Move" shots.

2 platoons enter! 1 platoon leaves!

IF, the Panthers engage first, moving to take first shots in the fight, then remain stationary to exchange fire until one platoon is dead.

THEN, the Panthers will be dead at the end of 7 rounds of shooting. 1.54 Tanks will remain in our hypothetical Armoured Platoon: .17 Shermans and 1.37 Fireflies.


IF, the Brits engage first, moving to take first shots in the fight, then remain stationary to exchange fire until one platoon is dead (no SIF on the first round).

THEN, the Panthers will be dead at the end of 7 rounds of shooting. 1.38 Tanks will remain in our hypothetical Armoured Platoon: .06 Shermans and 1.32 Fireflies.


THUS, the British Armoured platoon wins in terms of cost effectiveness in a straight up fight vs a Panther platoon - even when we incorporate a 50% effective Stormtrooper move.

This Panther's Stormtrooper was only 63% effective.
This result then begs the question: how effective does the Stormtrooper move have to be in order for a Panther platoon to defeat a British Armoured platoon of equal strength?

When we approximate a solution for X (solving exactly requires far more complicated mathematics), we find that roughly 75% of each successful Stormtrooper move must put all Panthers out of LoS in order to win the fight.



I'm sure most of you are saying by now "Those numbers are really friggin' great Riha, but - Whiskey Tango Foxtrot - what good is all of this going to do me?"

The goal of any mathematical analysis is to provide real-world guidance. Based on the results above, here's the bottom line:

A platoon of 3 Panthers beats a platoon of 2 Shermans and 2 Fireflies in the open at long range more often than not.

Engaging an equal or slightly lesser value of British Armoured Platoons with Panthers in a straight up fight (no Stormtroopering) is a losing proposition in a majority of tactical situations. A platoon of 5 Panthers (950 points) loses versus 2 British Armoured Platoons (870 points).

Skillful use of the Stormtrooper rule does allow the Panthers to gain the upper hand versus an equal value of British Armoured Platoons. It's not much of an upper hand, but the win is surely within reach.

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