So, I finally decided to bite the bullet and go through the math on how good Luke's ability is. Since a result of EFF (Evade Focus Focus) is the same as EEB as well as EFB, it's much more complicated than all of the other results.

So, rolling 2 evade dice without a focus results in .75 evades. With a focus, this is increased to 1.25, but you can only have 1 focus action (though you can get up to 3 focus tokens). Luke's ability grants him 1.19 evade, almost as good as the focus action. But lets take it a step further - how survivable can you make Luke?

If you give him R2-F2 and a Stealth, he is rolling 4 Evade dice, but his action is spent on R2-F2. This results in an average of 2.18 Evades being rolled. When the Stealth is finally stripped, he is down to 1.70 with just R2-F2. This compares to 1.50 and 1.13 for a standard X wing. Which means that Luke's ability gives him around 50% more evades than a standard X wing. While this number varies depending on number of dice, it ranges from 36% at 6 dice to 67% at 1 die.

So that's all fine and good. 50% additional evasion is great. When you look at the effective health of an X wing, which is the total health (hull+shields) divided by the expected damage received per attack, Luke has almost twice as much effective health.

X Wing effective health vs. 2 attack dice = 9.8
Luke effective health vs. 2 attack dice = 18.2
X Wing effective health vs. 3 attack dice = 5.7

Luke effective health vs. 3 attack dice = 8.6

X Wing effective health vs. 4 attack dice = 3.8

Luke effective health vs. 4 attack dice = 5.2

So... now we have a baseline to measure his ability. Let's compare it to taking an extra shield. If we ignore the +4 PS, a Red squadron w/ Shield upgrade is 27 points, and Luke is 28 points (but has 4 extra PS). Close enough for a comparison.

X Wing w/ Shield vs. 2 = 11.8

X Wing w/ Shield vs. 3 = 6.8

X Wing w/ Shield vs. 4 = 4.5

From this, it's very easy to determine that if you are debating between an X wing with a shield or Luke, if you have the 28 points to fit him into your build, you should. The follow up question then becomes do you put a shield or stealth on Luke? And what about R2-F2 or R2-D2?

A Shield increases his effective health to:

vs. 2 attack = 21.9

vs. 3 attack = 10.3

vs. 4 attack = 6.2

Which basically averages out to making him live through an additional two attacks. R2-F2 increases his effective health to:

vs. 2 attack = 35.7

vs. 3 attack = 14.2

vs. 4 attack = 7.7

If we do some fuzzy math, we can come to the conclusion that it will take 7 2 dice attacks , 3 3 dice attacks, and ~1.5 4 dice attacks to strip the stealth device. So then the stealth device provides the follow approximate effective health:

vs. 2 attack = 21.6

vs. 3 attack = 9.8

vs. 4 attack = 5.6

It would seem that by itself, the shield is still better on Luke than the stealth device. As for R2-D2 vs. R2-F2... each shield R2 regenerates tachs on 3.6/1.7/1.0 attacks from 2/3/4 dice. Which means that R2-D2 vs. R2-F2 is very dependent on what's attacking you... against 4 dice, if you regenerate 1 shield, you're already ahead. But against 2 dice attacks, it'll take 6 shields to match up. Don't forget that R2-F2 requires an action, and R2-D2 requires a green maneuver, each has it's own drawback.

But what about the ultimate dodging X wing in Luke + R2-F2 + Stealth? With 4 evade dice, Luke's effective health is 68.7/23.5/11.5. Which means it'll take ~13/5/2.4 hits to strip the evade die. Which means the fuzzy math puts his effective health at:

vs. 2 attack = 41

vs. 3 attack = 16.4

vs. 4 attack = 8.5

But this STILL comes up short compared to R2-F2 w/ Shield, which puts his effective health at:

vs. 2 attack = 42.8

vs. 3 attack = 17.0

vs. 4 attack = 9.2

So, what conclusions can be drawn from this? First off, the only ship that has more effective health than Luke is the Firespray (I didn't compare the other ships here, but it's true) Second off, for a pure point value point of view, it's better to take Luke over an X wing with a Shield. Third, the stealth device isn't quite as good as a shield, but only costs 3 points, so point for point it is better than a shield on Luke. Finally, R2-D2 is the better choice than R2-F2 against everything but swarms, though that doesn't take into account the positioning / predictability of the ship, or the loss of an action.

tl:dr - Luke is the best X wing due to his much greater defenses. He will live through twice as many shots as Wedge, which means he'll be around at least twice as long as Wedge, and therefore can do more damage in the long run.

