I'll use Lanchester's Law to get a Figure of Merit for the "regular" starfighters. I'll use a baseline of 120 points, because that's roughly the lowest common denominator. Note: the point level doesn't change the balance at all, it just avoids using "fractions" of a ship in the math, for most of the ships.

I think I have to disagree with your remark on points level not changing the balance of play. Within Lanchester's Law, that assumption works, but it hides the systematic error inherent to Lanchester's Law, i.e. the advantage of high hull/shield ships being able to fire for additional turns. This biases your result in favor of Ties and against survivable ships like the defender, so I think all in all the gap will be smaller than expected.

Also, one comment with respect to the way you treat defence dies in your model: if I understood correctly, they basically give a bonus to survivability based on defense dice. However, the worth of a defense die is hugely match-up dependent. Defense dice are most useful against many weak attacks. This should favor the Tie fighter against the Z-95 in a direct matchup, even if their performance against the average list is comparable.

Some points that I have already made in this thread, but are pertinent to your comment:

• Lanchester's assumes piecewise small changes which allow the use of differential equations, which means that yes, it assumes that damage output drops off as you start taking damage. The continuous time model 100% fixes this, because the damage stays at 100% until the exact moment the ship is destroyed. If you look several pages back, you'll see that the practical difference at around 90-120 points for 30 point TIE Defenders vs 12 point TIE Fighters was about 10% in favor of the TIE Defenders. If you increase the point limit, then this advantage disappears, and it tracks Lanchester's almost perfectly.
• The continuous time simulation unfairly gives a slight advantage to large hit point ships, because it assumes no wasted extra hits when destroying a ship. I.e. if you have 1 hull left and you eat 3 hits, the attacker still only did 1 damage. With more ships on your side to chew through, this will happen more often, and therefore slightly reduce your opponent's damage output. To quantify this, you really need to use a Salvo Combat model, and use the per-hit probability density functions, not just average damage.
• The points limit that you choose doesn't change the relative FoM. I.e. if you use a 60 point limit instead of a 120 point limit, every single FoM is decreased to 1/4 the value (FoM proportional to N^2), but the relative FoM between all the various ships remains identical.

Some new points:

• Different ship vs ship matchups will always have different results than merely the average. Some matchups will favor one ship vs the other. ANY method that tries to justify a point cost for a ship has to deal with this fact. The method I used is, so far that I have seen, the most "fair" approach when you want a single value that is an aggregate across the entire meta game. If you have a suggestion, I'm always tweaking my scripts and approach...

Some more musings on the TIE Defender:

So far, the only other TIE that does NOT have an evade action is the TIE Bomber. The evade action is available on the TIE Fighter, TIE Advanced, and TIE Interceptor. It would seem very strange if the PS1/PS3 TIE Defender had no way to get an evade token. I suppose you could justify that by arguing that has such a large profile that it's hard for it to evade, but the obvious counter point is that it was "one of the most advanced starfighters when it was created".

Likewise, it is implied that the TIE Defender is more maneuverable than the TIE Interceptor, given that they showed it having a green 3 turn, and it has a "new maneuver never before seen on a dial". And yet, it is lacking the Boost action, just like it is lacking the Evade action.

So, I can't help but wonder, if they are making it possible for the TIE Defender to take the boost and/or evade actions as part of it's maneuver dial somehow, i.e. something along the lines of the "yellow" maneuvers idea that has been floated around. Maybe something like a yellow maneuver says "After performing this maneuver, you may perform a free boost or evade action. If you do not, remove one stress token from this ship."

These are all just random musings. It will be interested to see what FFG has up their sleeves. I suspect that if they have read this thread, they are probably cackling and saying "ha ha ha, just you wait...."

I could see:

PS 1 Defender + HLC (37)

PS 1 Defender + IC (33)

Jonus + Flechette + IPM + Swarm Tactics (29)

Total = 99pts

As a possible dual Defender squad. What thinks thee?

(Overall I'm focusing on just two points here--for the sake of clarity and ease of response.)

I'll use Lanchester's Law to get a Figure of Merit for the "regular" starfighters. I'll use a baseline of 120 points, because that's roughly the lowest common denominator. Note: the point level doesn't change the balance at all, it just avoids using "fractions" of a ship in the math, for most of the ships.

Your Figures of Merit are invalid on their face, if you accept that Waves 1-3 are approximately balanced. Holding points per unit of merit constant, your table gives us the following approximate "correct" point costs for each fighter in the game (rounded to the nearest point):

• TIE Fighter: 12 points
• TIE Interceptor: 15 points
• TIE Advanced: 11 points
• TIE Defenders: 20 points
• Z-95 Headhunter: 13 points
• X-Wing: 18 points
• Y-Wing: 12 points
• B-Wing: 20 points
• A-wing: 13 points
• E-wing: 19 points

So the Figure of Merit is drastically underestimating the effectiveness of most ships: the only fighters that appear to be worth flying (that is, the only ships that don't appear to be drastically overcosted according to the model) are the TIE Fighter, Z-95, and (naked) B-wing. Perhaps your tournament experience reflects that no one flies anything but TIE Fighters and B-wings, but mine doesn't; saying that the Figure of Merit gets us "in the ballpark" ignores the fact that the Figure of Merit concludes that virtually everything is too expensive.

(It also ignores Large ships. The Lambda has a Figure of Merit of 116.3, and the Firespray has a Figure of Merit of just 64.5. Does it seem reasonable to conclude that the Lambda is the most competitively costed ship in the game by a substantial margin, and that the Firespray is overcosted as badly as the TIE Advanced?)

