I like building statistical models to estimate the relative cost efficiency of units in most of the games I play.

I wanted to share what I had for Legion.

It's a blend of :

(1) rigorous maths: What's the average damage that should be done by a given unit with a given weaponry against an average trooper or armored unit

and

(2) other factors that I attempt to put into numbers to the best of my knowledge (and what I consider being the most appropriate way to add that into the equation). This is the moving part that I keep refining after paying and watching more and more games between experienced players. It's attempting to put a number on questions like :

"How often does nimble proc in a game ?" "How often do you actually focus before firing - and then make precise X relevant ?" "How many more useful shots do you get with a range 4 instead of 3 ?" "How often are you able to make a relevant Melee attack when this would be your optimal action instead of a shot ?"

I also use input from others who play the game deeply to refine how I put a number on each of these questions. Yes, your published battle reports are put into numbers!

Last, I focus on everything related to combat, and some keywords are a bit more challenging to estimate in my cost-efficiency scope : Vader's relentless or Luke's charge can for example be formatted into an increase into the likelihood of them being able to deliver a melee attack, but there are other skills that I have set aside for now, Like Veers' "inspire", as it's quite hard to model as a 'per unit' skill. I also ignore almost everything related to movement.

I have separated the attack efficiency into two metrics : the efficiency vs. troopers and the one vs. armored units.

Describing every detail of the model would take pages and would only interest a fraction of potential readers, so let's jump to what I learned from the analysis.

There are a few units or upgrades I have not put in yet in the model, like grenades (I am not confident I have a good estimate of how likely a unit can use them rather than being engaged in melee, nor how many casualties it's usually suffered before being in grenade range), or a weapon like the flamethrower (I'd like a few more games to estimate how much "spray"usually provides)

Here are ratings for units (upgraded or not) - I have put them on an arbitrary scale, the most important one being the 'Global efficiency' that I have set to scale between 0 and 10 for an easier readability.

1 - The game's units are VERY WELL balanced

Trooper units are more cost efficient, but not by much, as they should be, as the statistical model does not consider movement and flexibility. For example, a T-47's mobility and disruption potential is a benefit that is not considered here. The game would be flawed if its jousting level was as good as cheaper units. Also, 'expensive' units HAVE to be less cost efficient, as a concentration of power is usually an asset (it can fight a fraction of the opposing forces one at a time, and benefits more from the precious first or last activation). Leaders also have to be less 'jousting-efficient' than other units due to the number of options they bring.

Everything really looks like it's where you'd expect to be in terms of efficiency for a top-notched balanced game

2 - Most units are (surprisingly?!) very close in terms of 'defensive efficiency'

naked AT-RT and troopers with no weapon upgrade are the only exceptions as the most cost-efficient units in defense, which is compensated by their clear lack of punch.

But everything else is between 1.1 and 1.5. The main conclusion is that besides the 'armor' battles, there is no 'naturally very fragile' unit.

Note that I considered Luke and Vader's 'deflect ability' and their relation to the 'free evades' from orders as 'defensive bonuses', as they effectively deter from targeting them rather than making them more solid. They would be lower based on their pure stats and against an opponent resolute to kill them despite the deflecting casualties.

3 - Speeder Bikes are confirmed to be the most cost-efficient 'armor-piercers' among raw units (as it was highlighted by early battle reports).

They are only beaten by MPL-57 ion troopers if you also consider upgraded units. Ioning armored units looked very solid in the test games I have seen, and I have tried to rate it appropriately.

4 - Upgraded or not, troopers are usually most efficient against troopers, vehicles against vehicles.

This is not much of a surprise, but an interesting confirmation : the game often revolves into forcing your opponent to shoot your units with inappropriate weapons, while you would not suffer from that. Baits and positioning

5 - Veers looks like a powerhouse.

He's decently cost efficient, and my model does not even include his 'sharpshooter' and 'inspire' abilities.

6 - Saber throw is a no-brainer

It would be crazy not to put in on Vader, and I don't think experienced players needed numbers to confirm that. It was more surprising to me that it was also a significant boost for Luke : it simply makes him able to deal vehicle damage at range, which is apparently not negligible for just 10 points.

7 - DLT-19 is very strong, making Stormtroopers with it the most cost-efficient unit in the game for now.

For only 13 points more than adding a trooper, this weapon looks very solid - red dice + impact almost guarantees damage whatever your target is. Also, range 4, and no negative issue using it. Weapon upgrades also look better on storm troopers than rebel troopers due to the combination of three things :

- they have weaker natural attack and could use more help there.

