I recently had a crush for X-wing, and as I usually like to back-up my 'in game feelings' with numbers, I have been trying to model the fire efficiency of each starship relatively to its cost.

1) Simulation details

Note that I chose not to attempt to put a 'handwavy' maneuverability coefficient on top of this simulation. Ships are just evaluated as a function of their attack and defense per point cost

Then you can figure by yourself how much you'd consider the enhanced maneuverability improves offense or defense.

here is how I measured things:

- the attack rating is based on the average number of turns you need to destroy an X-wing at range 2. I picked the X-wing as it has an agility of 2, which sounds like a good average of what you see in battle - Agilities are well distributed between 1,2 and 3. 2 looks a good average.

- the defense rating is based on the number of 3-dice & range 2 attacks you sustain in average before being destroyed. I think the majority of shots in this game are made with 3 dices. yes, swarms at range 2 or 3 shoot with 2 dices, but it looks like 3 with Howlrunner, they fire with 3 dices at short range. Nearly all the otehr ships that see play fire with 3 dices, 4 at range 1. 3 dices seems like a very good average.

This way of simulating things looked appropriate to me as it is very close to real combat, it has a few advantages above just 'number mainpulation' like ignoring the overhead damage, etc.

- I considered that *half* of the attacks are done with a 'focus' spent, and none of the defenses. Indeed, I think this seems legitimate as players usually (appropriately) focus fire of several of their ships, and on temporarily weaker targets (the ones that don't have actions or have already spent their focus). From my experience, I usually see more focusses spent on offense than defense. (I have started keeping track of the actual number of focusses spent on attack and defense in real battles and I think my assumption is reasonable). I have not considered target locks as the focus action is statisticlaly slightly better on a 3-dice attack.

- I am not considering critical hits, so one hull would be equivalent to one shield in this simulation.

- I am providing ratings of "defense per point", "attack per point" and "global efficiency" which is the product of both. (This means attack*defense/(points^2) )

- To take into account the higher pilot skills, I have downgraded the cost of each ship by 0.5 point per pilot skill down to a PS of 1. For example, Luke Skywalker downgraded cost is 28-(8-1)*0.5=24.5 - I know that 0.1 point per PS is appropriate for small ships, but 1 per point for expensive ships is probably better. It does not impact the results too much, but I will probably set a threshold for teh 1-to-1 conversion rate in a next version.

- Then, for an easier read, I have ranked the ships by how good they are in defense or offense compared to the average ship in this list ; and did the same for the global efficiency

- I have not included all ships, just most of the ones which have a direct effect of combat.

2) Results

So here are the results, ranked in terms of efficiency:

Name defense attack cost global
per point per point (downgraded to PS1) efficiency
*Night beast 1.61 1.04 13 1.68
Lambda shuttle 1.25 1.15 21.5 1.48
*Night beast + hull 1.73 0.85 16 1.47
*Dark Curse 1.37 1.01 13.5 1.42
Z-95 headhunter 1.11 1.18 11.5 1.35
*Dark curse + hull 1.54 0.82 16.5 1.31
TIE Phantom + ACD 0.87 1.41 28 1.27
TIE fighter 1.06 1.13 12 1.24
B wing 1.00 1.15 21.5 1.18
TIE Bomber 1.29 0.88 15.5 1.16
A-wing (g sq.)+pred+refit 0.89 1.26 19 1.16
TIE Inter (guard)+ptl+hull 1.09 0.97 25.5 1.09
*Colonel Vessery 0.85 1.21 32.5 1.07
*Luke Skywalker 1.02 1.01 24.5 1.06
A-wing + chardaan refit 1.13 0.91 15 1.05
TIE Int (guard) + ptl 0.93 1.10 22.5 1.05
*Tarn Mission 0.94 1.07 24 1.04
*Kath Scarlett + predator 0.94 1.04 38 1.01
TIE Interceptor + hull 0.83 1.18 21 1.00
*Krassis Trelix + HLC 0.87 1.10 41 0.99
TIE Interceptor 0.70 1.37 18 0.99
Y wing 1.23 0.78 17.5 0.98
*Kath + pred + gunner 0.83 1.14 43 0.98
*Wedge Antilles + pred 0.59 1.59 28 0.97
X wing 0.79 1.18 21 0.96
Firespray + gunner 0.97 0.93 37 0.93
Falcon+C3PO+gun+pred 0.92 0.95 51 0.90
TIE Phantom 0.53 1.65 24 0.90
Firespray 1.12 0.77 32 0.89
X wing (red)+R2-D6+pred 0.64 1.32 26 0.87
E wing 0.83 0.91 27 0.79
TIE Defender 0.92 0.82 30 0.78
E wing + gunner 0.70 1.08 32 0.78
Falcon + C3PO + gunner 0.98 0.72 48 0.72
TIE advanced 1.07 0.65 21 0.72
*Captain Kagi+EU+gunner 0.83 0.82 32.5 0.70
Falcon + C3PO 1.09 0.57 43 0.65
Decimator 0.94 0.63 39 0.61
Falcon 0.92 0.62 40 0.58
YT-1300 + C3PO + gunner 0.94 0.59 35 0.58
YT-1300 + C3PO 1.10 0.45 30 0.50