It's clear to me, and hopefully becoming clearer to you, that the Figure of Merit you've developed, and by extension this application of Lanchester's Law, substantially overvalues quantity with respect to quality. (This is essentially what I meant when I said you were making an unflattering comparison.) FFG has, in Waves 1-3, been at least fairly good at using the stuff you admit the Figure of Merit doesn't include--dial, actions, upgrades, synergies, named pilot abilities, and tactics--to account for the apparent discrepancies in cost that you've observed.

Accordingly, the direction and magnitude of the bias displayed by the model is sufficient to explain why the Defender appears overcosted, and until we know more, I'm more than willing to give them the benefit of any remaining doubt.

…and finally, this:

"It is better to be approximately correct than exactly wrong".

I am very much open to suggestions on how to improve the average damage calculation between 3 dice and 2! But, it is a huge stretch for you to dismiss the entire approach out of hand as "negligible", without providing any specific reasons as to why it is quantitatively wrong.

My adviser--at least, the member of my committee with the strongest quantitative modeling skills--would say that "approximately correct" isn't good enough; if you can't propose valid and defensible assumptions, you don't use the model. Your simulation approach (as distinct from the Lanchester's/Figure of Merit perspective addressed above) is negligible because it entirely omits a key element of the game's tactics.

If I'm unclear, I'm not suggesting that there are ways to improve your simulation that you're not considering--I'm suggesting that quantitative/statistical simulation is an infeasible approach given the time and computing constraints you're presumably working under. The action economy is too unpredictable, and too sensitive to variance in attack and defense rolls.

As a hopefully illustrative example, suppose your TIE Fighters are attacking my TIE Defender, and everyone on the table has a focus token. The expected damage for the first TIE Fighter's attack is 0.64 (mode and median are 0), but 28% of the time I don't have to spend my focus token--it's not likely to happen on any individual roll, but it's certainly not negligible overall. So the expected value of the second attack is either 0.64 or 1.22, depending on whether I still have my token, and if I still have it the same percentage applies to further attacks.

So for two TIE Fighter attacks against a TIE Defender with a focus token, what's the fairest expected value? Effectively, you have to account for every possible permutation of attack and defense rolls across both attacks, then take a weighted average. Because of the nature of the game, there's no clear, valid approximation for exactly what the value of that set of attacks is.

And it's incredibly meaningful that I can't easily answer a question so basic. I can simulate it (and I have), but that means that it requires a substantial investment of time and effort to answer even something as straightforward as how much damage we expect from two TIE Fighters if they're hanging motionless at Range 2 from a TIE Defender.

Simulating the effects of actions across an entire match for 11 separate fighters (8 TIEs and 3 Defenders) is an order of magnitude more difficult even if we ignore the complexities of positioning. I would submit that unless you're willing to engage in that effort (and I'm not actually suggesting that you should!), you're limited to looking at empirical data. Which we can't do for an unreleased ship, which is… basically my whole point, actually.

(EDIT: Fixed a copy-paste error.)

Your Figures of Merit are invalid on their face, if you accept that Waves 1-3 are approximately balanced. Holding points per unit of merit constant, your table gives us the following approximate "correct" point costs for each fighter in the game (rounded to the nearest point):

• TIE Fighter: 12 points
• TIE Interceptor: 15 points
• TIE Advanced: 11 points
• TIE Defenders: 20 points
• Z-95 Headhunter: 13 points
• X-Wing: 18 points
• Y-Wing: 12 points
• B-Wing: 20 points
• A-wing: 13 points
• E-wing: 19 points

(The methodology here is that the TIE Fighter is worth 1.2 points per point of merit contributed. Each ship's cost is adjusted down (or, in the case of the Z-95, up) in order to give it the same ratio of points per point of merit.)

I clearly stated on multiple occasions that the FoM can't be used as the only measure to compute a ship's balanced cost.

This obviously doesn't tell everything, because you still need to consider the dial, actions available, potential upgrades, synergies, named pilot abilities, and tactics, but it gets us in the approximate ballpark. The numbers here are remarkably close to how these ships are generally rated by the community, so you have to agree that this method has a high level of correlation with the "real" balance of each ship.

I bolded for emphasis the points that you ignored. I find your post strange, because you quoted me directly in this same context ("ballpark"), and yet proceeded then do exactly what I said cannot be done, in an apparent effort to "disprove" Lanchester's. The results will obviously show that if you completely discount the dial, actions available, upgrades, etc, that ships that pay for those abilities will appear overcosted. Well, that's exactly what I said, news at 11!

But I'll entertain your straw man argument for a moment.

• TIE Fighter: 1*1 = 1
• TIE Interceptor: 1.75*1 = 1.75
• TIE Advanced: (1.25*2 + 3)/3 = 1.83
• TIE Defender: 1.75*(1.25*3 + 3)/3 = 3.94
• Z-95 Headhunter: 1*0.7*(1.25*2 + 2)/3 = 1.05
• X-wing: 1.75*0.7*(1.25*2 + 3)/3 = 2.25
• Y-wing: 1*0.5*(1.25*3 + 5)/3 = 1.46
• B-wing: 1.75*0.5*(1.25*5 + 3)/3 = 2.70
• A-Wing: 1*(2*1.25 + 2)/3 = 1.5
• E-wing: 1.75*(3*1.25 + 2)/3 = 3.35

This sounds like the difference between a mathematician who works on just theory, versus an engineer who has to actually build something. Of course, I'm an engineer, so I'm biased.

