I was at Winter Offensive at the end of last week, enjoying some ASL and spending time with friends, new and old alike. Inevitably discussions about ASL and tactics abound. I engaged in a discussion on when to split firepower from one large group into smaller groups. Everyone had an opinion. Some had even done the math but were uncertain on the details. Most everyone had an opinion and rules-of-thumb they followed, including me.
I like rules-of-thumb. They help me make quick decisions when I am under pressure. It is important that you ground your rules-of-thumb in sound decision making. Everyone knows by now that I am a huge fan of Robert Medrow’s articles on ASL. The first three articles I reference in my resources page are Medrow’s. I like to think my decisions are based on his works but are they? Has my thinking drifted over time? In this article, we will find out together how sound my own rules-of-thumb are and provide guidance to anyone else reading.
The Model
I wrote a python program that can model IFT shots at different DRM against different target morale. The model accurately handles the IFT out to the 36 column. The model does not deal with Pins other than to note them. I am only examining KIA and breaking. The model notes the instances of K/# happening and accurately reflects whether the unit remaining breaks. These K/# results are in the tables below. Note, the KIA/Break/NE total to 100%. There may be some small drift because of rounding errors but I have seen none in the runs I have made so far.
The model accounts for cowering but only as applicable to the shot. Since the presumption is a multi-Location Fire Group a leader cannot take part. Thus every shot taken is subject to Cowering. If Cowering occurs, the model accurately shifts one column to the left and resolves the attack. The model does not account for a Conscript double Cowering. The model allows for Leadership to affect the Fire Group but it isn’t practical most times and thus I ignore it here unless otherwise noted.
My Rules-Of-Thumb
For Fire Grouping, I have the following rules-of-thumb:
- Break “down”/minus shots into separate groups
- Combine +2 or greater shots
- Zero and +1 shots are less clear so I have no clear rule
Notice I am not taking anything else into consideration. I am not concerned about which Fire Phase it is, what turn it is, etc. These can and should play into your decision making. That is where the true art is.
This article also assumes Mandatory Fire Grouping rules are not violated when shooting. If your shot is bound by Mandatory Fire Grouping, you cannot break one shot into many. The most likely chance for breaking into separate shots are Multi-Location Fire Groups.
Breaking Minus Shots into Separate Groups
Let’s first examine some -1 DRM shots and see what the results are. In the following chart, there are three groupings of results. The first shows a 6 -1 shot broken into three 2 -1 shots, a 12 -1 shot broken into three 4 -1 shots, and a 20 -1 broken into three 6 -1 shots. All targets have 7 morale.
From this table, we can see it is better to take as many minus shots as possible. This breaks down somewhat at the larger columns and is most easily seen in the Sum column. This is likely because of the awkward table breaks. It isn’t possible to break a 30 column attack into equal attacks that hit IFT columns.
The more interesting thing to me is breaking 12 -1 into two 6 -1 shots produces more KIA results over all. Even when cowering, an Original DR 2 still results in a KIA for each attack. Thus, taking two chances to roll a 1,1 is significantly better than one chance to roll a 1,1. It is also worth noting the 2 -1 shots produce no KIA’s since an Original 2 DR cowers to the one column where there are no possible KIA results.
Confirmation Plus
This confirms my first rule-of-thumb: take as many minus shots as you can. Mathematically, this should produce better overall results. Tactically, this leaves more units able to shoot at later targets if you roll low with an early shot. I also see a second rule-of-thumb: the data suggests a 6 -1 appears to be the sweet spot for producing KIA results. I suspect a 4 -2 would be another. One quick moment to confirm:
This isn’t as sweet as the 6 -1 so let’s examine the IFT to see if we can see why. Looking at the 12 column, we can see an Original DR 2,3, and 4 are a KIA EVEN if the shot cowers. This is because an Original 2,2 becomes a Final 2 on the 8 column which is a KIA. Looking at the 4 column, an Original 2 and 3 are a KIA on each column. There is no KIA on the 2 row of the 4 column accounting for the difference. While the 4 -2 isn’t as favorable as the 6 -1 column in terms of KIA, it is still significantly favorable to the single 12 -2 overall. It seems 4 -2 and 6 -1 are sweet spots on the IFT curve. That’s a good corollary to the first rule-of-thumb.