- but a better natural defense (to protect the additional weapon)

- they also have an offensive surge (that also benefits the additional weapon)

8 - Speeder bikes look very cost-efficient

They are barely behind troopers in terms of cost efficiency, which means you don't pay a high price for their mobility. My model considers that they should be able to use their front arc only fire most of the time though, which might be excessively optimistic !

9 - Naked AT-RT can be extremely strong if they can start their melee attacks early

They're only behind the Jedis at Melee range, but for a fraction of their cost. And they're the most solid unit in the game (relatively to their cost.)

A good sanity check of the quality of the balance of the game to me, and also a potentially useful educative resource on what's globally efficient for its cost.

The brain sometimes has a hard time making a mental image of the effect everything together (surges, dice color and numbers, range, cover and defense), even if it knows each piece in a vacuum - the computer does not.

Your research is very thorough and interesting. Thank you for doing this. This gives me a few ideas and honestly it sounds like using only the core box set units is a totally viable way to play right now. It's nice to see that statistically the game is very balanced and not too pay to win. The bigger, more expensive models don't invalidate the cheaper ones. I like seeing that.

Would be good to have your formulas for these results, otherwise it just looks like opinion posing as fact.
For example the Airspeeder having an efficiency of 0.6 vs troops just doesn't seem right to me seeing how troops melt to their 6 accurate dice attack.

8 minutes ago, Shraken said:

Would be good to have your formulas for these results, otherwise it just looks like opinion posing as fact.
For example the Airspeeder having an efficiency of 0.6 vs troops just doesn't seem right to me seeing how troops melt to their 6 accurate dice attack.

seems right to me, those 6 dice are very costly in terms of points.

Speeder bikes toss the same dice for a faction of the cost, and they have offensive surge.

(edit: almost the same dice, but offensive surge should make up for that)

Wow! Impressive work, makes me wish I could run a whole legion of DTL-19 troopers!

--

@Transmogrifier

How are you arriving at .8 for stormtroopers vs armor?

Stormtrooper dice only have a 1/8 chance of critting, that’s 0.125 per trooper, or 0.625 with 5 troopers (ie extra trooper).

And that is before we take into account the defense dice of the target, which would reduce the number of wounds even further.

39 minutes ago, Shraken said:

Would be good to have your formulas for these results, otherwise it just looks like opinion posing as fact.

Indeed my opinion is really present in this study - but certainly not at the unit level. My opinion is present to attempt to keywords into numbers or try to represent in numbers what actual more or less optimal play decisions would be.

I don't want this post to be a chain of equations, but i can provide the general idea :

1) I estimate the average number of hits and crits that an attack should generate (actually the breakdown between the outcomes) for different levels of cover.

2) I estimate what fraction should be blocked by an average defending unit

3) this gives me a base offensive rating for each shot

4) then I try to estimate 'how likely this shot is to happen each turn', this considers range, negative keywords, and the likelihood that the unit could use an even more favorable weapon (e.g. Luke would melee instead of firing if he has the choice)

5) the sum of these factors for each weapon **fire-able** in an average turn divided by the cost of the unit constitutes the offensive value (calculated both against armored units and trooper units) reported here

6) I then calculate the 'defensive value' of each unit, considering its number of hits points, the number of hits that should be prevented by armor, cover, evades, defensive dices and surges. This value divided by the point cost gives me the defensive value.

7) The global efficiency is the combination of these two factors, assessing a given weight between the anti-armor and anti-trooper attack rates, summing them up, and multiplying this sum with the defensive efficiency. It's quite similar to the logic behind Mathwing for X-wing, where MajorJuggler went into more details in his explanations. This base formula is well-admitted (not absolutely perfect, but very decent). Where I attempt to go farther in my modelling is in trying to model (4) and (5) where my input is all based on read and watched battle reports and personal plays.

For example the Airspeeder having an efficiency of 0.6 vs troops just doesn't seem right to me seeing how troops melt to their 6 accurate dice attack.

For the airspeeder's dual laser, it's indeed a strong attack, but certainly not the most cost-efficient : 4 speeder bikes (2 squads) are indeed a good example of a more efficient attack for the same cost. And two units of troopers with either Z-6 or DTL-19 would hit even harder for an even smaller cost.

6 minutes ago, Derrault said:

How are you arriving at .8 for stormtroopers vs armor?

Stormtrooper dice only have a 1/8 chance of critting, that’s 0.125 per trooper, or 0.625 with 5 troopers (ie extra trooper).