The fact is, even a first order approximation of the action economy as being "2/3 focus on offense and 1/2 focus on defense" is both valid and defensible within a certain degree of certainty. The empirical data (community perception of balance) also backs it up (predicted point costs in the earlier table), giving a reasonably good degree of certainty that future ship's balance (or equivalently how good the dial / upgrades need to be for the ship to be balanced) can be predicted to a large extent by the model.

Incidentally, the exact values in the "2/3, 1/2" model can get changed quite a bit without really changing the final predicted point balance, but that's beyond the scope of this discussion.

The irony, is that you missed my point entirely, while simultaneously proving it! My point was that it is better to:

• Have a rough approximation of where you should end up, and have even a basic model to start that gets you in that approximate ballpark

vs.

• making a really, really detailed model, but having no understanding of the physical system, and getting an answer that is way out in left field.

I put together a model, which, while not perfect, is still "pretty good". You tried to take that model, extend it further (without understanding it), and got answers that were obviously wrong by even a cursory inspection (12 points for a TIE Fighter and 11 points for a TIE Advanced???), and you didn't even catch the mistake.

Anyway, on a lighter note, the rest is really pretty trivial.

Two attacks at range 2 (unmodified attack dice) vs 3 defense dice with a focus for defense: 0.2876. The exact PDF is:

2x5 matrix, top vs bottom half differentiates the defender still having focus or having spent it, I'll let you figure out which is which.

And it's incredibly meaningful that I can't easily answer a question so basic.

It is meaningful, because I can easily answer that question in a matter of seconds. It probably says that I have spent too much time writing MATLAB code for X-wing.

I find your lack of faith disturbing.

It's not as bad as you would think, if you approach the problem correctly. Do you do any coding? I have all the needed lower level functions already written in MATLAB anyway, to calculate exact probability density functions, including multi-ship focus fire attacks with an arbitrary number of focus tokens and/or stealth devices on the defender.

So, I can't help but wonder, if they are making it possible for the TIE Defender to take the boost and/or evade actions as part of it's maneuver dial somehow, i.e. something along the lines of the "yellow" maneuvers idea that has been floated around. Maybe something like a yellow maneuver says "After performing this maneuver, you may perform a free boost or evade action. If you do not, remove one stress token from this ship."

There is an evade token on the picture of the Defender box contents, so its either a unique ability, or it comes from an EPT or its really baked on the dial - but: there is no 'Boost' rule card in the box (like provided with the E-Wing) - so no boost for the Defender without EU ... not even as an combined move or ability...

The middle card looks like it says "Outmanuver" to me. I would guess it might come for that.

So, I can't help but wonder, if they are making it possible for the TIE Defender to take the boost and/or evade actions as part of it's maneuver dial somehow, i.e. something along the lines of the "yellow" maneuvers idea that has been floated around. Maybe something like a yellow maneuver says "After performing this maneuver, you may perform a free boost or evade action. If you do not, remove one stress token from this ship."

There is an evade token on the picture of the Defender box contents, so its either a unique ability, or it comes from an EPT or its really baked on the dial - but: there is no 'Boost' rule card in the box (like provided with the E-Wing) - so no boost for the Defender without EU ... not even as an combined move or ability...

Ah, good catch, I hadn't thought of that. Well, maybe it has 135 degree turns to make up for the lack of boost. Or maybe it's really just not as maneuverable (or adaptable, in the case of using boost as an action) than the TIE Interceptor

I clearly stated on multiple occasions that the FoM can't be used as the only measure to compute a ship's balanced cost.

To put it another way, the problem is that you made those caveats in the context of a post that states that the TIE Defender appears drastically overcosted. So the various notes that boil down to "you can't really do what I'm doing here" are really trying to wriggle out from under the weight of your your point; either you can use the quantitative methods you suggest to estimate point costs, or those estimates are so inaccurate that they're meaningless. You're saying that FoM gets you at least in the ballpark, and I'm saying that's only true if your "ballpark" is trivially large.

The results will obviously show that if you completely discount the dial, actions available, upgrades, etc, that ships that pay for those abilities will appear overcosted. Well, that's exactly what I said, news at 11!

...With some quick off-the cuff points adjustments to account for those factors, the "balanced" points for the wave 1-3 ships are all within a point of what Lanchester's Square Law predicts…

A rank-ordered list of current ships, using the Figure of Merit resulting from this application of Lanchester's Law, goes like this (normalizing 3 Attack at 1.75):

• TIE Fighter
• B-wing
• TIE Bomber
• TIE Interceptor
• A-wing
• X-wing
• Y-wing
• TIE Advanced

Since you seem so adamant that Lanchester's Square Law is useless, I challenge you (or anyone!) to find even a single example in the above list for wave 1-3 ships where the predicted balanced point cost (after minor adjustments for dial, upgrades, etc) substantially differs from the community's general consensus.

Large base ships are trickier, but they can certainly also be modeled by Lanchester's Square Law, although it's not necessary to the discussion here.

One plausible answer to both issues is that Lanchester's/your Figure of Merit is, with respect to X-wing Minis, inappropriately biased toward quantity over quality. Which is what I was at pains to point out in my previous post.

My adviser--at least, the member of my committee with the strongest quantitative modeling skills--would say that "approximately correct" isn't good enough; if you can't propose valid and defensible assumptions, you don't use the model. Your simulation approach (as distinct from the Lanchester's/Figure of Merit perspective addressed above) is negligible because it entirely omits a key element of the game's tactics.

This sounds like the difference between a mathematician who works on just theory, versus an engineer who has to actually build something. Of course, I'm an engineer, so I'm biased.

