Statistical analysis of template weapons vs unit coherency.

[Bear]

Hey all :-D

 

Fun one for you today!
 

Has anyone ever done a proper statistical analysis of template weapons vs unit coherency?

 

If you are unsure of what I mean, it’s the age old question of “does it matter if you bunch your models together or painstakingly ensure every single model is exactly 2 inches (or max coherency) away from every other” question.

 

On the one hand, yes, bunching is going to cause more hits on a direct hit. But on the other hand, being spread out means scatters are more likely to still hit the unit.

 

I genuinely don’t know which is better / if it matters and this is the kinda nerdy question that is going to drive me nuts so was thinking about trying to do the analysis in my spare time but:

a) as template have existed in Warhammer for ~25 years (that I know of), surely someone has already done this yeah?

b) I’m not sure my maths / stats skills are up to the task (especially when taking into consideration the flamer template!) :-P

 

Does anyone know if this has been done before and, if so, can you please point me to it?

 

Even if you don’t know, feel free to let us know what you do / if you think it matters below :-D Personally I’m a buncher as don’t really think it matters in any significant way (plus messing around with each of my unit for 5 minutes every time I move them would suck all the fun outta the game for me :-P) :-D

[bushman101]

Blast/template weapons are a difficult thing to analyze. It assumes a lot from the template placement and placement of enemy models plus size of the unit and base size.

It's fair to consider 'ideal' or 'non-ideal' situations, where you examine the potential min/max of a given template. But the 'actual' result will be quite varied due to placement and unit size. And base size matters a good bit.

I don't mean this response to be dismissive, but rather to confront the grounded reality of play. It's quite different to place a large blast over bunched Guardsmen than 10 Terminators in a Conga-line.

I view templates/blasts as good to have but also a weapon of opportunity. They will have their good and bad moments.

[Bear]

3 hours ago, bushman101 said:

Blast/template weapons are a difficult thing to analyze. It assumes a lot from the template placement and placement of enemy models plus size of the unit and base size.

It's fair to consider 'ideal' or 'non-ideal' situations, where you examine the potential min/max of a given template. But the 'actual' result will be quite varied due to placement and unit size. And base size matters a good bit.

I don't mean this response to be dismissive, but rather to confront the grounded reality of play. It's quite different to place a large blast over bunched Guardsmen than 10 Terminators in a Conga-line.

I view templates/blasts as good to have but also a weapon of opportunity. They will have their good and bad moments.

No, doesn’t sound dismissive at all :-D Base size is something I had taken into consideration for a possible variable if I have to go down the route of attempting the analysis myself :-D

 

The variables I have identified are:

 

• small template
• large template
• flamer template
• unit size (I.e. 5 man squad vs 10 man squad vs 20 man squad)
• base size (as you mentioned)
• scatter dice (taking into consideration the 33% chance of a direct hit)
• scatter distance (and probabilities)
• flamer distance (I.e. if you are covered by the long end or if the squad is only hit by the middle of the “stream”)
• Scatter reroll

I feel like I am forgetting something I already thought of (please feel free to point out anything I’ve missed!) but, as you can tell, I have spent some time thinking about this :-P

Edit: Oh BS was the one I was thinking of earlier! Still please feel free to add to the list if you all see anything else though :-D

 

Not that it matters at all and it is unlikely to change the way I play but I just really want to see the numbers to satisfy my curiosity :-D

 

 

Edited April 20, 2023 by Bear

[dickyelsdon]

There are so many factors a player might consider with model position I dont think you can statistically model template coverage likelhood with any accuracy. Just go for max number of models under vs min (1 or none?) and average it out to determine if it means more or less hits per shot.

 

Does terrain let you spread out (only planet bowling-ball is likely to allow max coherency for a medium sized unit)

Weapon range, if i spread out is half my unit now ineffective.

Does it look good, i.e. does the player prefer placement to look more 'narrative' vs accurate blast avoiding placement

Enemy interaction, spacing to block, keep away from, get close enough to charge, 

etc,

etc,

 

 

 

[Xenith]

I have the feeling bunched will always see more hits than spread out.

 

Basically, if the target is spread out, you'll only ever be able to hit 2-4 models at once, even with scattering. If the models are bunched, there is an extremely high damage spike for a direct hit, but also since the average scatter is only 2" (back of the envelope, 1/3 chance of a direct hit, BS4+ = 3" scatter, 2/3 of the time, so scatter will be 3" 2/3, and 0" 1/3, so average 2") which will still hit a good few. 

