But was it because your math was correct, or the fact that the Falcon was a popular ship, which is seems to be the main reason not to bring Interceptors.

The only ship I struggle with using Interceptors is the Falcon and only then because of the turret weapon, high PS, Shields and Hull can all be dealt with but the turret when combined with those is a nightmare.

The real issue though is the Falcon is a go to ship in most Rebel tourney lists and in that environment it's a highly risky proposition to risk flying Int's.

I think the Defender will struggle far less with that issue as it can absorb the punishment like no other ship beyond the Firespray, but let's be honest, everything struggles with the named YT's, against all the other ships, I like the Defenders chances.

Maybe its dial bears a white 5 k-turn and a 1 straight.

Together with a HLC it should be possible to get yourself in a position in range 3 of the YT, firing focussed heavy laser bolts.

No need to try to get into range 1.

3 Shield (no crits) and 3 Hull, with 3 evade is a huge amount of survivability. Add to that the yet-unknown maneuver and we have a huge variable that's unaccounted for in simple math. The maneuvers and actions are a massive part of this game.

You know what I have done in the oh so terrible months since the last ships were released? Played the game.

Oh snap.

Just something that occurred to me, and I realize it would be difficult to simulate any way other than what you are doing, but isn't a "lowest pilot skill no upgrades" comparison heavily in favor of the tie fighters considering they are balance around large numbers and no upgrades? Would a match of 8 fighters with the leftover four points spent somehow against three defenders, one with HLC and stealth device change anything? Or three defenders two with autoblaster? Assault missiles? Some combination? I am genuinely curious. 8 points is 2/3s of a tie but it's also an upgrade from a rookie to Wedge.

And, again, that 27 points is "fair" compared to a PS1 Interceptor, which is almost assuredly overpriced to begin with. If a "fair" price for the Interceptor was 17 points, then the "fair cost" of the Defender would be in the range of 17*2.25^0.5 = 25.5, not 27. But the ship costs 30! Unless it can do something like get a free evade every round, I don't ever see it getting used competitively, regardless of its dial. We'll see though.

I'm betting on an evasive manuver that will do just so! Or a title/ept for cheap that does so. Otherwise, hmm... not impressive enough at all...

3 Shield (no crits) and 3 Hull, with 3 evade is a huge amount of survivability.

Actually, I'de be very interested to see the numbers that show how the evade value changes the weight of each point of shield/hull. I have no doubt in my mind that Major Juggler has already run this and collected the data in a neat table. I just haven't seen it in his past posts (most of which I thoroughly enjoy reading). Any ideas?

But was it because your math was correct, or the fact that the Falcon was a popular ship, which is seems to be the main reason not to bring Interceptors.

The two aren't mutually exclusive. Since so much of the Interceptor and A-wing's point cost goes into their maneuverability, a meta game that consistently has turrets will inherently decrease the overall value of those ships. But even if there were no turrets, I don't think either of those ships would see much competitive use.

3 Shield (no crits) and 3 Hull, with 3 evade is a huge amount of survivability. Add to that the yet-unknown maneuver and we have a huge variable that's unaccounted for in simple math. The maneuvers and actions are a massive part of this game.

3 Hull on a basic TIE Fighter at 3 evade.... 3 Hull and 3 Shields on a basic TIE Defender at 3 evade, hm....

3 Hull + 3 Shields > 3 Hull

Hey wait a minute. I see what you did there! You used MATH!

• 5 TIE Interceptors (90 points) have 15 hull vs 3 Defenders with 9 hull and 9 shields.
• 3 E-wings (54 points at PS1) have 4 hull and 6 shields, or 6 hull and 6 shields (60 points) with a hull upgrade.
• 2 Defenders (60 points) have 6 hull and 6 shields.
• 7 A-wings (119 points) have 14 hull and 14 shields vs 4 Defenders (120 points) with 12 hull and 12 shields.
• 3 TIE Advanced (63 points at PS2, equivalent cost of 60 points at PS1) have 9 hull and 6 shields.
• 5 TIE Fighters (60 points) have 15 hull @ 3 agility.

Ha ha, I was trying to lighten the mood, but I am getting the sense that every time Hexis posts here I need to put on my fire resistant suit.

You know what I have done in the last few months? Back to work full time while I am finishing my PhD on the side. I work at Sienar Systems, naturally. I might be able to hook you up with some cheap turbo-lasers or solar panels... shields and hyperdrives are harder to come by.

Actually, I'de be very interested to see the numbers that show how the evade value changes the weight of each point of shield/hull. I have no doubt in my mind that Major Juggler has already run this and collected the data in a neat table. I just haven't seen it in his past posts (most of which I thoroughly enjoy reading). Any ideas?