The problem with modeling in my field(s) is that if you screw up, the consequences are real and they happen to actual people. If my model overestimates the prevalence of suicidal ideation, finite resources are unnecessarily redirected to suicide prevention programs; if my model underestimates it, potential suicides don't have access to the help they need. Ditto students needing intervention to bring them up to grade level in math. Ditto NSF grant funding. If I publish a model, I had better have a really rock-solid defense for the assumptions and conclusions it entails.

Anyway, you're right that our fundamental disagreement is over where the tolerance for error is. A lot of my objection is that you're using what looks like a substantial amount of authority--e.g., you're being approvingly quoted over at BoardGameGeek--to announce that a ship is totally broken based on really incomplete evidence. There is no check on the accuracy of your model until we know more about the ship and until some people actually get it on the table; IMO, a smart modeler would hedge his bets and make conservative assumptions rather than aggressive ones.

I put together a model, which, while not perfect, is still "pretty good". You tried to take that model, extend it further (without understanding it), and got answers that were obviously wrong by even a cursory inspection (12 points for a TIE Fighter and 11 points for a TIE Advanced???), and you didn't even catch the mistake.

Yes, I applied a linear adjustment; as I said, I simply held "figure of merit per unit cost" constant, which implies a proportional weight. (The TIE Advanced costing 11 points was a typo, caused by hurried writing rather than stupidity; if the FoM for 126 points of TIE Advanced is 66, then the appropriate cost estimate using my methodology is 21 * (120/100) / (126/66) = 13.2.) My point was not to dictate a rigorous methodology--it was to point out, using something accomplished (literally) on the back of an envelope while I gave my son a bottle, that the FoM fails in epic fashion when used as a relative measure of value.

You're right that I failed to account for the fact that your Figure of Merit is an exponential scale--not because I didn't understand it, but because I was pitching my conversation toward an audience that for the most part wouldn't understand why I was adjusting costs by the square root of a proportion.

Two attacks at range 2 (unmodified attack dice) vs 3 defense dice with a focus for defense: 0.2876. The exact PDF is:

0.2651 0.0931 0.0218 0.0020 0

0.4999 0.0932 0.0230 0.0017 0.0002

2x5 matrix, top vs bottom half differentiates the defender still having focus or having spent it, I'll let you figure out which is which.

I find your lack of faith disturbing.

It's not as bad as you would think, if you approach the problem correctly. Do you do any coding? I have all the needed lower level functions already written in MATLAB anyway, to calculate exact probability density functions, including multi-ship focus fire attacks with an arbitrary number of focus tokens and/or stealth devices on the defender.

Hi Vorpal,

In general I'm not sure how to proceed. Lets recap.

1. You opened up your initial post with guns blazing in a slightly less than civil manner "I'm posting here after taking many months off just to tell you you're wrong". Erm, ok? I tried to be very civil at least in my first reply.
2. I replied to every one of your points, and pointed out that your premise that the numbers were skewed because of Howlrunner was an incorrect statement on your part. I also introduced the notion of FoM, although in retrospect I should have gone directly to the predicted baseline points cost.
3. You then tried to "disprove" Lanchester's Square Law by using the wrong math on the FoM.
4. I pointed out that your method of predicting balanced point costs based on Lanchester's and the related FoM, was obviously wrong, making all of your numerical arguments in that post incorrect and meaningless. I derived Lanchester's predicted balanced costs, and pointed out that the difference between the predicted costs and actual costs, for the ships that I listed in waves 1-3, can either be attributed to ship specific abilities (dial etc), or perceived imbalance (TIE Advanced).
5. You admitted that you KNEW you were using incorrect math, but are continuing to defend yourself anyway, without addressing any of my points, and certainly never saying "oops, yeah, my bad, you were right", about...

• Howlrunner not biasing the results in favor of the TIE Fighters
• ... or that comparing 3/3/3/3 Defenders vs 3/3/3/0 Interceptors is actually the best available comparison
• ... or Defenders somehow being unfairly biased against in the continuous time simulation (the reverse is true, for multiple reasons)
• ... or you getting the Square relation wrong.

What exactly would you have me DO, if you were in my shoes? I get the sense that every time you are corrected, you're just going to ignore it, and keep arguing anyway.

either you can use the quantitative methods you suggest to estimate point costs, or those estimates are so inaccurate that they're meaningless.

You have a very polarized way of thinking. (sorry, couldn't resist throwing in an Emag pun since you mentioned your background ... and this thread is becoming heated, so I am trying to "Fly Casual" )

The world is analog, not digital. Another entire category of options is: the quantitative methods can be used as a baseline which then requires more detailed analysis to consider the specifics of the ship in question. Ultimately, the non-statistical factors can be mapped into effectively changing the attack and defense values. This is neither post-hoc nor arbitrary, and demonizing it as such is really not an effective debate method.

You might as well argue that all FFG forum posters are EITHER homicidal maniacs that make Adolf Hitler look like a pacifist, OR they are saints that Mother Theresa isn't worthy tying the sandals of.

Here is the list again of predicted baseline costs BEFORE considering upgrades / dials etc (including 3 of the wave 4 ships) so there is no room for confusion. I re-ordered by percentage of point inefficiencies, it to be consistent with the notion of ranking in your (not numerically cited) list, and also added TIE Bombers:

• TIE Fighter: 12 (12) - 100%
• TIE Bomber 14.2 (15) - 95%
• B-Wing: 19.7 (21) - 94%
• X-Wing: 18.0 (20) - 90%
• TIE Interceptor: 15.9 (18) - 88%
• A-Wing: 14.7 (17) - 86%
• Y-Wing: 14.5 (17) - 85%
• TIE Advanced: 16.2 (20) - 81%

Wave 4, obviously no consensus by which to judge:

• Z-95 Headhunter: 12.3 (11) - 112%
• E-wing: 22.0 (27) - 81%
• TIE Defender: 23.8 (30) - 79%

I don't mean to make this sound like a personal attack, but honestly, at this point since you keep digging in your heels and insisting that the entire Lanchester's process is wrong, your 3 options are to either:

1. define how "trivially large" you believe the error in Lanchester's prediction is (either in points or in percentages) in direct response to the challenge above, pointing out which ship you believe to be in error
2. admit that you might have been wrong
3. cover your ears, avoid the point completely, and keeping arguing in an attempt to drown out the issue.