Notes about how I simulated specific ships:
*Night beast: I assume he always does a green maneuver (favorable assumption) and gets a free evade for one of two shots he suffers.
*TIE phantom + advanced cloaking device: I assume it is fighting lower PS pilots and has a shot every turn to cloak (favorable assumption)
*Colonel vessery: I assume his target already has a red target lock (favorable assumption)
*Luke skywalker: note that I assume that ships don't focus for their evades in this simulation, except for Luke (once per fight) (favorable asumption)
*TIE Interceptor + Push the Limits: I assume that it gets a free evade from PtL, for one of two shots he suffers
*Tarn Mission: I assume he gets successful attack dices rerolled for one of two shots he suffers
*gunners: note that 'gunner' battles are more complex than what I have been assuming (reroll when no hit). First, one of the main effect of the gunner is to strip your opponent from its defense tokens to get a poorly-defended second shot. Second, it sometimes makes sense to endure one hit and keep evade/focus tokens to avoid an even bloodier second shot.
*C3PO: I have been assuming that C3PO worked for one shot out of two.

3) Interpretation

The results look really reasonable to me. Because maneuvers, rear arcs & turrets are not considered in the simulation, it is legitimate to have ships like the lambda shuttle up in the ranks and falcons ranked poorly, as their unconsidered advantages actually make a huge difference.

- Upgrades worthy for some ships, but bad for others.

as expected, the expensive "gunners" are worthy upgrades for very solid ships like falcon or firespray, but they are downgrading teh overall cost efficiency of more fragile ships like the e-wing. Another example of upgrade that's beneficial on some ships but not on others: hull upgrade increases the global efficiency of TIE interceptors, that woudl not say no to a little more life, but less on TIE fighters. This all follows intuition, but it is nice to have that back-ed up with numbers.

- As expected, TIE fighters and Z-95 rank really high in this s tudy. And indeed, in a pure shooting simulation, I think swarms are nearly unbeatable.

- Just for the records, the most defensive ship is Night beast doing a green maneuver for focus and evade. Worst target ever. And the scariest 'glass cannon' is a naked TIE phantom focussing you, but it ranks pretty low overall due its low defense rating.

- B-wing ranks quite high, especially considering that it is full of shields and I did not put critics in my simulation. X-wing, E-wing, TIE defender rank pretty poorly, and TIE advanced even worse, as expected. A little minus to have in mind : blue B-wings suffer from predator, and upgraded & named B-wings are quite expensive.

- Even if it is low on this list, Falcon + C3PO has a defense per cost above average, really tanky for such an expensive ship ! And with a gunner, predator or both to boost offense, it catches up on the offensive part to nearly reach the global efficiency average of regular ships ... but that's ignoring its crazy maneuverability and most importantly its turret ! This means that you will -- barely -- have the edge if you manage to focus the shots of your regular squadron at it. But it's more likely it will arc dodge some of them and things should then turn bad for you. What a crazy ship !

Interesting, I have done something similar here:

http://community.fantasyflightgames.com/index.php?/topic/100360-using-lanchesters-square-law-to-predict-ships-jousting-values-and-fair-point-values-work-in-progress/

I include a variety of ranges and targets to shoot at, so the numbers are more well-rounded than, say, just looking at range 2 vs an X-wing. I only consider the base stat line of the ships themselves, and not pilot abilities. I use average damage numbers, and DO consider the effects of critical hits. I'm going to update it later with the exact "hits to kill" from the probability density function, based on the same assumptions.