And that is before we take into account the defense dice of the target, which would reduce the number of wounds even further.

0.8 is not a number of crits.

It's a value based on an arbitrary scale that considers indeed the 4 or 5 times 0.125 from the base troopers for its average number of crits ... then accounts for their chance of being focusing and able to re-roll with precise, then divides it by the potential block, then by the cost of the stormtrooper unit, then multiplies by an arbitrary number for an easier readability.

I certainly don't expect my poor naked stormtroopers to average at 0.8 damage against these nasty airspeeders

12 minutes ago, Fanfan said:

0.8 is not a number of crits.

It's a value based on an arbitrary scale that considers indeed the 4 or 5 times 0.125 from the base troopers for its average number of crits ... then accounts for their chance of being focusing and able to re-roll with precise, then divides it by the potential block, then by the cost of the stormtrooper unit, then multiplies by an arbitrary number for an easier readability.

I certainly don't expect my poor naked stormtroopers to average at 0.8 damage against these nasty airspeeders

That value should be inherently different than the rebel troopers (whose aim only gives 2 re-rolls to the stormtroopers 3).

Unless you’re using two entirely different arbitrary numbers, as that final step...in which case it sounds like you’re saying the final numbers have no meaning at all.

2 minutes ago, Derrault said:

That value should be inherently different than the rebel troopers (whose aim only gives 2 re-rolls to the stormtroopers 3).

Unless you’re using two entirely different arbitrary numbers, as that final step...in which case it sounds like you’re saying the final numbers have no meaning at all.

It's a little bit higher indeed (one more re-roll in case you have a focus), but it's compensated by the 10% lower cost of rebel troopers.

Of course the arbitrary number is the same for all units or the whole thing would not have any meaning indeed.

Not here to argue with the math, just an observation assuming the numbers are accurate:

My Luke has been my saving Grace in almost all my games so far. He can do basically whatever I need him to do. It's interesting that his efficiency number is so low. I guess the reason you can't just quantitatively build your armies is because it doesn't take a lot of human experiences (luck, better decision-making, etc.) Into consideration.

Anyway it's a nice reference! And looks like a lot of hard work. Great job!

12 minutes ago, Xiervak said:

Not here to argue with the math, just an observation assuming the numbers are accurate:

My Luke has been my saving Grace in almost all my games so far. He can do basically whatever I need him to do. It's interesting that his efficiency number is so low. I guess the reason you can't just quantitatively build your armies is because it doesn't take a lot of human experiences (luck, better decision-making, etc.) Into consideration.

Anyway it's a nice reference! And looks like a lot of hard work. Great job!

Units are just studied there in a vacuum. There are a lot of things that are not considered in this model, that all play to Luke's benefit :

- his courage value,

- the massive benefits he gets from command cards (and the way they are in synergy with Luke's charge and deflect abilities)

- the fact he does not lose an ounce of offensive power when damaged (which does not happen to squads and damaged vehicles) - which I will consider in a later edition, but it's not there yet. I also acknowledge that my model might currently be underestimating the 'charge' keyword (on a speed 2 - leap unit who tremendously benefits from one more action like evade once exposed)

His efficiency with saber throw is actually identical to Vader's, but I think his move 2 makes him better (master of the force, infinite courage and relentless instead of charge on Vader's side don't do enough to compensate for that to my taste.)

The fact that such a concentration of power is significantly lower in global efficiency is actually reassuring. The game would be flawed if on top of all his singular benefits, he would also be more cost efficient than a raw number of troops and vehicles.

1 hour ago, Fanfan said:

Units are just studied there in a vacuum. There are a lot of things that are not considered in this model, that all play to Luke's benefit :

- his courage value,

- the massive benefits he gets from command cards (and the way they are in synergy with Luke's charge and deflect abilities)

- the fact he does not lose an ounce of offensive power when damaged (which does not happen to squads and damaged vehicles) - which I will consider in a later edition, but it's not there yet. I also acknowledge that my model might currently be underestimating the 'charge' keyword (on a speed 2 - leap unit who tremendously benefits from one more action like evade once exposed)

His efficiency with saber throw is actually identical to Vader's, but I think his move 2 makes him better (master of the force, infinite courage and relentless instead of charge on Vader's side don't do enough to compensate for that to my taste.)

The fact that such a concentration of power is significantly lower in global efficiency is actually reassuring. The game would be flawed if on top of all his singular benefits, he would also be more cost efficient than a raw number of troops and vehicles.