A ranked list without numbers isn't particularly informative, and presumably used the same flawed math to generate the numbers for this ranking, since it disagrees with my above list that is correctly ranked by baseline point efficiency. So lets use the numbers that are derived correctly, and stop propagating incorrect information, OK?

All interesting, and all completely irrelevant to the point here. OK, yes, that's important, but not here on FFG Forums. I don't want to get drawn into a chest-thumping exercise about whose field more is important how, and how that translates into having more insightful comments. Just the raw facts, please.

I fixed that for you. The only "failure in epic fashion" was your incorrect application of math.

Up to this point, everything to this point has been a somewhat understandable difference in opinion, but this is a gigantic red flag and I am going to draw a line in the sand here.

• You used a method that you knew was wrong, and therefore would yield incorrect results.
• You did this because you didn't think that the community members were intelligent enough to understand the correct method, so you wanted to give them "something" to chew on, even if it was clearly wrong.
• In this case the misinformation conveniently made it look like Lanchester's Square Law was wrong, which you have been trying (unsuccessfully) to disprove this whole time. Unfortunately I called you out on it.

I have 2 very simple parting thoughts:

• You never EVER EVER, falsify the data or intentionally provide misleading information. I am abhorred that someone who is a PhD student / candidate would even think of doing this. I have zero tolerance for falsifying data and plagiarism.
• I have enough faith in the intelligence and goodwill of the community, so that even if not everyone can follow all the math, they still deserve nothing but the best and most unbiased information possible.

I think the FoM does a really good job showing the risk of flying upgradable ships naked. What was said earlier about Y wings rang true for me, I always add an astromech and a turret.

Yeah, but since the only way to run a 5 ship rebel build is by dipping down into either a Y-wing or an A-wing, and numbers REALLY matter in this game, it makes the naked Gold Squadron Y-wing more appealing at a 100 point squad limit. With the introduction of the 12-point PS2 Z-95, I think you'll see far less Y-wing and A-wing filler. Even if the Z-95 has a dial as bad as the Y-wing, it's still a better ship if run naked.

I think the Y-wing has a pretty good dial, though I have been flying a lot of shuttle lately so that may be coloring my recollection. In any case I agree completely that the z95 will be the new filler in rebel lists. I think the A-wing will retain a place in the flanking role but y's are likely to be flown only with upgrades.

"You're right that I failed to account for the fact that your Figure of Merit is an exponential scale--not because I didn't understand it, but because I was pitching my conversation toward an audience that for the most part wouldn't understand why I was adjusting costs by the square root of a proportion." -Vorpal Sword

That is really uncool VS. The level of contempt you just articulated puts everything else you wrote into a very negative and highly suspect light.

Whats the name of the 2nd rule card btw, next to the ion rule card? It starts with 'M' ... the Z-95 and the Phantom has it, too.

(EDIT: Fixed a bunch of broken quotes; stray size tags were gumming up the works.)

First: I wasn't attempting to address every point you made because I ran up against the forum software's limit on the number of quotes I'm allowed to use. Yes, you're right (e.g.) that I assumed when you said "7 TIE swarm" you meant a Howlrunner swarm, as well as in a couple of other places.

Now, on to the rest:

The world is analog, not digital. Another entire category of options is: the quantitative methods can be used as a baseline which then requires more detailed analysis to consider the specifics of the ship in question. Ultimately, the non-statistical factors can be mapped into effectively changing the attack and defense values. This is neither post-hoc nor arbitrary, and demonizing it as such is really not an effective debate method.

There's no demonizing, and I wasn't feeling particularly heated (see the note on fraud for why this is no longer true). I came back to these boards because you sound hyperbolic at best, and because people appear to be listening to you.

The central thrust of my posts are that we don't know anything about the Defender except its stat line, base cost, actions, and upgrades; you've concluded, based on not just that extremely limited information but a subset of it, that the Defender is badly overcosted and will be essentially useless from a competitive standpoint.

As I've said multiple times, apparently not as clearly as I'd hoped: your reasoning is based on catastrophically incomplete data and a model that does a relatively poor job of predicting empirical performance. And you've admitted that the data is incomplete and that the model's results require adjustment, but somehow without compromising your faith in your basic conclusion. I don't understand that, and it's why I'm still bothering to discus the issue.

I will re-iterate my challenge:

Since you seem so adamant that Lanchester's Square Law is useless, I challenge you (or anyone!) to find even a single example in the above list for wave 1-3 ships where the predicted balanced point cost (after minor adjustments for dial, upgrades, etc) substantially differs from the community's general consensus.

Was my response unclear? The fact that your model requires substantial post-hoc adjustment to every ship except your baseline bring it into alignment with reality makes it a bad model, and (again) I don't understand why you're maintaining that it's okay.

The option you've chosen is to pretend that the FoM/Lanchester model is still appropriate despite the fact that it gets every single ship wrong. You can find post-hoc rationalizations for every costing "error", but the fact that you have to do so should worry you.

