Profile photo of Klutz By Klutz On March 17, 2014 Posted In X-Wing Miniatures Game

Focus, Evade, R2-F2 and multiple attacks

Profile photo of Klutz
March 17, 2014
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I was looking to build a list using Biggs, and was wondering if R2-F2 was a worthwhile droid for him. I found a couple articles discussing the subject, but none of them had the mathematical depth I wanted, nor did they consider the number of attacks that would be directed at your ship. So I pulled out some python and set about to simulate the results!

So, these are the variables we will be considering:

  • Your ship’s base agility
  • Number of attacks it will be suffering this round
  • It’s action (nothing, focus, evade or R2-F2)

If your ship has 1 agility

A forgone conclusion is that an evade token is always better than a focus (from the purely defensive standpoint this article adopts). R2-F2 is also always better than focus. But, is Evade or R2-F2 better? Turns out it depends on how many times you’re going to get attacked – and the tipping point is between 2 and 3 attacks.

Only getting attacked twice? Take an evade. Getting shot at 3 or more times? Go for R2-F2.

If your ship has 2 agility

This is the scenario which started me on the path to this short article: Biggs has 2 agility.

As when we were rolling a single defense die, an evade is better than a focus [technically, if you’re getting shot at 4 times, an evade will squeeze out 0.03 extra evades]. Choosing between focus and R2-F2 (if you don’t have an evade action) or an evade and R2-F2 is a little more complicated – and depends on how many attacks will be directed your way. Once again, R2-F2 shines if you’re getting shot at 3+ times!

If you’re getting attacked twice, take an evade (or a focus). If you’re getting attacked more than twice, use R2-F2.

If your ship has 3 agility

This is the scenario we’re aiming to put Biggs in: in multiple firing arcs, at range 3.

Here’s what you should prioritize, depending on how many times you’re getting shot at:

  • If you’re getting shot at once: evade, focus, then R2-F2.
  • If you’re getting shot at twice: focus, evade, then R2-F2.
  • If you’re getting shot at three times: focus, R2-F2, then evade.
  • If you’re getting shot at four times or more: R2-F2, focus, then evade.

If your ship has 4 agility

Surprisingly (at least, I find), Focus is better option than evade or R2-F2 up to 4 attacks against you. At 4 attacks against you, Focus and R2-F2 are pretty much equivalent. At 5+ enemies shooting at you, R2-F2 comes out on top.

What if you can transfer over a focus, or take 2 actions?

Simply put, using R2-F2 and a having a Focus token is always better than having 2 Focus tokens.

Conclusion?

I think R2-F2 is worth it on Biggs and that it’s a better droid for him than R2-D2. Why? Two reasons:

  1. It doesn’t require a green maneuver so you’re more maneuverable.
  2. It cancels hits instead of replenishing them during the activation phase. This means you are more likely to survive for another round. Which means that’s one more round where your opponent’s high-PS ships will be firing at Biggs. Every time Biggs with R2-F2 ends a round with 1 hull point left, he’s likely to have died if you had chosen R2-D2!
  3. Bonus: It’s cheaper by 1 point!

Note: All the calculations for Focus tokens are considering that you spend the eyeball on your first defense roll with at least 1 eyeball.

You could, of course, hold on to your token and maybe use it on a roll with more eyeballs. However, even if you manage to use the focus token on your defense roll with the most eyeball results, the results are only slightly better. Even looking at a scenario where you’re rolling 3 evade dice and getting attacked 4 times this round, the difference is only so that you’ll be getting, on average, 0.25 more evades by timing your token’s use perfectly!

I’d therefore always recommend spending your focus token as soon as possible for defense.

Note: The averages for no-action, evade and R2-F2 were computed precisely (using a binominal distribution). On the other had, the results for focus are averages of 500,000 simulated die rolls.

    1. I’ve added in the data for dual Focus tokens and Focus + R2-F2. R2-F2 and a Focus token is easily the best-case scenario!

      Stealth device doesn’t really come into the equation here, as I’m simply comparing what actions are better – supposing you put R2-F2 on your ship. If you’re going to put Stealth Device on him, I’d say R2-F2 is an easy choice if you want a droid – MUCH better than R2-D2 in this case.

      However, if you’re looking into using either Stealth Device OR R2-F2, then the analysis is much more involved – you need to start looking at how many attacks you can evade before taking damage and losing Stealth Device, which will depend on your opponent’s attack value, focus/TL, etc… Too many variables to get a complete picture if you ask me.