In this particular case, it doesn't matter since all the ships we are comparing against each other all have 3 agility. So the ships' relative durability directly scales with the number of hull / shields present, with some heavier weighting for shields, obviously.

I have sort of done what you have described. The easiest way to present the data is all the raw data, but that's not as helpful. Getting an aggregate average, based on the kinds of attacks that are typically made is much more useful, but requires some estimates as to what kinds of shots are made during a game, on average.

That being said, it's on my list to make some charts and start a thread for, along with several other similar topics.

• 7 A-wings (119 points) have 14 hull and 14 shields vs 3 Defenders (120 points) with 12 hull and 12 shields.

This should be 4 Defenders then i guess ...

How about a white 5 K-turn, a straight 1, and a red -1 K-turn?

You know what I have done in the oh so terrible months since the last ships were released? Played the game.

Ha ha, I was trying to lighten the mood, but I am getting the sense that every time Hexis posts here I need to put on my fire resistant suit.

You know what I have done in the last few months? Back to work full time while I am finishing my PhD on the side. I work at Sienar Systems, naturally. I might be able to hook you up with some cheap turbo-lasers or solar panels... shields and hyperdrives are harder to come by.

I signed in here for the first time in months to point out that Hexis is right, and you are wrong. You're not the only one working while finishing a Ph.D. (and I have a two-month-old!), but you're the only one who's filled a thread with invalid results proceeding directly from invalid assumptions.

But most fundamentally, of course the Defender can't compete with a TIE swarm. You have to be aware that the TIE Fighter is among the most efficient ships in the game on both offense and defense, with only the Lambda shuttle for real competition (and no question which has the more effective dial). And you've combined that with an estimate of how the Defender would fare against a Howlrunner swarm, which is even worse: Howlrunner is by far the most effective support ship in the game, as well as one of the cheapest.

Frankly, I'd be worried if I thought FFG was engineering new ships to beat a Howlrunner swarm in terms of raw statistical survivability, because that would be evidence of power creep.

Which brings us to the Interceptor comparison, which is still not terribly fair on the merits (since the Interceptor is the most efficient ship on offense in waves 1-3) but is at least fairer. But that comparison leads me to call your simulation into question. As I understand it, you're using a range profile from the 2013 Worlds championship, and assigning focus tokens to a consistent fraction of all rolls. But the action economy doesn't actually work that way, and that alone means your first-approximation estimate is negligible; furthermore, it seems very strange to me to regard the Worlds match as a typical encounter. In fact, there's a solid prima facie case that it's actually highly atypical, since it features two extremely skilled players rather than two typical players (or even typical competitive players).

So in your simulation you ignore the way the action economy actually functions, and you use a range profile that is unlikely to reflect the way most players function, and (to put the final nail in the coffin) you've done so while we still don't know anything about the TIE Defender's dial or named pilots.

You might possibly make this case after the Defender is released (or completely spoiled), but trying to do so now--based on incomplete information, and based on comparisons that are as unflattering as possible to an expensive ship aiming for balance between offense and defense--is certainly a mistake.

• 7 A-wings (119 points) have 14 hull and 14 shields vs 3 Defenders (120 points) with 12 hull and 12 shields.

This should be 4 Defenders then i guess ...

How about a white 5 K-turn, a straight 1, and a red -1 K-turn?

Oops, yes, 4 Defenders. Fixing that typo now, good catch.

I signed in here for the first time in months to point out that Hexis is right, and you are wrong. You're not the only one working while finishing a Ph.D. (and I have a two-month-old!), but you're the only one who's filled a thread with invalid results proceeding directly from invalid assumptions.

First off, thank you for posting! It's folks like you that have well thought out comments that helps make the X-wing community so great. It really is a pleasure for you to join in the dialogue, even if we seem to have differing opinions. And congratulations on your 2 month old! Awesome!

Now, allow me to respond to your main points.

The PS1 TIE Fighter (and now the PS2 Z-95 Headhunter) certainly are the most point efficient ships, with everything else coming in behind them. So yeah, we are in agreement on that part. I certainly also agree that there shouldn't be power creep, and that if a ship's base stats allowed it to beat a a Howlrunner swarm consistently, then that would be horribly broken. In fact, I will actually go one step further than you. I would replace "Howlrunner" with TIE Fighter" in your comment:

I'd be worried if I thought FFG was engineering new ships to beat a TIE Fighter swarm in terms of raw statistical survivability, because that would be evidence of power creep.