But I'll bite on your challenge (again): please explain why the perceived error in costing the A-wing is the same as the error with the Interceptor, despite the fact that the community as a whole would agree that Interceptor is an effective ship but the A-wing is not. Please explain why the the Y-wing's access to the turret plus access to target lock is worth 2.5 points, while the X-wing's access to target lock alone is worth 2 points. Please explain why FoM ranks the TIE Bomber so highly, when most players see it as a fairly ineffective dogfighter.

And you still haven't really addressed the Lambda and Firespray, which are respectively at the high and low extremes of the list (FoM 107 and 59) in sharp contrast to their levels of acceptance in the competitive community.

A ranked list without numbers isn't particularly informative, and presumably used the same flawed math to generate the numbers for this ranking, since it disagrees with my above list that is correctly ranked by baseline point efficiency. So lets use the numbers that are derived correctly, and stop propagating incorrect information, OK?

You can find a link to my derivation of Figures of Merit here. The only difference between this and what you've done is that I used fractional numbers for every ship--the FoM is based in each case on the fractional number of ships that will fit in a 120-point list, so I can skip the annoying step of (e.g.) having to compare 126 points of X-wings with 120 points of TIE Fighters.

All interesting, and all completely irrelevant to the point here. OK, yes, that's important, but not here on FFG Forums. I don't want to get drawn into a chest-thumping exercise about whose field more is important how, and how that translates into having more insightful comments. Just the raw facts, please.

It wasn't chest thumping; it was an attempt to explain, in a collegial fashion, where I'm coming from--why my tolerance for error might be substantially smaller than yours.

I rarely even lurk on the BGG forums, and certainly was not aware that I was being approvingly quoted there. How, then, could I be using that as "authority"? The only authority that I have presented in this thread are the raw facts and how well the historical data lines up with the predicted values from the model. Which, again, I invite you to critique.

When people say smart-sounding, sciencey things, lots of other people often listen uncritically--again, that's the authority I mean. And that's fine, as long as the smart-sounding sciencey person is right. At the risk of verging on the political, this is how anti-vaccination crackpots and "Intelligent Design" propagandists get a foothold: their target audience doesn't know enough to spot the gaps.

But if someone says "If humans evolved from monkeys, why are there still monkeys?" and others are inclined to swallow it whole, you have two choices: you can spend a few hours attempting to explain the modern definition of species as primarily a statistical and behavioral phenomenon, or you can simply say "If you were born from your parents, why do you still have parents?" and let your audience work it out from there. It's not really true that parents and children have the same relationship as related species, but it's illustrative and meaningful even though it's not correct in the most technical sense.

I failed to account for the fact that your Figure of Merit is an exponential scale--not because I didn't understand it, but because I was pitching my conversation toward an audience that for the most part wouldn't understand

Up to this point, everything to this point has been a somewhat understandable difference in opinion, but this is a gigantic red flag and I am going to draw a line in the sand here.

When I sat down to apply your methodology in a way that demonstrated its fundamental mismatch with the empirical data--that is, in an attempt to demonstrate exactly how often the "ballpark" estimates you're discussing are off--it honestly didn't occur to me initially to treat it as a nonlinear scale. That is, given just a list of Figures of Merit, the most straightforward approach is to treat a ship with a 66 FoM as being 66% as efficient/effective as a ship with 100 FoM.

It then occurred to me as I was previewing my post that perhaps I should have treated it as an exponential scale, meaning a ship with a 66 FoM is sqrt(66/100) = 81% as efficient. But I really didn't want to get into the distinction between linear scales and exponential ones, I didn't want to get sidetracked explaining why 66% is really 81%, and honestly I had chores to do and didn't want to go back and recalculate everything using the square root of the normalized FoM. So I went with the more straightforward version--while explaining exactly what I'd done, clearly enough that you understood it perfectly.

And then, instead of actually addressing the fact that the FoM model spits out incorrect values for every single ship except the TIE Fighter, you decided to focus on the fact that the wrong values I got out of the model weren't the same as the wrong values you got out of it.

So, it's a fair cop; mea culpa. I screwed up when (admittedly in the name of convenience and ease of explanation) I approximated FoM as a linear scale, rather than an exponential one. I've now admitted--twice!--that I had the wrong wrong values, while you have the right wrong values.

• You used a method that you knew was wrong, and therefore would yield incorrect results.
• You did this because you didn't think that the community members were intelligent enough to understand the correct method, so you wanted to give them "something" to chew on, even if it was clearly wrong.
• In this case the misinformation conveniently made it look like Lanchester's Square Law was wrong, which you have been trying (unsuccessfully) to disprove this whole time. Unfortunately I called you out on it.

I have 2 very simple parting thoughts:

• You never EVER EVER, falsify the data or intentionally provide misleading information. I am abhorred that someone who is a PhD student / candidate would even think of doing this. I have zero tolerance for falsifying data and plagiarism.
• I have enough faith in the intelligence and goodwill of the community, so that even if not everyone can follow all the math, they still deserve nothing but the best and most unbiased information possible.

First, Lanchester's Square Law is wrong--or, more precisely, the application you're making here is inappropriate. You used a well-known (if somewhat controversial) theoretical relationship between force ratios and casualties to derive a "figure of merit" that doesn't have anything whatsoever to do with force ratios or casualties, and used it to model relative effectiveness for these ships despite the fact that it simply doesn't do a good job of actually explaining ship costs.

Second, I've been trying to keep this on the level, but now you've accused me of fraud. I've been completely open about the issue you think makes me a dishonest actor, to the point of explaining my methodology so that anyone could check my work. You can explain why approximating FoM as a linear scale isn't particularly defensible on technical grounds, and I'll even agree with you in hindsight, but it's a drastic and unsupportable exaggeration to claim that I deliberately misled people because I thought they were too stupid to tell.