Luke is so good. Kind of, the best. I always take him. I took wedge over Luke once and regretted it. Both is good too.

Good research, nice to see some numbers crunched without doing a ton of work myself . This just confirms how survivable he is.

Usually I don't fly him, but against him (being a biased Imp player). Thus the one addition I would add for the majority of the time, you want to add offensive upgrades to Luke, or at least upgrades that don't sacrifice damage. Thus I would usually want R2-D2 instead of R2-F2 (since losing a focus or TL action is too big of a loss of damage output). But you may not even need that, and go with no astromech, or the standard R2. If the enemy is shooting at Luke first, then you probably have a big advantage already.

In too much of a rush to processs all the math posted but Luke's ability gets better the more times a round someone attacks him though the simple fact of him being able to save his focus and even after he spends it he has a "semi-focus". He's awesome.

I kind of want a master-list of every ship in the game with this type of survivability analysis.


I CAN tell you that if you're dealing with 4 or more agility dice, Focusing becomes a better option than Evading. 3 or fewer, Evade is the better action, assuming you do not care for offense.
I have not yet done the math for barrel-rolling / boosting into a more distant Range or behind an obstruction, but barrel-rolling / boosting into a position where none may shoot you is clearly the best defensive action in the game.

I kind of want a master-list of every ship in the game with this type of survivability analysis.

I CAN tell you that if you're dealing with 4 or more agility dice, Focusing becomes a better option than Evading. 3 or fewer, Evade is the better action, assuming you do not care for offense.

I have not yet done the math for barrel-rolling / boosting into a more distant Range or behind an obstruction, but barrel-rolling / boosting into a position where none may shoot you is clearly the best defensive action in the game.

Mostly true. At 3 Evade dice, using the evade action produces 3.12 evades, while focus only produces 1.88. Clearly evade is the better option from a math point of view (though it could be contested that if you're going to be getting shot at multiple times, it would be better to wait for two focuses to turn up and then use it then to dodge 2 damage). At 4 dice, they're 2.50 and 2.50 both, so at this point they're mathematically equal. Depending on how many times you're being shot at might determine your action as focus gets better the more times you're rolling (increasing the probability that you roll a multi-focus roll and therefore dodge 2+ via focus instead of just the 1 via Evade). At 5 dice, Focus puts out 3.13 evades, while evade only averages 2.88, clearly making Focus the better action.

As far as a master list, I've essentially put one together for the permutations of # of attack / defense dice, and actions, for both average hits/evades rolled, and expected damage. But Luke required quite a bit of more work since a single focus counts as an evade, but the rest count as blanks. I'm also thinking about adding in capt Jonus / Howlrunner / Krassis (which should be the same math as howlrunner) abilities to see how much they actually help out.

I suppose I could post my spreadsheet up somewhere, but I don't really know where.

I kind of want a master-list of every ship in the game with this type of survivability analysis.

I CAN tell you that if you're dealing with 4 or more agility dice, Focusing becomes a better option than Evading. 3 or fewer, Evade is the better action, assuming you do not care for offense.

I have not yet done the math for barrel-rolling / boosting into a more distant Range or behind an obstruction, but barrel-rolling / boosting into a position where none may shoot you is clearly the best defensive action in the game.

Mostly true. At 3 Evade dice, using the evade action produces 3.12 evades, while focus only produces 1.88. Clearly evade is the better option from a math point of view (though it could be contested that if you're going to be getting shot at multiple times, it would be better to wait for two focuses to turn up and then use it then to dodge 2 damage). At 4 dice, they're 2.50 and 2.50 both, so at this point they're mathematically equal. Depending on how many times you're being shot at might determine your action as focus gets better the more times you're rolling (increasing the probability that you roll a multi-focus roll and therefore dodge 2+ via focus instead of just the 1 via Evade). At 5 dice, Focus puts out 3.13 evades, while evade only averages 2.88, clearly making Focus the better action.