I agree with you completely regarding the state of the game. Regarding Luke, SoS can literally be a game changer.

19 hours ago, Shraken said:

Would be good to have your formulas for these results, otherwise it just looks like opinion posing as fact.
For example the Airspeeder having an efficiency of 0.6 vs troops just doesn't seem right to me seeing how troops melt to their 6 accurate dice attack.

The trick that this is all "per point". An Airspeeder melts a unit, sure, but it has to do that 4-5 times for its dice to pay back what they cost, and realistically they're not so effective as to actually remove a unit a turn. Meanwhile, each point of health on the speeder itself costs 25 points per health on it. A unit only needs to deal a couple wounds to it to pay for itself. Overall, the game's pretty good about this. I ran some numbers and came across fairly similar results. The big question mark for me is the value of the armor keyword. There's definitely some good math here to include it.

As for Saber Throw, I think the big reason its better on Vader than Luke is that it combos with Relentless and not Charge. The extra +2" threat on it is pretty marginal, but where I really find value is in doing things like walking out of cover, throwing the saber then retreating back to safety. I still think Luke is stupid good for his points though, almost entirely on the back of how little counterplay there is to Son of Skywalker.

is saber throw on luke really that useful, considering he also has a (pretty good) pistol? sure, he loses impact and a die, but gains better dice in return. i don't see myself ever taking saber throw for luke, to be honest. those 2 force slots are too valuable for stuff other than pure damage (on armored targets, the pistol kills troopers nicely), reflexes, mind trick and push have to battle for these spots as it is.

This is really cool, would you be interested in doing durability/health efficiency?

23 hours ago, Shraken said:

Would be good to have your formulas for these results, otherwise it just looks like opinion posing as fact.
For example the Airspeeder having an efficiency of 0.6 vs troops just doesn't seem right to me seeing how troops melt to their 6 accurate dice attack.

There is too much chaos in a game to apply an accurate algorithm. This is clearly an opinion, but one with a lot of thought and detailed analysis. It is still interesting to see how the different units line up on this guys point scale and a lot of the rankings he gives seems to be backed upped by the anecdotal battle reports. Is a DLT-19 storm trooper really twice a good as an air speeder? It could be, depending on the objectives and terrain. Is it always? - No.

2 hours ago, shlominus said:

is saber throw on luke really that useful, considering he also has a (pretty good) pistol? sure, he loses impact and a die, but gains better dice in return. i don't see myself ever taking saber throw for luke, to be honest. those 2 force slots are too valuable for stuff other than pure damage (on armored targets, the pistol kills troopers nicely), reflexes, mind trick and push have to battle for these spots as it is.

I agree : I'd say this was one of the main surprises of the results to me. Luke's red-piercing-dice gun looked really solid to me and I would not have considered the throw as the option-to-go before running this model ! So, I double checked the numbers before posting yesterday.

It looks like the combination of pierce and impact is really efficient - when you get these precious damage through armor, you'd better have them matter! Saber throw is really threatening vehicles at range. From my experience, AT-ST have to avoid the 'melee death zone' of Luke, but aren't much scared of his gun. Saber throw change that deal.

I guess the model rates it as a very worthy upgrade because it's only a few points more (10 vs. 160), so really a small fraction of the cost to significantly expand Luke's anti-armor threat range, which combines very well with a unit both flexible and solid.

I have not considered the other force powers yet (Saber throw was much easier to implement ), so the maximum force powers cap is not an issue (yet) in the model.

1 hour ago, Oberron said:

This is really cool, would you be interested in doing durability/health efficiency?

Yes, the 'defensive efficiency' is the third column in the table and it captures the effect of health, armor, defensive surges, and all other defensive keywords to estimate the number of hits a unit can sustain, then divides it by the unit cost for a fair comparison.

55 minutes ago, Mep said:

There is too much chaos in a game to apply an accurate algorithm. This is clearly an opinion, but one with a lot of thought and detailed analysis. It is still interesting to see how the different units line up on this guys point scale and a lot of the rankings he gives seems to be backed upped by the anecdotal battle reports. Is a DLT-19 storm trooper really twice a good as an air speeder? It could be, depending on the objectives and terrain. Is it always? - No.

The model says that a pure firing joust between speeders and an equivalent cost of Troopers with DLT-19s would most likely favor the troopers (well, not exactly, as they're both not the best targets against each other - the speeder is not making the best use of its impact, and the troopers are a better against non-armored units), but it says that in general, the trooper unit is more efficient at firing and taking shots for its cost than the speeder.