But now that you've made it personal, let's go back to the first parting thought: you're standing behind a model that fails to model every available data point. Furthermore, you claim that it's really okay because it reflects conclusions you like, after you adjust the results to reflect those conclusions, and then you use it to extrapolate--without performing the same kind of post-hoc adjustments. So whenever you're done spinning the fact that your model requires post-hoc adjustments to match any data point, please explain to me how what you've done here is anything short of malpractice.

"You're right that I failed to account for the fact that your Figure of Merit is an exponential scale--not because I didn't understand it, but because I was pitching my conversation toward an audience that for the most part wouldn't understand why I was adjusting costs by the square root of a proportion." -Vorpal Sword

That is really uncool VS. The level of contempt you just articulated puts everything else you wrote into a very negative and highly suspect light.

This forum has a lot of smart people, but one facet of my job is explaining highly technical material to people who don't have the relevant technical expertise. Intelligence doesn't come into it; being an expert in one field doesn't make someone an expert in another. So I tend to simplify as much as possible in a setting where I can't be confident in my audience's expertise, while explaining what I've done--and professionally, I usually refer readers/listeners to an appendix or reference where those who have the skills and interest can find out more.

Vorpal,

If the explanation needed was more than, "since the model uses exponential scale and not a linear one these numbers are scaled appropriately (bit o algebra here)". I would be a lot more understanding. You may not have intended to be condescending, however as someone who also spends a lot of time explaining technical stuff to those not familiar with it that came across as a huge load of hubris.

Take that critique for what it is worth.

My abstraction of the conversation above with M J is that you both recognize his model isn't exact. However I think you are misrepresenting him. For starters the Y wing has an additional torpedo slot in your X vs Y comparison. I also think you are reading the hyperbole in the initial post as the point he holds. Juggler repeatedly qualified his analysis with the expectation that something will need to be very good about the dial and pilots to make the defender worth it. That is not at all the same as the unvarnished claim that the defender will be total crap.

I think you are both triggered and seem to be talking past each other. Why not take some time off this thread?

I believe all that MajorJuggler has done here is put out his hypothesis with the knowledge we have: no more, no less. As of right now, I am tempted to agree: the Defender does seem overcosted, but only time will tell. Models are just that, models. Coming from a chemistry background, I can say that all that has been given here, from both Juggler and Vorpal are THEORIES—like any other theory (such as the theory of evolution) it can only be disproven, never proven. The only thing that will convert this theory into a fact is when the model is released and we can play test it. Even then, it only takes one good squad to completely turn the theory of Defender-uselessness on its head.

Everyone remember that this is just a game, we play it to have fun, not to start accusing each other of falsifying data or malpractice. Everyone is entitled to their own opinion, right or wrong; at this point we don't know which it will be. Even if Lanchester's Law is not completely accurate, if it can successfully determine which ships will be used more, then so be it. If not, then it's back to the drawing board to find a new algorithm. It is not anything for anyone to start a fight over. I really expect more from two supposed adults, who are claiming to be educated people but are still acting like kindergarteners fighting over who has the best toy. Honestly, just cool down and enjoy the game.

Okay, rant over now.

I think you should remodel based on a Stochastic Salvo combat model. I think there are far more parallels there, and it'd be worth it to see what results show up comparative to what you have now.

Regardless of how we model, we've got fairly large areas that just aren't treated by lanchester's laws - Assault missiles for one, they're almost like a "nuke" since they can hit so many targets at one time. Another is the simultaneous fire rule - IF I recall correctly (That's a big if) Lanchester's laws don't account for simultaneous destruction of two combatants. Additionally, Initial ship placement and asteroid placement also give rise to non-negligable variance to initial conditions in the combat - given that millimeters and arc minutes of angle in ship placement cause important issues later - it's often said that x-wing is "A game of millimeters." I don't think Lanchester's square law is a terrible model to glean something about the combat - especially in a head on jousting kind of way.

One thing that I've found - and I can't recall the thread where I posted it, was that each ship seems to have value to players based on customization points. (This doesn't necessarily match by point based, but it does fit rather well with popularity polls for different ships.) As time goes on, upgrade slots / pilot choices are only going to increase - meaning the value for ships with certain upgrade slots should always get better as more upgrades become available

Customization points are roughly as follows -

Pilot Skill options, pilot ability choices, upgrade slot choices, and modification / titles. (Anti pursuit lasers for example aren't an applicable modification to a tie fighter). The value of each type of slot is hard to judge, but can be tied to the number of available upgrades, and pilot skill is deeply intertwined with pilot ability - so we may just refer to "number of different pilots" available. Missile slots are probably more valuable than torpedo slots (as of wave 3)

When we look at these - two ships has more options than any other - and ironically one is the tie fighter, the other is the firespray (which has the most upgrade slots of any ship), but the tie fighter has 9 ship choices, EPT and modification (total 11) Now, one might set the ship as a point, and just declare ties to have only a value of 3, but I think as the ship choice carries the other choices in the build, it's worth counting them seperately, when it comes to looking at full configurations - and while an EPT icon on one ship gives it the same options as any other ship. I would really prefer to rank them with (#of pilots - Upgrade options) and just rank them in order of higher number...

Interestingly, I think the amount of customization a ship can have actually answers VorpalSwords Challenge

"But I'll bite on your challenge (again): please explain why the perceived error in costing the A-wing is the same as the error with the Interceptor, despite the fact that the community as a whole would agree that Interceptor is an effective ship but the A-wing is not."

