I think people are getting their hopes up a little to high with the new Maneuver. There doesn't seem to be a card for rules of a new maneuver, so it has to be within the framework of the rulebook. And considering we are STILL getting rule cards for Ion weapons, I highly, highly doubt FFG is going to create a new rule for a new bearing or difficulty without a card.

Good or bad, I'm still getting 3. I love the Defender.

MajorJuggler, don't you think your model looses something through the assumption of a continuous rather than discrete behaviour for the small number of ships typically involved? I tried to approximate a turn by turn sequence using the squads you suggested and your value for the expected damage of a defender. Assuming the defenders have initiative, the result is actually pretty close, though the regular Ties still come out on top. However, in their first salvo, the Defenders just barely miss killing a second Tie (3*1.9 for 5.7 expected damage) whereas the 6 surviving Ties just reach the expected value for killing off one Defender. This means a slight run of good luck early on swings the battle towards the Defenders. While the Ties still appear to be the better deal, the difference is not so big that it could not be accounted for by the maneuver dial.

Could your model be adapted to give a distribution of likely results to take the variance of the dice into account?

Yes, good thoughts and thanks for asking.

The continuous time quick simulation is what I would consider a "second order" approximation. It's better than a "first order" approximation, which would be squad combat figure of merits from Lanchester's Laws. An even better approximation, say a "third order" approximation, would be a round-based combat simulator that takes into account the actual probability density functions for each individual attack, and generates the resulting squad-based damage probability density functions after each round. You would then recompute from each data point until one squad is completely dead. The final output would tell you the probability of how much life each squad would have. I.e. If squad 1 has 21 hit points and squad 2 has 18 hit points, then the x-axis will go from -21 to +18, and the y-axis is the probability of ending up with that particular result.

I did this for Axis and Allies, and what you get out is a bimodal Gaussian distribution: there's one peak centered around a positive x-axis value, corresponding to a squad 2 victory, and there's another peak centered around a negative x-axis value, corresponding to a squad 1 victory. The squad that is more likely to win will have the larger peak. If they are both about equal, then the two peaks sometimes start to converge in the center. I say sometimes, because many times it is actually more statistically likely that even if two squads are evenly matched, the first round or two will randomly favor one side, at which point the whole thing snowballs into a decisive victory.

I will undoubtedly end up creating a similar sort of program for X-wing, but not for a while. I have other things to work on in the meantime that I need to get wrapped up.

A fourth order approximation would be to somehow change the attack / defense values over time, using some sort of heuristics to figure out what range shots would likely be made based on how long into the game you are. You can keep going to the nth degree, but ultimately, the question is

1. How much confidence do you have in the model, i.e. does it even reflect reality.
2. Is it sufficient for the task at hand.

In this case, for the TIE Defender, it's an off-the-cuff estimate that points us in the right direction. On a completely made-up scale of 1 (yuck I would never fly 5 naked HWKs!) to 10 (wow this ship is absolutely awesome and broken overpowered), the TIE Defender, from what we know so far, is probably sitting somewhere around the 2-4 range, with a big "but wait... there's more" that could push it higher. Like if it gets a free evade every round, or something absurd like that.

Edit: Also, a VERY important note: going to a round based model (3rd order example), you wouldn't use the normalized attack numbers (I.e. 1.9 in this case). You would use the actual damage numbers per attack/defense roll. Incidentally they are pretty close to that anyway, so you would already be in the ballpark.

Thanks for the explanation! Very interesting stuff, in particular the double gaussian for final results in Axis and Allies. I'd expect that to be a rather general pattern for this type of game.

In your terminology, I guess what I was trying to do was a sort of 2.5th order approximation, i.e. take into account the timing of ships being destroyed without going to simulating die rolls. I'd expect more detailed simulation to swing the balance a bit more towards ships with large hitpoint pools, as they start dropping their attack strength later, and an extra round of fire from a big ship can be quite significant. Either way, I'd not be too surprised if the big and shiny ship is not the most efficient. It's basically a Timmy-card for X-wing.

Thanks for the explanation! Very interesting stuff, in particular the double gaussian for final results in Axis and Allies. I'd expect that to be a rather general pattern for this type of game.