      Just you your gut feeling/experience. Or the force. Just use the force.

      Personally, I feel that putting both R2-F2 and Stealth Device on Biggs might be putting too many points into a ship that is doomed to die.

      In a tournament setting, if you only lose Biggs with R2-F2, that’s 28 points. If you’re up against a TIE swarm you just need to take out an Academy Pilot and Howlrunner for 30 points to win 😛

  1. It may also be worthwhile to extend the math beyond Agility 3. Range 3, stealth, rocks in the way and R2-F2 can bring him up to 6 green dice :)

    Somewhat related note: had Biggs soak fire from 8 TIE fighters the other day and live thanks to R2-F2. Survived I think three attacks after being reduced to his final hull point… twas glorious. Could have been better if Garven hadn’t clipped a rock by a hair’s width that turn… no focus to share as a result.

    1. I added the data for 4 agility!

      I don’t think I’ll be going higher seeing as Focus just becomes more and more interesting.

      ALTHOUGH, just thought of this…

      If you’re rolling 4 defense dice and being targeted by 3 other ships, yes focus will allow you to roll a higher TOTAL number of evades (on average) – BUT rolling 4 evades against a 2 or 3 die attack is useless. Maybe R2-F2 is better since he helps you on every die roll, and might increase your average USEFUL evades per roll.

      Hmmm… Food for thought…

  2. I noticed that with your tables, you have added the Focus defense boon to the first shot at you. This makes for an inaccurate comparison to R2-F2, because the odds of getting to spend your Focus on the first shot are not 100%.

    A single Focus would be a spread potential boon over 4 attacks:

    AGI 1 >> (.25), (.25 x .75), (.25 x .75^2), (.25 x .75^3)
    AGI 2 >> (.44), (.44 x .56), (.44 x .56^2), (.44 x .56^3)
    AGI 3 >> (.58), (.58 x .42), (.58 x .42^2), (.58 x .42^3)
    AGI 4 >> (.68), (.68 x .32), (.68 x .32^2), (.68 x .32^3)
    -vs-
    R2-F2 >> (.375), (.375), (.375), (.375)

    Cumulatively, that’s “plus” this (over no action’s base numbers):

    AGI 1 >> (.25), (.44), (.58), (.68)
    AGI 2 >> (.44), (.68), (.82), (.90)
    AGI 3 >> (.58), (.82), (.92), (.96)
    AGI 4 >> (.68), (.90), (.97), (.99)
    -vs-
    R2-F2 >> (.38), (.75), (1.13), (1.50)

    These are not references to the number of shots your way, by the way. These are, as are your own numbers, references to shots your way where your choice mattered. It’s possible and sometimes likely that you’ll see shots your way where the Focus/R2-F2 decision is moot (because the attacker misses without your action helping the result), so the “fourth attack” column is much less important that the “third attack” column in looking at heavy fire your way (except in the case of swarms which see 5th, 6th, and even 7th attacks).

    The boon from R2-F2 is relatively small here. The 3pts is helping, but it’s not doing a whole lot. Remember that these numbers represent damage, and very likely the limit of how much health R2-F2 is likely to protect relative to a Focus. It’s less than 1 health, per game. It can be enough to save Biggs for a second round (where he’ll Focus and draw 1-2 enemy shots) — a potential game-winning effect, but potentially 3pts for nothing as well. I think I’d rather buy Hull or Shield Upgrade here, which is more reliable for a better effect (because you get the 1 health boon for sure AND a Focus action).

    This makes R2-F2 a swarm counter, mainly. It stacks up impressive numbers there, easily buying 2-3 (2.25 minimally and very likely more) health for whatever ship it’s on. If your list otherwise struggles vs swarms, R2-F2 for Biggs is a strong buy. It’s also a good meta shaping card. Bring R2-F2 a few times and players will move off of swarms to get past your chosen defense. I really like R2-F2 pretty much because swarms are otherwise hard to deal with for most squads. There aren’t too many ways to counter them.

    I also noticed that you don’t have “both R2-F2 and Focus” columns or x2 Focus columns, to compare R2-F2 to Focus in lists that can boon Biggs with a free Focus. Biggs has strong synergy with ships like Garvin so leaving out the comparison really hurts any inspection of R2-F2.

    If you would like I will share those numbers as well.