 

If someone max spaces, the chances of always hitting something are higher, but the total overall damage potential per hit is much lower. Like max 2 models dead per hit for 32mm bases and 2" spacing. 

 

Conversely, tightly packed models, you can easily hit 7 on a direct, and maybe still 2-3 if you scatter. So even a bad roll on tightly clumped is as good or better than an average roll on spread out targets. 

 

The math would just be bonkers also. Assuming that 3" scatter, and hitting zero models on scatter. For 3 templates, you hit 7, 0 and 0 models, for a total of 7.

For 2" spaced models, youd hit 2, 2 and 2, so lower than base to base packed.

 

Then think about the spike values - 3 direct hits gets you 7, 7 and 7 for 21 hits on packed models, vs 2, 2 and 2 on 2" spaced, for 6. 

 

The moral of the story is to space your models out when facing blast weapons. 

[SlickSamos]

The best analysis for something like this is grabbing as much real-world data as possible and/or running a Monte-Carlo type analysis rather than attempting it analytically as there are too many variables to account for.  

 

With respect to templates, spacing models and units out is always going to win for large units as there is always a high chance of direct hit (or near to direct hit).  However, where it starts to look the other way around is for really small units (of three or less) where bunching them up might be the right call as any significant scatter will dramatically drop the potential damage.  

 

I don't know where the switch happens between the two cases but it'll be there somewhere.  (Which I guess is your original question, so tl:dr IDK)

[bushman101]

Another option is just looking at extremes. 

How many Guard bases (25mm?) fit under a template. Then how many Leviathans fit? 

Then look at values considering these, while acknowledging that these are best/worst case scenarios. 

[Gorgoff]

I deploy ten men units in a circle because in my experience that leads often to not hit at all

[arnesh88]

How dense the terrain is on a table is also a factor. I tend to play on dense tables, so the optimal scenario of the unit spread 2" between each other is extremely rare, Some players also don't spread out as much because of their personal experiences not encountering blast/template weapons. This statistical problem has too many variables to calculate, and the only way you can reasonably know is to literally gather enough samples of it happening in real time. And even then, the data can be skewed based on what pool of players and local metas you're pulling from. While my experience can lead to average 3-4 models for 3", 7-8 models for 5", and 3-5 models for templates, others can have averages of 1-2/3-5/0-2, respectively.

 

Also also, a lot of the times, I don't go for optimal distances, just because I want to make sure we actually can get through a game in time. There comes a point where playing optimal leads to unfinished, tedious, unfun games. So I just quick eyeball, erring on the closer distance than spreading out too far.

Edited April 21, 2023 by arnesh88

[Mandragola]

23 hours ago, Gorgoff said:

I deploy ten men units in a circle because in my experience that leads often to not hit at all

There’s something in this approach, I agree. If there’s a hole in the middle of your formation then there won’t be a target to put the template on where it could hit everyone. Instead it’ll probably get three models, which tends to be the minimum possible with a 5” blast. In ideal circumstances large models can get better spacing but that tends to be impractical in my experience. 
 

Blasts are pretty accurate really. 1/3 are direct hits but even a miss can end up with little or no scatter due to BS. It’s also pretty easy to get rerolls to hit thanks to twin-linked, nuncio voxes and so on. 
 

Barrage is different. That will scatter 2/3 times and, due to the distribution of results when rolling 2D6, will be 5-9” from its aiming point 2/3 times when it does. So for models that are out of sight and threatened by barrage, it may make sense to bunch up rather than risk being exposed to direct fire.
 

This “all or nothing” approach may also be sensible if you’re likely to be pinned if you get hit, as this makes you non-scoring. If spreading out increases the chance of having to take a pinning test, but even a single survivor of a unit that takes a direct hit is enough, you should probably bunch up. 
 

Edit: someone mentioned above that spreading out isn’t fluffy, but it absolutely is. In reality, troops huddled close together are far more vulnerable to pretty much all weapons - not just high explosives. Infantry patrolling would be spread out far beyond the equivalent of a 2” coherency. 

Edited April 22, 2023 by Mandragola

[bushman101]

Just as an aside, it's interesting to note why players bunch up or spread out models.

 

In my experience, people spread out models for defensive purposes or to deny the opponent access to part of the table (Deep Strike denial).

Players bunch up to make better use of offense (get in range) or move around terrain. 

 

Unless you are playing a static gun line, there will be an ebb-and-flow on how far apart troop models will be.