In your terminology, I guess what I was trying to do was a sort of 2.5th order approximation, i.e. take into account the timing of ships being destroyed without going to simulating die rolls. I'd expect more detailed simulation to swing the balance a bit more towards ships with large hitpoint pools, as they start dropping their attack strength later, and an extra round of fire from a big ship can be quite significant. Either way, I'd not be too surprised if the big and shiny ship is not the most efficient. It's basically a Timmy-card for X-wing.

1. Timing only matters if you have different pilot skills, unless you want to get into the order that focus tokens are spent, in which case you're looking at per-attack rolls.
2. The 2nd order method (which was used earlier in this thread) inherently takes into account the "large hit point bonus" that isn't reflected by Lanchester's Law for small squad sizes. So no worries there.
3. I already have scripts written that calculate exact damage probabilities, so I only need to write the higher level functions.
4. A squad power is proportional to N^2*A*D where N is the number of ships, A is the damage output per ship, and D is the health per ship. Then the bigger ships get a "ghost bonus" because their damage takes longer to get eliminated. But the simulation covers that.

If I understood it right, the second order assumption does not account for the possibility of a ship being eliminated before ever firing, since all ships contribute to the damage up to the first elimination. This may not be hugely significant for ships with weak attack, but since early turn effects are highly significant here, it might still matter...

Also, how do you derive that formula and what does squad power mean in this context? Is the relative power associated with the probability win?

If I understood it right, the second order assumption does not account for the possibility of a ship being eliminated before ever firing, since all ships contribute to the damage up to the first elimination. This may not be hugely significant for ships with weak attack, but since early turn effects are highly significant here, it might still matter...

Also, how do you derive that formula and what does squad power mean in this context? Is the relative power associated with the probability win?

The way it's written and described, yes. But ships that have the same pilot skill can't get eliminated before firing due to the simultaneous attack rule. I was comparing PS1 Defenders with PS1 TIE Fighters, so that makes it simple.

Lanchester's Law is based on based on differential equations. His derivation shows that the power of an attack squad is proportional to the number of units squared. If you linearly increase each units attack or health, then the attack power goes up linearly.

"Squad power" is just a figure of merit that tries to wrap up everything into three variables: number of ships, average damage done per ship, and hit points per ship. If you have a higher figure of merit, then yeah, you're more likely to win, all else being equal. The trick is to get some sort of reasonable approximation for damage mitigation that occurs in the form of better maneuvering, or if applicable, higher PS that lets you snipe enemy ships before they shoot.

Has anyone actually figured out the system FFG uses to point their ships?

Has anyone actually figured out the system FFG uses to point their ships?

This would be an excellent interview question for them.

I'm sticking with evasive maneuver that adds an evade token. They didn't give the most advanced fighter in the galaxy, known for its evasive nature, the evade action...yet packaged it with evade tokens AND are going us a "new maneuver". Not a new speed, not a new bearing, not a new combo... New maneuver.

They are liking new movement options and ways of giving us "double actions" without giving us 2 actions: lorrir, new Astromech... Makes too much sense, feels unique, feels advanced, and makes it worth the points.

I have to ask, is this a hunch, or have you heard something?

I have the same info as everyone else. Of course if I had more info that means I have a NDA and I would have to say that I don't know anything special. So you have to ask yourself... Does it all make sense? Does it sound plausible and simple and in flavor? Wouldn't FFG omit a little something from the pic for a big reveal later? Would they even bother mentioning a simple Kturn as a big deal?

Do you believe? Take the red pill. Take the blue pill. Come on down the rabbit hole.

I'm sticking with evasive maneuver that adds an evade token. They didn't give the most advanced fighter in the galaxy, known for its evasive nature, the evade action...yet packaged it with evade tokens AND are going us a "new maneuver". Not a new speed, not a new bearing, not a new combo... New maneuver.

They are liking new movement options and ways of giving us "double actions" without giving us 2 actions: lorrir, new Astromech... Makes too much sense, feels unique, feels advanced, and makes it worth the points.

I have to ask, is this a hunch, or have you heard something?

I have the same info as everyone else. Of course if I had more info that means I have a NDA and I would have to say that I don't know anything special. So you have to ask yourself... Does it all make sense? Does it sound plausible and simple and in flavor? Wouldn't FFG omit a little something from the pic for a big reveal later? Would they even bother mentioning a simple Kturn as a big deal?