The A-wing has 4 pilot choices, ept, mod and missile for a total of 7 (on this single numbered scale) - while the Interceptor (Pre imperial Aces) - has 6 pilot choices, and ept + mod. (8 on the scale) - that puts them pretty close to eachother - but Aces jumps us up to 11 ship choices, and extra modification options... which certainly puts the interceptor way higher up on the cool list.... Interestingly, the like the a-wing, the Tie Advanced is tied for fewest pilots and upgrade points (4 pilots, missile, ept, modification)

EDIT - ah-ha , I found the post I was looking for over on BGG,
I called it flexibility, and ordered them like this.. (Ignoring modifications and titles)

(11) Tie Interceptor w Aces (11 pilots, 0-1* slots)
(9) Tie-Bomber (4 pilots, 5-6 slots)
(9) Tie-Fighter (9 pilots, 0-1* slots)
(8) Firespray* (4* pilots, 4-5 slots)
(8) B-wing (4 pilots, 4-5 slots)
(8) Shuttle (4* pilots, 4 slots)
(8) Y-wing (4 pilots, 4 slots)
(8) X-wing (6* pilots, 2-3 slots)
(6) Falcon** (4* pilots, 2-4 slots)
(6) Hwk-290 (4* pilots, 2-3 slots)
(6) Tie Interceptor w/o aces (6* pilots, 0-1* slots)
(5) A-wing (4 pilots, 1-2* slots)
(5) Tie Advanced (4 pilots, 1-2 slots)

(* The firespray can gain an additional slot via slave-1 (bumping it up to the near top of the list)
(** Of note is the ORS which is a bit less customizable than the falcon)

Tie Defender would fall at - (6) 4 pilots, 2-3? slots (Assuming there's an EPT on any of the pilots - we don't know if that's the case though. )

I have tried so hard to keep up with all of this but I finally just have to put my foot down. This thread has gotten out of hand and at this point is just kinda redundant. We get it, the **** thing is probably a waste of points. It isn't worth it. It's garbage. Don't buy it. Don't read about it. DON'T LOOK AT IT.

Here is my issue with this thread: Why would we ever take 3 of these things in a list? One might make sense but three?

Also, we have no idea what the hell the dial is going to look like. It could be as good as an A-Wing or as boring as a Y-Wing. We simply don't know! So with that said, can't we all just agree that at the moment they don't look that great and when we learn more we can truly have this debate?

I really expect more from two supposed adults, who are claiming to be educated people but are still acting like kindergarteners fighting over who has the best toy. Honestly, just cool down and enjoy the game.

Okay, rant over now.

Yeah, I will agree that things got heated, but neither of them is acting like a kindergartener. That is needlessly derogatory to both of them, by rather a lot.

We get it, the **** thing is probably a waste of points. It isn't worth it. It's garbage. Don't buy it. Don't read about it. DON'T LOOK AT IT...

Also, we have no idea what the hell the dial is going to look like. It could be as good as an A-Wing or as boring as a Y-Wing. We simply don't know! So with that said, can't we all just agree that at the moment they don't look that great and when we learn more we can truly have this debate?

If the explanation needed was more than, "since the model uses exponential scale and not a linear one these numbers are scaled appropriately (bit o algebra here)". I would be a lot more understanding. You may not have intended to be condescending, however as someone who also spends a lot of time explaining technical stuff to those not familiar with it that came across as a huge load of hubris.

Take that critique for what it is worth.

Understood, and I appreciate it. I'm busy, sleep-deprived, and irritated not with MajorJuggler in particular but with the whole massive jump-to-unwarranted-conclusions contingent of X-wing fandom; I'd ask that you chalk my tone up to impatience and general frustration, rather than contempt.

My abstraction of the conversation above with M J is that you both recognize his model isn't exact… Juggler repeatedly qualified his analysis with the expectation that something will need to be very good about the dial and pilots to make the defender worth it. That is not at all the same as the unvarnished claim that the defender will be total crap.

Quoting from the OP:

"However, I am predicting right now, that the TIE Defender will NEVER get used competitively successfully, unless its new maneuverability dial/ability is insanely overpowered."

Not much varnish there, unfortunately, and it's a long way from "will need to be very good" to "unless… insanely overpowered". I think it's very likely that MJ will turn out to be wrong, but I'm absolutely certain that he can't support his claim based on the evidence that's publicly available.

Why not take some time off this thread?

Should the tie defender elite really have PS1 pilots? I think they start at 4!

Should the tie defender elite really have PS1 pilots? I think they start at 4!

Honestly that is something that has puzzled me with other ships in the game as well, particularly the TIE interceptor and A-wing. They are both ships flown by "elite" pilots and yet their base pilot skill is lower than or equal to the basic version. Interceptors at least have PS 4 and 6 generics with an EPT slot but it's just bizarre that the highest A-wings can go is PS3 without spending a lot more points to get to Tycho.

I just want to say that I've appreciated Vorpal Sword's discussion on Major Juggler's numbers, and I don't mean that to be a negative on MJ, but there really hasn't been a lot of actual discussion on his level and his points have often been pretty much accepted as fact. IMO, That's never really a good thing.

I'll admit that I don't have the background to follow this discussion completely, but the calculations have never sat well with me because of what's omitted and I found the adjustments too convenient, even if they were eruditely explained. Again, though, I give him the benefit of the doubt in that no one else has done this work and I find it interesting.

This thread and title has bothered me as the conclusions are far too definitive for knowing little and of course we have a caveat if things don't turn out the way this thread started. Maybe when all the info comes out, MJ can get ahead of the curve and calculate all the variables in advance and accurately predict it's effectiveness, which would be quite a feat.