Combining Plus Two Or Greater
Next we can examine some +2 shots against 7 morale troops:
Again, my original rule-of-thumb holds here. It is better to take one large shot against a +2 DRM. Large shots also bring KIA and K/# results into play which are missing from the lower end of the table when positive IFT DRM are in play.
Examining +2 shots against troops with lower and higher morale yields no hidden advantage.
In each case it is better to shoot the larger shot than it is to break them apart. From these last two tables, my original rules-of-thumb continue to hold. Combining larger shots at DRM greater than or equal to 2 makes the most mathematical sense.
Zero And Plus One Shots
Now we get to where my original rules-of-thumb are sketchy. They seem to be more art than match. Let us see if we can change that.
Looking closely at this chart, a pattern emerges. For +1 shots, breaking into smaller columns less than or equal to 6 seems to be counterproductive mathematically. Breaking into separate shots on the 8 or greater columns is close to a wash for broken results. KIA results disappear below the 16 column so we must consider that. As a rule-of-thumb, it makes mathematical sense to take the one combined shot, especially when shooting a stack and the effects of a KIA result. Tactically, it probably makes more sense to break these shots up, especially if the smaller shots are on the 8 or better column. You stand a fair chance to get a result with the reduced firepower while leaving yourself tactical flexibility with the remaining firepower.
This second chart covers +0 DRM shots. Here, it seems pretty clear the shots are a wash as far as “break or better” is concerned. The frequency of KIA results are significantly diminished on the smaller columns. So if shooting at a stack of units the larger shot is preferable.
From these last two charts, I can likely clarify my original rules-of-thumb. If shooting +1 shots, don’t break into separate attacks unless the broken attack has 8 firepower or better. If shooting at a stack of units, favor the combined shot since a KIA would break the entire stack. When shooting a +0 shot, breaking these into separate attacks makes the most sense unless targeting a stack of units. When shooting a stack, again favor the combined attack because of the greater chance of a KIA result.
Summation
After running the model, I now have the four rules-of-thumb when comes to Fire Grouping:
- Take as many minus shots as you can
- Breaking into 6 column shots is a sweet spot
- Combine +2 or greater shots
- Only break +1 shots into 8 column (or greater shots)
- Favor combined shot if shooting at a stack
- Break even shots into smaller shots
- Favor a combined shot if shooting at a stack
After all these years, it is good to see I was mostly right on the first two. I wonder how often the last two have bitten me but I doubt it is often. I rarely achieve such large combined fire power. At least I know now.
Conclusion
I hope you enjoyed this article. For the code nerds out there, I pulled this together in python using a Jupyter notebook. If you want the code, let me know and I will share a copy with you. Like me, it isn’t pretty but it works.
I am also very interested to hear from you what your rules-of-thumb are for breaking up shots. Based on the discussion I had a WO, there are a lot of them out there. Feel free to comment below. If there is something interesting mentioned, I will see if I can model it. Until next time.
Amazing, great work, thanks.
Great work! The conclusions are mostly what I would have expected, but it is nice that someone did crunch the numbers.
Of course there are other tactical factors to take into account. The possibility of an early low roll when splitting is one that definitely is in favor of splitting (if you achieve your result with the first shot, most of the time you will save the other for a different target).
Does you program analyze exactly the probabilities of all results, or is it based on a simulations and reporting statistics on these simulations? Exact analysis of, say, 3 attacks potentially computing probabilities for 6 DRs (for a single target) so is still within the realm of the reasonable, but it will become more costly if you want to include multiple targets.
Thanks Philippe.
I direct attacks against one unit and stop attacking when either the unit breaks/is KIA’d or I reach max number of attacking units. I record all breaks (even if it is the remainder of a K/#), KIA, and NE results for later tally. My interest was only directed at the first attack so I have no provisions to do as you suggest.