Do you believe? Take the red pill. Take the blue pill. Come on down the rabbit hole.

Oh, it's plausible, that's why I asked lol. It still could be a 1 KTurn, and we're just the ones making a big deal about it though. As a matter of fact, the reason I think it's a 1 K is because of the wording "maneuver never seen on a dial". Tetran Cowell has access to that maneuver, but it's not on his dial.

So we have faith in FFG that they priced the Tie Phantom correctly, but not that they priced the Defender correctly?!?

Didn't alot of people say that a statline of 3-3-3-3 would need a point cost of at least 33 points?!?

Why doubt when you've seen so little of the ship?!?

Isn't the ability to NOT get one-shotted a point increase consideration?

Doesn't every bloody ship get fawned over and critiqued when they're announced, then it comes out and people calm down?

The fact that they have 6 hit points and 3 agility makes each and every one of those hit points harder to take…means it's just not as simple as adding 3 shield upgrades.

Cmon people…have faith in FFG.

Juggler,

Apologies if you did and I missed it, but have you done any modeling in your comparison if the defenders get an evade as a free action? I think that is possible and it would be interesting to see how that changes things.

Alternately it looks like a hell of a platform for a HLC especially in Imp vs Reb fights so I'm sure it will see use.

So first off....I wanted to say that I dig the math analysis. But I would make this challenge.

Is there a list out there that can stack up mathematically to a 7 tie swarm?

When I read this first, I thought the 3 defender list was more comparable statswise to a 3 fire spray list than it was to the interceptor.

Defender=6 hit points and 3 agility,

Firespray= 10 hit points and 2 agility.

both fire with 3 dice.

So I am curious how 3 BH list would do in the math challenge vs. a 7 tie swarm. I suspect about the same. But we know it is a viable list.

And also, is there any list that matches up vs. a 7 tie swarm in your model?

In response to the possible 1k turn. I think not. It seems a bit off for them to give it to a ship, when it has not even come out in the aces pack yet. The 1k is what makes Cowell unique. I have a hard time believing they would take away his one of a kind ability before he even has a chance to use it.

If I understood it right, the second order assumption does not account for the possibility of a ship being eliminated before ever firing, since all ships contribute to the damage up to the first elimination. This may not be hugely significant for ships with weak attack, but since early turn effects are highly significant here, it might still matter...

Also, how do you derive that formula and what does squad power mean in this context? Is the relative power associated with the probability win?

The way it's written and described, yes. But ships that have the same pilot skill can't get eliminated before firing due to the simultaneous attack rule. I was comparing PS1 Defenders with PS1 TIE Fighters, so that makes it simple.

Lanchester's Law is based on based on differential equations. His derivation shows that the power of an attack squad is proportional to the number of units squared. If you linearly increase each units attack or health, then the attack power goes up linearly.

"Squad power" is just a figure of merit that tries to wrap up everything into three variables: number of ships, average damage done per ship, and hit points per ship. If you have a higher figure of merit, then yeah, you're more likely to win, all else being equal. The trick is to get some sort of reasonable approximation for damage mitigation that occurs in the form of better maneuvering, or if applicable, higher PS that lets you snipe enemy ships before they shoot.

Thanks for the clarification! Iknow my differential equations, but this area of application is somewhat new to me, so I'm mostly going by Wikipedia. Apparently, what I've been trying to do is a kind of Salvo Combat Model. When running that with simultaneous shooting, the results also clearly favor the regular Ties.

I've also made a quick attempt at 3 Firesprays vs 8 Academy Ties, which ends after 8 turns with 4 Ties to no surviving Firesprays.

I also tried that approach for 2 HLC Bwings vs 5 Academy Ties. When assuming that the Bwings shoot first every turn, and all actions are taken as offensive focus, I end up with a single Bwing at half HP remaining after 5 turns. This is not 100 points thoug, if the Ties get the firepower to knock out one of the Bs on turn one, that could change the equation.

Juggler,

Apologies if you did and I missed it, but have you done any modeling in your comparison if the defenders get an evade as a free action? I think that is possible and it would be interesting to see how that changes things.

Not yet, because FFG hasn't revealed that yet. It would be fairly easy to add that into the super-fancy round based simulator (that doesn't exist), but more difficult for the continuous time approximation that I whipped up.