    1. I think you’ve misinterpreted my tables… If you take the 3.190 value in the Agility 2 table, for a focus action with 3 attacks coming your way, here’s what I did:
      – Simulate 3 consecutive die rolls with 2 defence dice each.
      – Find the first roll that has at least one focus and flip it to an evade.
      – Add up all evades for all 3 rolls.
      – Do this 500,000 times to get an average of, in this case, 3.190 total evades.

      Sorry if that wasn’t made clear in the article.

      Considering this is the data presented in the tables, I’m not sure what you mean by “you have added the Focus defense boon to the first shot at you”. Since the “X attacks this round” column represents the total expected number of evades you’ll roll (over all X attacks) with Y defence dice, considering any modifiers (e.g. focus tokens), it is normal for a focus token to result in a higher expected number of evades, even if you’re only being attacked once.

      If you want to see the data as a “extra evades, compared to the no-action scenario”, we would get the following for a ship with 2 agility being targeted by 4 attacks:
      – Focus will give, on average 1 extra evade (4.029 – 3)
      – R2-F2 will give, on average 1.5 extra evades (4.5 – 3)

      I don’t know which version of the article you’re, but I did include the data for 2xFocus and Focus + R2-F2 in an edit, maybe 2 hours after the initial posting.

      I do agree it is not clear cut that R2-F2 is a good choice. However, paired with someone who can pass over a focus, it’s numbers are great. And I wholeheartedly agree with your assessment that it is a great Swarm-counter!

      1. Oh, yes, you are right — I did misinterpret what you’d done, and my guess is our numbers are quasi-identical then. Your numbers may in fact be a bit more accurate then, as it will account for those rolls where action choice didn’t matter. The difference is minimal, but does exist.

        I do very much recommend Hull for Biggs as the first buy for him, if you have the card (Imperial Aces). It’s a sure +1 to health, and he really doesn’t need it to be a Shield so much because he already has those. It will outperform R2-F2 vs most squads, and you can always switch to R2-F2 (or add R2-F2) if your meta becomes overridden with swarms.

      2. Yeah, I don’t actually have the card yet, nor do I have stealth device (no big ships yet). I should be getting Imperial Aces + TIE Interceptor this week though – can’t wait to fly them!

        And I actually just flew a Biggs for the first time tonight in this squad :
        Biggs+R2-F2, Wedge and 2xRookies

        It went quite well, used R2-F2 the first 2 rounds, before I was able to take 2-3 TIE Fighters off the mini-swarm.

    2. Also… I think your numbers are wrong!

      For example, when you say:

      A single Focus would be a spread potential boon over 4 attacks:
      AGI 4 >> (.68), (.68 x .32), (.68 x .32^2), (.68 x .32^3)

      Your 0.68 is wrong. You DO have 68% chance of USING your focus token on your first roll. However, it will be worth, on average 1 extra evade.

      Considering only the first die roll, what you actually have is this distribution:
      >> 0 eyeballs 32% of the time
      >> 1 eyeball 42% of the time
      >> 2 eyeballs 21% of the time
      >> 3 eyeballs 5% of the time
      >> 4 eyeballs 0.4% of the time

      Therefore, the average value of your focus token is :
      1 * 0.42 + 2 * 0.21 + 3 * 0.05 + 4 * 0.004 = 1.000

      You forget to factor in the number of eyeballs, which can make your focus token be worth more than a single evade!

      1. Actually no, there’s a reason that I didn’t do that. There is definitely a portion of rolls where you see 2+ unstopped hits and 2+ eyes that need to become evades in order to stop the damage, but it’s an extremely small ratio of rolls even in ideal attacker/target cases. Generally speaking, even when you roll multiple eyes your Focus is only defending against 1 damage. A lot of the calculations people have done with Focus is just what you did there, and it overvalues Focus defensively. It’s a numbers inflation that has little/no practical meaning.

        If we could store unused Evade results toward a future roll, what you have put forward would be correct.

      2. Yes, I do agree with you there. And it reflects the thought I had when replying to Immaterium (see my other comment).

        However, taking the attacker’s dice into account in a simulation is more complicated – which is why I was simply looking at the expected number of total evades.

        I might try my hand at it though… Shouldn’t be that hard… You could specify defender’s Agility/Shield/Hull value and action each round, the attacker’s Attack value, their action/modifiers, and the number of attacks each round. Then run the simulation lot’s of times and average out the number of attacks it takes to take him out – since that’s what we’re trying to optimize for with Biggs!

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