Perspective #4

All of the above numbers assume that Howlrunner doesn't exist. If you compare 2 dice with 1 reroll vs 3 dice, the 3 dice advantage is reduced to around 1.2-1.25. So a squad of 7 TIE Fighters including Howlrunner is going to make the Defenders look pathetically outclassed. This might be a biased comparison because a 7-TIE Swarm is undeniably one of the best (if not the best) squads in the game, but it is the standard by which other competitive squads are measured against.

Next point.

Which brings us to the Interceptor comparison, which is still not terribly fair on the merits (since the Interceptor is the most efficient ship on offense in waves 1-3) but is at least fairer.

Since all the ships are fundamentally different, it is indeed difficult to directly compare many of the ships to each other. We have at least 5 basic categories in which every base ship differs:

1. number of attack dice
2. number of defense dice
3. hull and shields
4. available actions
5. potential upgrades

The first 3 can be directly statistically compared. The last 2 cannot. Since a ship's actual in-game attack output and damage intake are highly dependent on the how many attack dice and defense dice it has respectively, the best comparison is to compare the 3/3/3/3 Defender with a 3/3/X/X ship. It is possible to compare it directly to, say, a 2/3/3/0 TIE Fighter, but the margin for error is much higher since you have to estimate how effective the 3rd attack dice is. So the TIE Interceptor seems to be the best comparison available. If you have another suggestion I am all ears.

The TIE Interceptor certainly has the most damage output per points spent through wave 1-3. 2 TIE Interceptors have slightly more damage output than 3 TIE Fighters, excluding the effects of Howlrunner. But, I fail to see why the comparison is "still not terribly fair on the merits". Please offer a rationale on why you believe this to be the case, because the counter point, which you have completely avoided, is that this is inherently considered in the N^2*A*D Lanchester's Figure of Merit, and it is also in the continuous time simulation.

This is a very good point. The inputs that I have been using to the Lanchester's Figure of Merit, and the continuous time simulation, both assume that 3 dice will do 1.9x the damage of 2 dice. I have greatly simplified the action economy, to having focus 2/3 the time on attack and defense 1/2 the time. It's not intended as an exact measure, but I think it is a pretty good start. As my adviser says,

"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.

(highlighted for emphasis)

Which comparisons am I making that are as unflattering as possible for just the TIE Defender, when I am using the same exact approach for all the ships? Again, hit points vs cost is inherently considered in both Lanchester's and the continuous time simulation, so your concerns that the approach doesn't scale for expensive ships is unfounded.

The only real "variable" into the above equations is the expected attack damage. When I first calculated this, I weighed the ranges as 25%, 50%, 25% for ranges 1-3, and equally weighed the probability of shooting at ships with 1, 2, and 3 defense dice.

Without any rerolls (i.e. Howlrunner, target lock action stacking), the mean damages are 1.2066 for 3 attack dice, and 0.6851 for 2 attack dice, for a ratio of 1.76. If we use the World's Final 2013 match to get the range results instead (but still using 1,2,3 defense dice equally weighted), we get mean damages of 1.2122 for 3 attack dice, and 0.6964 for 2 attack dice, for a ratio of 1.7405.

But then I also looked at a few specific matchups: for example, if you know that the target has 3 defense dice, and you use the Worlds range, then the mean damages are 0.8636 for 3 attack dice, and 0.4435 for 2 attack dice, for a ratio of 1.95.

So, by using a ratio of 1.9, I actually used a number that is actually very close to the best possible matchup for the TIE Defender, not the average ratio of ~1.75. I then proceeded to use that assumption for ALL of the numerical analysis in this thread. So, ironically, your last point about giving the Defender an unfair disadvantage is exactly opposite: if anything, I gave it an unfair advantage!

In summary, my basic premise is this:

The TIE Defender is going to need a REALLY good dial and / or an easy way to get evade tokens in order to be balanced relative to the other tier 1 ships.

You believe that this prediction is based on invalid assumptions. I have read and replied to your entire comment, looking for a single legitimate example of an invalid assumption in my methodology, because, as I stated in the OP, I would very much like to be wrong. The Defender is, after all, an awesome craft. Sadly, I couldn't find anything.

Again, I don't mean to make it personal or anything, it's simply the raw data and assumptions that go with it - and if anything I would like you to be right! So please feel free to continue to offer feedback. I don't want to scare you away from posting on the forums for another few months, but if you're busy nowadays and just lurk occasionally, working on that PhD while keeping up with your 2 month old, then I totally understand.