As far as a master list, I've essentially put one together for the permutations of # of attack / defense dice, and actions, for both average hits/evades rolled, and expected damage. But Luke required quite a bit of more work since a single focus counts as an evade, but the rest count as blanks. I'm also thinking about adding in capt Jonus / Howlrunner / Krassis (which should be the same math as howlrunner) abilities to see how much they actually help out.

I suppose I could post my spreadsheet up somewhere, but I don't really know where.

At 4 dice, Focus gives you a better shot at dodging specifically 2, 3, and 4 damage (in a bell-curve that maxes at a 5% difference of dodging 3 hits). The Evade is the only one with a shot at dodging 5 damage, and cannot be hit by only the 1 damage, so I feel that Focus does more work there.

I kind of want a master-list of every ship in the game with this type of survivability analysis.

I CAN tell you that if you're dealing with 4 or more agility dice, Focusing becomes a better option than Evading. 3 or fewer, Evade is the better action, assuming you do not care for offense.

I have not yet done the math for barrel-rolling / boosting into a more distant Range or behind an obstruction, but barrel-rolling / boosting into a position where none may shoot you is clearly the best defensive action in the game.

Mostly true. At 3 Evade dice, using the evade action produces 3.12 evades, while focus only produces 1.88. Clearly evade is the better option from a math point of view (though it could be contested that if you're going to be getting shot at multiple times, it would be better to wait for two focuses to turn up and then use it then to dodge 2 damage). At 4 dice, they're 2.50 and 2.50 both, so at this point they're mathematically equal. Depending on how many times you're being shot at might determine your action as focus gets better the more times you're rolling (increasing the probability that you roll a multi-focus roll and therefore dodge 2+ via focus instead of just the 1 via Evade). At 5 dice, Focus puts out 3.13 evades, while evade only averages 2.88, clearly making Focus the better action.

As far as a master list, I've essentially put one together for the permutations of # of attack / defense dice, and actions, for both average hits/evades rolled, and expected damage. But Luke required quite a bit of more work since a single focus counts as an evade, but the rest count as blanks. I'm also thinking about adding in capt Jonus / Howlrunner / Krassis (which should be the same math as howlrunner) abilities to see how much they actually help out.

I suppose I could post my spreadsheet up somewhere, but I don't really know where.

At 4 dice, Focus gives you a better shot at dodging specifically 2, 3, and 4 damage (in a bell-curve that maxes at a 5% difference of dodging 3 hits). The Evade is the only one with a shot at dodging 5 damage, and cannot be hit by only the 1 damage, so I feel that Focus does more work there.

2 Focused attack vs. 4 Focused defense = .10 estimated damage

2 Focused attack vs. 4 Evaded defense = .09 estimated damage

3 Focused attack vs. 4 Focused defense = .35 estimated damage

3 Focused attack vs. 4 Evaded defense = .35 estimated damage

4 Focused attack vs. 4 Focused defense = .79 estimated damage

4 Focused attack vs. 4 Evaded defense = .80 estimated damage

This is taking into account all the permutations of the attacker rolling 0 hits from his 4 dice and the defender rolling 4 evades (which is still 0 damage) all the way to the attacker rolling 4 hits and the defender rolling 0 evades. As you can see, mathematically there really isn't a difference between the two. But as I said earlier, the more people shooting at you, the better the chances of the single focus token canceling two hits become. I don't have the full math as far as when will you roll 2+ focuses when you need them, but the odds of rolling 2+ focuses with 4 evade dice is 15%. If 4 or more people are shooting you, there's a 50% chance that at least once you will roll more than 2 focuses. And that roll may come on an attackers' whiff.

So, since the estimated damage comes out to be the same, that must mean that if you have a 15% chance of rolling two focuses, then there's a 85% chance that you'll roll 1 or none (Specifically, 32% of none, 53% of 1). So your focus is still a gamble, whereas the evade is a sure thing.

I kind of want a master-list of every ship in the game with this type of survivability analysis.

I'll add it to my to-do list. No guarantees when I'll get around to it, I have a dissertation to write first.

Actually, it would probably only take around an hour since I already have all the hooks set up in my scripts to do focus fire probability density functions.

Stupid question, anyone know how to upload images to this site? Or do I have to link to them on an externally hosted site? I have a bunch of figures (tiffs, usually a couple hundred KB per) that my scripts generate.