The model tells more about 'what you pay' for all the speed and flexibility the speeder brings. Its efficiency at suppressing units by flying over them, its insane speed, its efficiency at being the unit saved for the sweet first or last activation spot, its immunity to melee are all advantages not accounted in the model.

The model ranking it as the 'worst' non-commander unit, but still not by such a large factor, is exactly what you would expect from a very well balanced game, as it's the unit that has the most advantages that are NOT considered in this jousting efficiency model.

If it was as efficient as the top units in this list on top of all its other advantages, it would be an overpowered and "no-brainer maximum fill" in competitive lists.

3 hours ago, shlominus said:

is saber throw on luke really that useful, considering he also has a (pretty good) pistol? sure, he loses impact and a die, but gains better dice in return. i don't see myself ever taking saber throw for luke, to be honest. those 2 force slots are too valuable for stuff other than pure damage (on armored targets, the pistol kills troopers nicely), reflexes, mind trick and push have to battle for these spots as it is.

12 minutes ago, Fanfan said:

I agree : I'd say this was one of the main surprises of the results to me. Luke's red-piercing-dice gun looked really solid to me and I would not have considered the throw as the option-to-go before running this model ! So, I double checked the numbers before posting yesterday.

It looks like the combination of pierce and impact is really efficient - when you get these precious damage through armor, you'd better have them matter! Saber throw is really threatening vehicles at range. From my experience, AT-ST have to avoid the 'melee death zone' of Luke, but aren't much scared of his gun. Saber throw change that deal.

I guess the model rates it as a very worthy upgrade because it's only a few points more (10 vs. 160), so really a small fraction of the cost to significantly expand Luke's anti-armor threat range, which combines very well with a unit both flexible and solid.

I have not considered the other force powers yet (Saber throw was much easier to implement ), so the maximum force powers cap is not an issue (yet) in the model.

One other thing I forgot to mention about saber throw on Luke, that I think can be quite significant : it also makes him threatening against the nasty melee-immune airspeeders. Vanilla Luke is really not much threatening to them. That's important as rebel lists often have just a few solid options against air-speeders, that each require a significant investment. With saber throw, I can well imagine Luke scoring two damages twice (in two rounds) against a speeder, which can be game-deciding.

I notice you didn’t do a rating for the flamethrower AT-RT. Is that because of the variable dice? What are your thoughts on that build?

6 hours ago, Fanfan said:

Yes, the 'defensive efficiency' is the third column in the table and it captures the effect of health, armor, defensive surges, and all other defensive keywords to estimate the number of hits a unit can sustain, then divides it by the unit cost for a fair comparison.

Ah thanks that was some quick work. Also i found my brain on the floor and dusted it off, i can thinky think betterer now.

On 4/7/2018 at 9:48 PM, Orkimedes said:

I notice you didn’t do a rating for the flamethrower AT-RT. Is that because of the variable dice? What are your thoughts on that build?

Yes, i am still struggling with this one ... I think it's a solid upgrade, potentially terrifying to troopers.

But I don't have a clear estimate of how much 'spray' should be providing.

Also, the unit has a very solid melee attack, certainly not as efficient but decent anyway if you don't have a flamethrower when getting close. I want to test it a little more to figure what the breakdown between its usual weapon and flamethrower (with how many sprays) should be during the course of an average game. It also has a major dependency on how large trooper units are (between 4 and 6 heads). I also suspect people will play them much more 'spread around building walls' when facing flamethrowers.

With my current 'best guesses' : the attack is terrifying, but only against troopers, and only at range 1 :

On real tables, I can well imagine flame-throwing AT-RTs being a major thing in a meta dominated by large and upgraded trooper forces.

1 hour ago, Fanfan said:

On real tables

I do think its important to remember that cost efficiency is mostly a guideline. It gives you a place to start. As you play the game you might find it worthwhile to take less efficient options to better tech against what you're up against. For example, the DLT is amazing, no doubt, but the HH does more to turn the white dice from Stormtroopers into something than can crack armor by having more Impact than you are likely to get hits out of the rocket itself. If you're finding yourself up against double AT-ST or triple AT-RT/double speeder or something; the Rocket might work out better.

The best thing to take away from understanding the efficiency of models in a game is reaching a point where you accept that you've done what you can to get the most out of the army building portion of the game. With that as a baseline, its a lot easier to improve play by looking at ways to make better decisions on the table or find the value in less valuable options.