Wouldn't the Salvo Combat Model be more appropriate than the Lanchester Laws? Lanchester Laws tend to discount the ability to intercept or evade ordinance and also were meant to show statistics on high volume, low damage attacks like bullets from in land battles. After having a discussion with one of my more mathematically inclined friends, he pointed out that the Salvo Combat model is used in modern navies because missiles are fired in low quantity, highly accurate missiles attacks, and include the ability to intercept them.

It seems to me that the Salvo Model may be more appropriate because we have such a low volume of accurate attacks (especially with focus or TL) from a ships that can be discounted through evasion (in effect working like shots being intercepted). The problem of course is that I tend to go cross eyed when numbers are involved so I'm just providing this statement as food for thought.

Wouldn't the Salvo Combat Model be more appropriate than the Lanchester Laws? Lanchester Laws tend to discount the ability to intercept or evade ordinance and also were meant to show statistics on high volume, low damage attacks like bullets from in land battles. After having a discussion with one of my more mathematically inclined friends, he pointed out that the Salvo Combat model is used in modern navies because missiles are fired in low quantity, highly accurate missiles attacks, and include the ability to intercept them.

It seems to me that the Salvo Model may be more appropriate because we have such a low volume of accurate attacks (especially with focus or TL) from a ships that can be discounted through evasion (in effect working like shots being intercepted). The problem of course is that I tend to go cross eyed when numbers are involved so I'm just providing this statement as food for thought.

This is very true, and if you go back a couple pages you'll see where I said that a better method would be to calculate the per-attack probability density functions, a.k.a. the Salvo Model but using distributions rather than average damage numbers.

The continuous time model that I put together in Excel basically ends up agreeing with Lanchester's, but gives larger hit point ships an "buff" for staying alive longer and retaining their damage output the entire time. Lanchester's assumes piece wise small changes which allow for the application of differential equations, and resulting derivation of N^2*A*D.

I'm going to assume that the numbers back you up, it just seems odd to me that the Salvo Model as explained to me would give more of an impact to a ship that can discount a large number of hits...cause math?

I'm going to assume that the numbers back you up, it just seems odd to me that the Salvo Model as explained to me would give more of an impact to a ship that can discount a large number of hits...cause math?

Well, I haven't built a Salvo Model for X-wing yet, so I couldn't say either way.

But so far, every way that it has been looked at so far, either by Lanchester's, or by continuous time simulation, or other less formal comparisons, they all point to the TIE Defender being pretty well overcosted, even compared to other highly maneuverable ships.

Also, what I had in mind on the loop maneuver was, as others have discussed elsewhere, a red maneuver that moves you backwards 1 without changing your heading. If you collide and cannot complete the maneuver, then you rotate your ship 180 degrees, and back it up until it collides.

If it has a red 1 loop, a couple of white K-turns, and a ton of green for everywhere else, then that would help yank it back towards being balanced. Add in a cheap way to get an evade and it could be competitive. It would still be overcosted against turret builds, but that isn't inherently a bad thing, it just means the game has a good core paper/rock/scissors approach.

Looking at some of your analysis, I do see some issue. Mainly with how you were describing the E-wing. You are giving it points for Sensors, but not Astromech. We have 2-3 Astromechs with the Transport, along with the 2 in the E-wing. And if any of them are anywhere close to how good R7-T1 is, I'm thinking having an Astromech slot may be slightly better than a Sensor spot.

Also, the fact that you don't have the dial's there as a 6th factor of comparison, seems to be a rather important thing to not to take into consideration. What maneuvers are red, white, and green, and what actual maneuvers they have, is a rather important figure.

And the Defender will do much better than the high point Interceptors will against Turrets. Why, because the Falcon can't kill one in one shot.

Looking at some of your analysis, I do see some issue. Mainly with how you were describing the E-wing. You are giving it points for Sensors, but not Astromech. We have 2-3 Astromechs with the Transport, along with the 2 in the E-wing. And if any of them are anywhere close to how good R7-T1 is, I'm thinking having an Astromech slot may be slightly better than a Sensor spot.

Also, the fact that you don't have the dial's there as a 6th factor of comparison, seems to be a rather important thing to not to take into consideration. What maneuvers are red, white, and green, and what actual maneuvers they have, is a rather important figure.

And the Defender will do much better than the high point Interceptors will against Turrets. Why, because the Falcon can't kill one in one shot.

Actually, I didn't consider ANY upgrades for ANY of the ships. I verbally listed Advanced Sensors on the E-wing as an advantage over the TIE-Defender, but you're right, Astromech upgrades count too!