Great analysis! I just checked all your numbers from your first post with my own scripts and they matched, up to the fuzzy math part about knocking out stealth device.

Well, you had one minor typo: X-Wing vs 3 = 6.8 should be 6.7 (6.6928...). I think I'll let that slide though.

Seriously though, great work. I haven't seen anyone else do this level of analysis before, outside my own scripts.

You should also include the results of an enemy with X dice focusing too. I would say that at least half the time, ships fire with focus, so it is another important data point. Here are the exact PDFs including "SuperLuke" with 4 evade dice:

The stealth device case is interesting. Lets look at that with non-fuzzy math. Summary of SuperLuke's damage PDF:

0 hits 1+ hits 2+ hits 3+ hits 4 hits

93.2 6.78 0.494 SuperLuke damage from 2 dice, 0 attack focus, 0.0728 avg damage

I didn't include results from 1 free reroll from Howlrunner, which would result in another set of data points.

Thanks for confirming my math there. Yeah, I have the Focus and F+TL data on my own spreadsheet but I didn't feel like typing it all out into here. Sorry bout the typo But anyways, the trend continues as you add Focus into the attacker equation, and Howlrunner, and Krassis and F+TL and F+TL+Expose, but the overall ratio of how much harder is it to kill Luke vs. these others doesn't really change much. Actually, it goes up when you add in F+TL over just F. Luke's ratio of "survivability" over a regular X wing ranges from 1.85 (2attack) down to 1.23 (4F attack), with the average at 1.52, meaning he's 52% harder to kill.

The way I did my "fuzzy math" was to give Luke the stealth device and calculate out how many attacks it would take to kill him. Divide that by 5 to account for 1 hit, which strips the stealth device. And then add that to how many attacks it would take to kill Luke without a stealth device, multiplied by .8 to account for his 4 remaining health after the stealth was stripped. I realize that this isn't really accurate, as the stealth can be stripped on the first turn, or can last for the entire game, but the fuzzy math should give a ballpark idea of which to take. Personally I'm not a big fan of stealth on ships that can't evade (or maybe it's that I'm not a big fan of stealth on ships with only 2 defense dice).

I suppose I could post my spreadsheet up somewhere, but I don't really know where.

the best way would be to make it into a google doc in drive.google.com and then sharing it with everyone via a link here. if you need you can email me the spreadsheet & I'll do it for you or host it on my website. I love this stuff and I find it really interesting. thanks for the work!!

Thanks for confirming my math there. Yeah, I have the Focus and F+TL data on my own spreadsheet but I didn't feel like typing it all out into here. Sorry bout the typo But anyways, the trend continues as you add Focus into the attacker equation, and Howlrunner, and Krassis and F+TL and F+TL+Expose, but the overall ratio of how much harder is it to kill Luke vs. these others doesn't really change much. Actually, it goes up when you add in F+TL over just F. Luke's ratio of "survivability" over a regular X wing ranges from 1.85 (2attack) down to 1.23 (4F attack), with the average at 1.52, meaning he's 52% harder to kill.

The way I did my "fuzzy math" was to give Luke the stealth device and calculate out how many attacks it would take to kill him. Divide that by 5 to account for 1 hit, which strips the stealth device. And then add that to how many attacks it would take to kill Luke without a stealth device, multiplied by .8 to account for his 4 remaining health after the stealth was stripped. I realize that this isn't really accurate, as the stealth can be stripped on the first turn, or can last for the entire game, but the fuzzy math should give a ballpark idea of which to take. Personally I'm not a big fan of stealth on ships that can't evade (or maybe it's that I'm not a big fan of stealth on ships with only 2 defense dice).

No problem. Fuzzy math would be slightly more accurate if you used the probabilities above, just assume that you lose the stealth device at the ~50% mark and go from there.

At some point soon, I'll update my "FocusFire" script to account for keeping or losing Stealth Device across multiple attacks, and can report the exact results here. I already do this with focus, where the results get tabulated in a 2 dimensional matrix, one axis for hits and one axis for focus tokens remaining. I can add Stealth Device without adding another axis, since the 1+ hits means the device is gone. I'll just have to add one more dimension for evade tokens, although it doesn't matter for this case.

Wow, really impressive stuff! Thanks for going through the work to put this together.