I could probably sort out the average number of DR’s per trial but I am not sure what it would tell us.
No, my question was more whether you are doing simulations (repeat N times: roll virtual DR for the attack, potentially roll virtual DR for any Morale Check, compute result, add to previous statistics), or doing exact computations: there are 36×36=1296 possible results of two DRs, so you can just count how many result in each possible outcome and get exact probabilities.
If you are doing the former with N larger than 1296, the latter would probably be faster (and yield exact results). But it is more costly to generalize to more than one target for an attack (two targets mean 2 DRs for their MCs, so the number of rolls is 36×1296; three targets takes that to more than a million).
I am picking a column (8 FP), assigning a target morale, and rolling dice to see what the effect of an attack. In the case of multiple attacks, I am checking to see if the target is KIA/broken before rolling the second or third attack. The “round” ends when the target is broken/KIA or the total number of attacks is exceeded.
I am not a mathematician. I can do VERY BASIC statistics. I am a programmer so I can write code that follows a path to get the answer, it just takes me longer than it does a smart person.
I like my approach for some things. It worked really well with OBA modeling where I measure card draws in terms of “game turns”. Saying you draw 3.5 cards a game doesn’t mean anything. A Red card takes one player turn. A Black card is minimum 3 player turns.
Here, math probably would have been easier but how do I account for cowering? It is those details I cannot du through math. 🙁
Maybe the rule of thumb for the +1 shots should take into account the enemy sniper value to be the guiding factor? Good sniper numbers 5(maybe),6 and 7s should dictate taking less chances, perhaps?
Snipers are certainly something to keep in mind, but I personally tend to ignore them. Let’s say you have a SAN 7. That means you get a chance to activate your SAN once every six rolls on average. A “2” SAN is generally not a threat. So so for EVERY SAN chance, there is a 1 in 6 you’re going to feel the pain. The chance of a SAN hurting you is about 2.8%. Even if you’re worried about ANY SAN, the chance is about 6%. As long as your odds to inflict damage are around the same, at least you’re giving what you’re getting. And this is as threatening as it ever gets. A SAN 5 has less than a 2% chance to activate. It is slightly less than a 4% chance for a 1 or 2.
Snipers are threat. There are times when a high value asset may be at risk and you need to consider it, but don’t let them paralyze you. It’s not like that counter is under anyone’s control.
Ah .. thanks for examining (and testing) the basics. REALLY appreciate it!
You’re most certainly welcome.
Another wonderful article, thank you!
As others have said, I think I’ve unconsciously used these rules of thumb but it’s nice to see them gamed out in this fashion.
A few tidbits to add to the ‘art’ part of this discussion:
Someone already mentioned Snipers. I agree you can and should often ignore them, but for those low odd shots, if the only roll that will get you a result will activate the Sniper then I may generally pass (especially if the other guy has mainly high morale troops that will most likely pass an NMC).
Playing against the IJA. As a rule of thumb, you need to ‘tag’ an IJA squad 3 times to take him out of action. So if you’re on the fence about 1 shot vs > 1 shot, this is something to consider too.
Thanks again!
Excellent article as usual!
The one important observation I think you are missing is that these kinds of rules of thumb only work well in the middle of the IFT where there is an important relationship between dividing and column shifts. Specifically the number of column shifts equaling the divisor. For instance for a 12 attack dividing by 2 is 2 column shifts and dividing by 3 is 3 column shifts. This is true for the 8 and twelve columns as well. For the 16 column it is true for divide by 2 but not divide by 3. For 20 and above it is never true.
As soon as you are at an IFT and divisor that is worse than this (i.e. you must shift more columns than the divisor) then you are additionally penalized for dividing worse than the rule of thumb implies. The way the IFT is built it counterintuitively means splitting smaller IFT attacks is more favorable than splitting larger IFT attacks! Your simulations bear this out for the 30 column.
No we aren’t often lucky to have huge FG of such power, but it is worth remembering if we do that these rules of thumb often don’t apply the same way.
Of course if there is more than one juicy target to shoot at then you might have other motivations to split a 36 attack up!