So first off....I wanted to say that I dig the math analysis. But I would make this challenge.

Is there a list out there that can stack up mathematically to a 7 tie swarm?

The 8 TIE Swarm! I'm actually not kidding - 7 TIEs including Howlrunner is around the same level as straight-up 8 TIES.

I can easily plug in different numbers though. I just ran 8 TIEs vs 3 Bounty Hunters. TIE average damage is 0.66. Bounty Average damage is 0.86. The TIE Fighters win with 4 TIEs left, 12 HP total. Simulating the effect of Howlrunner is harder, but a 7 TIE Swarm with Howlrunner for a round or two should be at least as good as 8 naked TIEs.

Edit: Fixed the values. I accidentally ran it the first time with the BHs having 3 evade. Oops. I thought it looked funny.

Thanks for the clarification! Iknow my differential equations, but this area of application is somewhat new to me, so I'm mostly going by Wikipedia. Apparently, what I've been trying to do is a kind of Salvo Combat Model. When running that with simultaneous shooting, the results also clearly favor the regular Ties.

I've also made a quick attempt at 3 Firesprays vs 8 Academy Ties, which ends after 8 turns with 4 Ties to no surviving Firesprays.

I also tried that approach for 2 HLC Bwings vs 5 Academy Ties. When assuming that the Bwings shoot first every turn, and all actions are taken as offensive focus, I end up with a single Bwing at half HP remaining after 5 turns. This is not 100 points thoug, if the Ties get the firepower to knock out one of the Bs on turn one, that could change the equation.

You still need to know how much average damage each side is going to do to the other, otherwise your inputs are going to be wrong. Speaking of, I had the wrong numbers in the above 8 vs 3 battle. Updating!

Okay, that is very interesting. If I use a (too) simplistic expected damage model with the action used for attack, I get 1.125 per shot for the BH shooting the Tie, and 0.75 the other way around. Meaning my damage ratio is about 2:3, whereas yours is almost 1:2. Any idea where the difference comes from?

OK, I noticed a minor problem with my earlier 10 TIEs vs 3 Defender math. I accidentally had the "Howlrunner" switch on, so all 10 TIEs and all 3 Defenders were getting 1 free reroll each when calculating their average damage. I turned the switch off, and the numbers actually didn't change much: the Defenders relative damage went from 1.9 to 1.9472. (0.8636 vs 0.4435 to be exact).

As a result, the percentage of TIE Fighters that need to NOT have a shot every round, went from 31% to 29.5%. So it's basically still the same result. Just thought I would update in full disclosure.

Put another way, if it's 10 ships vs 4, and the 4 ships have 2x the hit points, then they need to put out 2.78 times the damage, on a per-ship basis, than the TIEs to make it even. THAT much is fact, the only question is whether or not the maneuver dial and other goodies can actually get your Defender squad to that point.

Okay, that is very interesting. If I use a (too) simplistic expected damage model with the action used for attack, I get 1.125 per shot for the BH shooting the Tie, and 0.75 the other way around. Meaning my damage ratio is about 2:3, whereas yours is almost 1:2. Any idea where the difference comes from?

I am calculating a weighted average for all the possible attack vs defense probability density functions. If you're looking at just range 2 shots, for example, you won't get a complete picture. I'm looking at range 1-4 shots, with defensive focus applied 1/2 the time, offensive focus 2/3 the time, and the ranged shots at the ratio observed in the Worlds 2013 Final Match. (numbers earlier in the thread).

That approach looks solid and is definitely more elaborate than what I'm doing, I'm just trying to understand where the shift in relative power comes from. The effect seems a bit much for some adjustments in range and actions that should affect both sides similarly.

Have you ever tried running your model for just specific range bands or action selections? That way one could find the range band/action that favors a specific ship in a given matchup, so you could use the model to evaluate strategy.

In response to the possible 1k turn. I think not. It seems a bit off for them to give it to a ship, when it has not even come out in the aces pack yet. The 1k is what makes Cowell unique. I have a hard time believing they would take away his one of a kind ability before he even has a chance to use it.

Hopefully Aces will be out before Wave 4 lol. Besides, Cowell's ability to change his K-turn distance will still make him unique.