It doesn't change any of the baseline "Figure of Merit" numbers though. If you look at how the Figure of Merits were calculated, it should be obvious.

Re: dial - it's noted as obviously being of critical importance, but not calculated - see here.

Since all the ships are fundamentally different, it is indeed difficult to directly compare many of the ships to each other. We have at least 5 basic categories in which every base ship differs:

1. number of attack dice
2. number of defense dice
3. hull and shields
4. available actions
5. potential upgrades

The first 3 can be directly statistically compared. The last 2 cannot. Since a ship's actual in-game attack output and damage intake are highly dependent on the how many attack dice and defense dice it has respectively, the best comparison is to compare the 3/3/3/3 Defender with a 3/3/X/X ship. It is possible to compare it directly to, say, a 2/3/3/0 TIE Fighter, but the margin for error is much higher since you have to estimate how effective the 3rd attack dice is. So the TIE Interceptor seems to be the best comparison available. If you have another suggestion I am all ears.

There's no magic formula to translate the dial into direct points cost, I'm not claiming that I did nor should I try - rather the Figure of Merits are the baseline numbers from the first 3 items that CAN be measured statistically. From there, you have to figure out how much it's worth to have a better dial.

What you CAN do, is figure out how much more efficient you have to be with a better dial to get your points back that you spent on it.

For example, if you can make 30% of the TIEs have no shot every round, then their Figure of Merit gets multiplied by 0.7, so they're down to 70, which is about on par with the TIE Defenders (low to mid 60's, depending if you count their attack as 1.75x or 1.9x better than 2 dice). Not coincidentally, if you change the "attack coefficient" in the continuous time model, you arrive at the same conclusion: you need to make the TIEs have no shot 30% of the time to break even with them.

Here's another way to put it in perspective:

• The TIE Fighter has a better FoM than the TIE Interceptor by about 28% (conservatively, if we use the 1.75x attack number for 3 dice vs 2 dice)
• The TIE Interceptor has a better FoM than the TIE Defender by about 24%.
• Therefore, the TIE Defender needs to be able to outmaneuver the TIE Interceptor by about the equivalent amount that the TIE Interceptor can outmaneuver the TIE Fighter.

Think about that last point for a moment. Now look at the TIE Defender dial: it has no boost action. So unless the TIE Defender is getting some 135 degree green/white turns, and/or white K-turns, that is going to be VERY difficult to accomplish.

Your last point is the most interesting one: low PS Defenders will be able to get shots off for 2-3 rounds against Turrets whereas low PS Interceptors will only get to fire 0-1 rounds. What this ignores, however, is that there will be multiple Interceptors for every Defender, so even if one Interceptor gets one-hit, the other Interceptors still do damage. In the most straightforward example, 5 Interceptors compared to 3 Defenders, if 3 damage is done, then it's 4 Interceptors firing vs 3 Defenders firing, or if 6+ damage is done its 3 Interceptors vs 2 Defenders firing.

In this example, which is the absolute worst-case nightmare scenario for the Interceptors, the Defenders will hopefully do better. So, that's a silver lining at least.

I'd be curious how the TIE Phantom would come out in your analysis. Obviously the cloak action will mess with things a lot, but I'm curious about how well costed it is.

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.

I'd be curious how the TIE Phantom would come out in your analysis. Obviously the cloak action will mess with things a lot, but I'm curious about how well costed it is.

Good question. First we need to figure out how much damage 4 attack dice do.

Using Worlds Finals ranges and equally weighted defense dice of 1, 2, and 3, we get an average damage of:

2 dice: 0.6964, normalized = 1

3 dice: 1.2122, normalized = 1.74

4 dice: 1.7966, normalized = 2.58

Using only targets with 3 defense dice, we get:

2 dice: 0.4435, normalized = 1

3 dice: 0.8636, normalized = 1.94

4 dice: 1.3861, normalized = 3.12

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.

First off, Major Juggler, old egghead and E-Wing lover, I think you are of great value to this forum and the X-Wing community.

In this case it depends on the dial (a white k-turn would make a big difference) ... and if the PS3 pilots have an EPT - just like the A-Wing PS3 pilots.

If the PS3 pilots could use Veteran Instincts, Adrenaline Rush, Deadeye (together with a homing), or be able to chaingang a high PS with swarm tactics, the whole Defender line would be put a good step in direction to the competitivity we want to have.

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.

Thanks for running the math for me! I'm pretty sure that's 25 points for the PS 3 Phantom. Which also would bring up the hard-to-include factor of: you can run 4 naked Phantoms, but your 3 defender list is going to have upgrades which aren't accounted for.