The biggest limitation is the assumption of the action economy. Do you have any measured in-game data on the likelihood of how often ships have focus for attack and defense? I'm thinking of using VASSAL logs as a good data set.

Thank you for your feedback. I like what you have been doing with the gathering of the tournament reports. That's been really interesing.

I have not read everything you have done so my feeling may be wrong, but it looks to me that Lanchester's Square Law is inapropriate for x-wing simulations. You have another variable in x-wing that each unit composing an army has significantly different individual attack and defense ratings and the fact that your opponent can prioritize targets according to this, which is not taken into account in Lanchester's quare law.

I think the average shot in x-wing is really close to 3-dice attacker at range 2 of a 2-dice defender. But I agree the most appropriate tool would be to study the distribution of these three variables (and how they are modified) in the frame of competitive games. But i think what I picked is a very reasonable compromise ; it also allows handling upgrades and pilote skills easily. Base ships only is very restrictive.

I read you are in Massachusetts ... in the Boston area ?

well, after reading it a little more, it sounds like we did many things the same way. like adjusting the PS, and other things that were intringuingly similar.

And that Lanchester may not be too bad, although I prefer simulating real combats to prevent damage over-runs. It also makes it easier to simulate the variety of pilot skills and upgrades. I am considering the benefit of trying to model the actual distribution of shots (range, attack dice, defense dices and modifications) in competitive gaming. Looks like a good improvement.

Your idea of investigate Vassal logs sounds great. have you already investigated that ?

I have not considered target locks as the focus action is statisticlaly slightly better on a 3-dice attack.

Could you elaborate on this?

In my calculations for offense, focus is statistically equal to target lock whatever the number of dices and slightly better when considering crits.

focus: 6/8 hits per dice

lock : 6/8 hits per dice

The odds are the same per dice, so the expected result/distribution of results should be the same.

For 3dices;

0 hit ; 1.6%

1 hit : 14.1%

2 hits ; 42.2%

3 hits : 42.2%

Yes, my statement is wrong - I agree both are prefectly equal for attack if you do not consider crits. I think it is target lock that is better if you consider crits.

Where it gets interesting is the fact that you can keep a target lock from one turn to the other, which you really only want to do when you roll full hits/crits - And rolling full hits happens less frequently the more dices you roll. So, in that sense, target lock is increasingly better for offense when you have a lower number of attack dices.

Yes, my statement is wrong - I agree both are prefectly equal for attack if you do not consider crits. I think it is target lock that is better if you consider crits.

So the question between target lock and focus is not one of relative value to the dice, but one of longevity vs. versatility. The target lock can remain unused, whereas the focus is use-it-or-lose-it, but you can also use it for defense.

Thanks for the confirmation that they have essentially equal value on the dice themselves.

Thanks for the confirmation that they have essentially equal value on the dice themselves.

yes, if

1) you are sure you are not going to be shot this turn, and

2) you know your target and don't need the possibility to change your mind

3) you don't bother by the fact you tell your opponent where you are going to shoot later during teh action phase

and actually 1-2-3 happen quite frequently

then target lock is strictly better, as it

1) increases your chances of crits

2) can be kept for next turn in case you roll perfectly (or whatever other good reason you may attempt to find)

This is amazing! I was thinking of doing exactly this same thing but had no clue which program to use. It's so wonderful to be able to see the different ships numerically compared to each other in vacuum. Thank you again for your hard work and for posting the results!

The bigger issue is that Lanchester's is continuous time, and X-wing is turn based, but this is also addressed. There is, of course, always room for improvement.

Unless you are trying to analyze a very particular scenario, you really should include all ranges and then figure out how to weight everything. Same thing with the action economy, which you're already weighting. In effect you're already doing this with the range bins, but you're setting range 2 at 100% and everything else at 0. Likewise on the base attack and defense dice. What you'll find is that different stat lines are going to prefer different engagement ranges, and different base attack/defense dice to pair up against. For example 3 agility loves to fight against 2 attack dice, especially at longer ranges, because the defense is proportionately better.

If you are trying to get an overall "value" for a given ship across the entire metagame, or as a subset of that, how many shots it takes to kill something, then you need to consider a variety of attacks.

You can, of course, determine ship durability in a particular matchup by simply narrowing the criteria.