Also, there's still a couple obvious things that aren't considered in the continuous time model:

1. critical hits (affects TIEs more than Defenders, obviously)
2. "wasted" damage from getting extra, unneeded hits against a craft you just destroyed.

#1 Artificially favors the TIEs in the simulation. #2 Artificially favors the Defenders. for example, say you roll 2 hits and then 3 hits. If the target is a TIE Fighter, then the extra 2 hits on the 2nd shot are wasted, so your average damage goes down.

Also, for reference, the "figure of merit" for the 4 ship Defender and 10 ship TIE Fighter squads that come out equivalent are:

TIEs: 10^2*0.31*3 = 93

Defenders: 4^2*0.86*6 = 82.5

So Lanchester's Law underestimates the Defenders by about 12%, because their damage takes 6 hits to get reduced instead of 3. On the other hand, the above simulation is NOT considering point #2 above, so realistically the Defenders would need to have more attack to make up for the slight loss to their average damage.

FYI, if you run 100 TIEs vs 40 Defenders with the above numbers (that's a draw at 10 vs 4) then the TIEs win with ~31 ships left over, since the "large ship bonus" approximates to a continuous function, and the figure of merit is all that matters.

Beautifully stated! An interceptor can easily outmaneuver anything the rebels have. People have this mind set of DMG , much have right away. Take a few turns with your Int and do some maneuvers, focus /evade , hang back , k turn .... Don't worry about shooting them. Just make sure they don't have a shot you. By turn 2 or 3 they will get pissed and make a bad move. Then boost into range one focus and throw 4 dice. Repeat.... Yes yes I know hour time limit. It's all good trust me. Just wait till aces.... 4 pushed RG"s.

I've flown 5 Interceptor squads (as well as 4 Interceptor Squads), I'd say about 16 games so far. I win a bit more than 2 out of 3, loosing mostly to early One-Shot-Kills (all blanks on Def rolls and such). I never won a game with Ints only vs HSF lists. Never. As far as my experience goes, I believe it's not possible unless the dice gods are on your side. Even with only decent rolls on the Rebel side you will most likely loose a ship every turn (as soon as combat starts).

All your maneuverability is nice and looks good when played well, but it's worthless against HSF (or similar builds with gunner, like Chewy+gunner lists). I will definitely play an all-Int list on one of the tournaments here, but I already know that besides all my skill I will quite some luck to make a good rank - and hoping to not face a HSF list.

Only the gunner-enhanced YTs are a problem, Ints do good against everything else (Firesprays - no problem, Y-Wing with turrets - also no problem, same goes for HWK). You simply pay a certain amount of points for something that you can't use (gives you no benefit) vs YT/Turrets, that's the incredible dial of the Interceptor.

The Defender will see similar problems, although you can't OSK it, which has quite some value. I can see Defenders mixed in with some Ints, the defender providing the main pressure on the YT (and such), diverting fire from the more fragile Ints.

Yeah that's my thoughts too, hopefully something to add more strategic depth! It could certainly make its cost balanced as well, if it had enough yellow maneuvers. Time will tell.

The only thing that REALLY absolutely does not make sense is a PS1 Defender, given that "only the Empire’s most elite pilots were allowed to fly the TIE defender". You would think it would be PS2 and PS4.

Think of it as the burden of the ship holding the pilot back. That same PS1 might fly an Interceptor at PS6.

Yeah that's my thoughts too, hopefully something to add more strategic depth! It could certainly make its cost balanced as well, if it had enough yellow maneuvers. Time will tell.

The only thing that REALLY absolutely does not make sense is a PS1 Defender, given that "only the Empire’s most elite pilots were allowed to fly the TIE defender". You would think it would be PS2 and PS4.

Think of it as the burden of the ship holding the pilot back. That same PS1 might fly an Interceptor at PS6.

"only the Empire’s most elite pilots were allowed to fly the TIE defender during the Galatic Civil War" -- FFG

"Imperial High Command decided that defender pilots would only be selected from TIE interceptor pilots who had flown at least twenty combat missions and survived. We're either the best pilots in the Imperial fleet or the luckiest." -- Rexler Brath

It still makes no sense to me from a lore perspective. It does make sense from a Combat Doctrine perspective, where it fits in with the other PS 1/3 dogfighting TIEs.