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Monday, April 2, 2012

Flames of War Statistics 101 (pt 3)

Hello again everyone, and welcome back to the final article in my FoW Statistics series: Tactical Application.

Over the past two articles (part 2) (part 1), we've looked at two very important concepts. Expected Value is a calculated value of what we 'expect' to occur given a specific scenario and set of conditions. It allows us to answer questions like, "how many Panthers can I expect to kill with Semi-Indirect fire from 2 Fireflies?" or "which is a better way to engage a platoon of StuG G's with my Sherman 76mm platoon?" Potential Value is another calculated value that represents the most extreme scenario in one way or the other. It allows us to answer questions like, "how many Shermans will I lose of all of those Panzer III shots hit?" or "if I don't kill this platoon now, how many tanks could I lose in return fire?".

Both of these values allow us to create possible future scenarios for our actions and give us the ability to "see" the results of them in advance. Unlike the game of Chess (where no chance is involved), probabilities must be calculated in order to see 'turns ahead' in Flames of War. EV and PV give us the tools to create these scenarios and be prepared for whichever way the die falls.

As a brief aside, there have been a few comments regarding EV and Binomial Calculations, and the accuracy of Expected Value. It should be known that Expected Value is not the exact percentage chance to kill a particular number of vehicles, tanks, teams, etc. - it is roughly what we can 'expect' to occur in a given scenario. However, what it does allow us to do, is compare tactical options quickly and effectively. If you would like to spend some time furthering your statistics knowledge with Binomial Calculations, a good resource (pointed out by CaulynDarr) is

As I mentioned in the previous article on Potential Values, it is not simply possible to play a game of FoW where you expect your opponent to roll a '6' on every die roll and you to roll a '1'. While it is important to create 'back-up' scenarios for when these results occur, it is (virtually) impossible for an entire game to go that way. (I ran the numbers - you could 'walk' to Alpha Centauri before you had a game like that, or if you prefer, 1000 monkeys on 1000 typewriters would write A Tale of Two Cities first)

If this is true, the next logical question is: If we can't rely on Expected Value or Potential Value all the time, how can we reliably apply them to a game of Flames of War?

The answer is, unfortunately, even more complicated: Apply both concepts in tandem, leaning heavier on PV the higher the risk is to your troops.

Risk Mitigation is a term you'll hear some of the top-tier players throw around, and it revolves around the concept of keeping your troops as safe as possible while continuing to engage/maneuver/delay/etc. the enemy. We all already do this when we play and it is largely built into the Flames of War system as a default, though some players obviously do it better than others.

For instance, the risk of being engaged by a platoon of tanks on the move is naturally mitigated by the possibility of Full RoF return fire. If I have equal numbers of equally matched tanks, the first player to move & fire may not score enough kills to sufficiently reduce the number of shots coming back at them. We can also act to further mitigate the risk of such a platoon by having infantry near by that can assault the enemy tanks, or other AT weapons that can join in should the enemy move out to engage.

No, not THAT Risk
"Risk" can be broadly calculated as your opponent's Potential Value for the action he is likely to perform in response to what you do. "Mitigating" that Risk can be broadly calculated as the "Risk" you impose upon your opponent if he engages in that first action.
For example, I am considering moving up 4 White Scout Cars full of Rota dudes to MG a platoon of dug-in infantry. My opponent has a platoon of 4 Shermans nearby that can move and fire on the White Scout cars - this is the "Risk" of performing my move. I should therefore "Mitigate" that Risk by moving my platoon of 8 T-34/85's behind the Rota platoon to cover my action - providing a "Risk" to my opponent of engaging the Rota platoon.

So now we have three terms - Expected Value, Potential Value, and Risk Mitigation - floating around. How can we use these concepts to make us better at Flames of War?

Generally speaking, we want to chose actions that have high EV and low Risk - the higher the EV and lower the Risk, the better. As the game progresses, we may be forced to take higher and higher Risk maneuvers, but the concept will always remain the same.

To make use of our EV values in regards to Risk Mitigation, I use what I call the "Rule of 2" - the EV of whatever action I take should be double the EV of whatever action my opponent can take. Essentially, I want my expected 'chances' to be twice as good as my opponent's 'chances'. This way, even if things swing in my opponent's favor, the sub-par scenario should roughly be an even exchange.

For example, let's say I have 6 Wiking Panthers looking to engage 4 ISU-122's (no Kannone or Rat this time). Currently, we are 36" apart, with clear LoS between us. I want to know if moving to 31", firing, and stormtroopering back to 34" is a good move. It sounds good in my head, but there are an awful lot of variables in there.

First, we find the EV of our shots:

So we can expect our proposed maneuver to kill exactly 1 ISU-122. Next, we find the EV of our opponent's shots under two conditions - successful stormtrooper & unsuccessful stormtrooper. One will give them standing RoF and the other moving RoF.

Stormtrooper success:

Stormtrooper failure:

We can then combine both scenarios (Stormtrooper fail & success), to give a combined EV for our opponent's return fire. Since our % chance to Stormtrooper with Wiking Panzers is 50%, we can multiply both EV's by .50 and add them together to get our weighted result.

.556 * .50 + .833 * .50 = .6945

Given this scenario, it seems like the Panthers would have the upper-hand in a game of averages - especially since there is a fair chance the ISU's will be down by one vehicle when conducting return fire.

Sean says "Screw you, Rule of 2!"
However, given my 'Rule of 2', I would personally not make this maneuver unless there were external variables that called for it (running out of time, needed to draw fire from another platoon, part of a concentration of fire on the enemy platoon, etc. ). The chances of 'confirming the kill' are relatively low with the number of shots I have, and my opponent could roll well and blow up a few of my Panthers. Furthermore, since my Panthers are more expensive than his ISU's, the loss would be more detrimental to my army than to his.

If, however, there were a small copse of trees nearby.....


Now I could stormtrooper back inside the treeline, however, the EV of his shots is really low. In fact, I'd want him to stand and shoot at me, just so I can get full RoF back at him the next turn. Even if he manages to double his EV and kill 1 Panther, 10 shots in return fire could be devastating to that ISU platoon.

So even though the initial move may be just outside my 'Rule of 2', it can result in a situation that becomes heavily in my favor should my opponent make the wrong decision. And if he makes the 'right' decision and disengages, then I have completely mitigated my risk - essentially trading 6 Panther shots at his ISU's for nothing! This is what good players call giving your opponent the choice between two bad decisions - either he can stand and fight against the odds, or he can back down at no cost to me.

The one exception I and other players will make to the 'Rule of 2' is ALWAYS CONFIRM THE KILL. If you knock an enemy platoon below half strength half-way through your shooting, NEVER rely on your opponent failing his platoon morale check. ALWAYS expect your opponent to pass platoon morale and plan every move accordingly - you should consider any failed morale check as 'free bonus kills'. If that enemy platoon is a threat, the last thing you want to do is stop firing at it and choose to fire at lesser threats/tertiary targets. Applying the concepts in these articles, find the full Potential Value for kills from the enemy platoon that is now understrength. If it is a threat to any of your planned actions, in the words of Dark Helmet, "Keep firing, Assholes!"

I hope these past few articles have been informative. I have really enjoyed writing them and I hope to be back to throw out some more FoW Mathemagic!

Eric Riha
FoW Mathemagician


Unknown said...

I can't say enough about how awesome these articles are! Thanks Eric

Diragi said...

Might be worth rolling up the math into a decision tree (diagram)

wargamerabbit said...

Stats 101 and 102 classes in university. Best classes for this gamer since sliced bread. Excellent overview on the subject.

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