Well, you need to be able to model the base ships correctly first, before you can add additional layers.

I read you are in Massachusetts ... in the Boston area ?

About an hour south of Boston.

And that Lanchester may not be too bad, although I prefer simulating real combats to prevent damage over-runs. It also makes it easier to simulate the variety of pilot skills and upgrades. I am considering the benefit of trying to model the actual distribution of shots (range, attack dice, defense dices and modifications) in competitive gaming. Looks like a good improvement.

Yeah a real battle simulator is a really interesting prospect. I wrote one for Axis and Allies to get the exact army win / health remaining distribution (none of this Monte Carlo nonsense ) Someday I'll build one for X-Wing. Not yet though.... see below.

and this is how us gi's do mathhammer:

me move ship

me dice roll

math

you ship hit

boom.

disclaimer: 'm not picking on anything here and actually really appreciate all you guys do. I enjoyed your previous thread as well majorjuggler. It is interesting to read the findings even if the results are slightly skewed from so many different variables. Thanks for the hard work fanfan!

I have lots of vassal log files that you can use for sample data if you would like. I'm not sure what kind of sample size you need. I have over 200 games logged, and that's just for this last tournament. I still have logs from past tournaments as well. I would be happy to share this with you if it would help.

I have lots of vassal log files that you can use for sample data if you would like. I'm not sure what kind of sample size you need. I have over 200 games logged, and that's just for this last tournament. I still have logs from past tournaments as well. I would be happy to share this with you if it would help.

Thanks for the offer, I will certainly take you up on this someday. The problem is manual entry, logging every single shot. I will have to think of a way to enter the data as quickly as possible.

Unless the data itself (actions + attacks) are actually in the log files themselves, and we can pull them out... sounds like a question for Mu0n... that would be ideal.

I have lots of vassal log files that you can use for sample data if you would like. I'm not sure what kind of sample size you need. I have over 200 games logged, and that's just for this last tournament. I still have logs from past tournaments as well. I would be happy to share this with you if it would help.

I woulkd be very glad to access those - Have you been flying very diverse squads ?

The best way to guess how much we can extract from this logs is to start looking at them !

Sozin has a python program called Lady Luck that reads the logs and outputs stats, maybe you could use that?

I have lots of vassal log files that you can use for sample data if you would like. I'm not sure what kind of sample size you need. I have over 200 games logged, and that's just for this last tournament. I still have logs from past tournaments as well. I would be happy to share this with you if it would help.

I woulkd be very glad to access those - Have you been flying very diverse squads ?

The best way to guess how much we can extract from this logs is to start looking at them !

Here's a link to Lady Luck right now it has 342 games in there. It doesn't give much details in terms of squads.

I really liked how you stated you assumptions. This kind of analysis is impossible without them and I think they were all pretty reasonable.

However your assumptions have skewed your analysis from what a more subjective approach would find. For example after Nightbeast the Lambda shuttle scored the best, but everyone knows its biggest weakness is its dial. If I can get even get 75% as many shots with my shuttle as other ships it is doing well. And of course any one who has ever flown Interceptors will tell you that their dial, boost and barrel roll (the ability to get out of firing arcs) is where they shine.

Finally by setting the standard attack to 3 dice your favor ships like the shuttle, YT-1300 and B-wing that don't rely so much on agility as their defense, but their large amount of shields and hull.

That being said, I really enjoyed reading this. And even though I new your assumptions would lead to over rating the shuttle, I didn't expect it to do so awesome.

I'm also not sure if I would square the point cost in my calculations. But I would ask Juggler on that one.

I'm also not sure if I would square the point cost in my calculations. But I would ask Juggler on that one.

It's an extremely good starting point. At higher point levels (30+) it doesn't track as well, since the continuous time assumptions of the differential equations don't hold up. Your ship comprises so many points in the squad that your damage stays higher for longer than it normally would, increasing its value.

I use an exponent of 1.92, and that seems to work well up to high 30's. I'm going to re-evaluate the curve fit eventually, after I run calculations on hits required to kill a given stat line.

Edit: I just noticed that some of the PS1 equivalent costs look like they need some tweaking. 1 PS = 1 point, except for TIE's and Z-95's for their first PS bump. Lambda shuttle should be 20 points. (yes that'll make it look even better)

Dark Curse should probably be 13 as well as Night Beast. They both pay the same for their PS.