More on Focus and Evade

Update!

While responding to a comment, I found an error in the original post: the cumulative damage against a fighter with Evade ought to be 1.51, not 0.92. Fixing this error also changes the interpretation of the data–basically, it explains some things that were previously ambiguous. Please see the updated post here.

Introduction

When last we spoke, I was making a mathematical point about the use of Focus over Evade. Conversation has continued, both here at at the BoardGameGeek thread that inspired my original post.

In response to my assertion that Focus is a better choice if you expect to be fired on by two or more opponents, user Theorist made the following point (among others):

I also agree that over 2 defensive rolls, a Focus token provides more eye results than an Evade token. But where I disagree is in what that means in gameplay — an Evade token is used intelligently to knock off 1 damage, but it means less to turn 3 eyes into 3 evades when the attacking ship only rolled 1 strike. Focus is unpredictable, often rolling high at the wrong times or not being usable (42.2%) when needed.

The conclusion is similar. Focus if you have a shot you’ll get to take. Evade if you don’t because it provides better defense.

My response was to offer to run a simulation of multiple X-wings attacking a single TIE fighter, and see which action choice for the TIE resulted in less damage. Read on for the results!

A Brief Note On Method

Here’s what I did using the software package SAS, one million times:

• Simulate three attack rolls, each using three Attack dice and rerolling blanks and eyeball results, as if three X-wings were attacking with Target Lock at Range 2.
• Simulate one defense roll using three Agility dice, as if a TIE fighter were defending against the X-wings’ attacks at Range 2.
• Assign and use tokens:
• In the “Evade” run, assign an Evade token to the TIE and use it the first time the TIE would take uncanceled damage results.
• In the “Focus” run, assign a Focus token to the TIE and use it the first time there are uncanceled damage results and there is at least one eyeball result. (That is, it’s not saved for some “intelligent” time–it’s just used the first time it would do any good.)
• I used the same set of random seeds for both runs, meaning that the dice rolls are identical each time. The only difference between the two simulations is which defensive token the TIE has at the start of the attack.
• I didn’t stop the simulation when the “TIE” accrued enough damage to be destroyed. Think of this as a situation where all three X-wings have only this TIE in their firing arcs, so any damage they would have dealt beyond 3 is wasted.

Expected Results

Based on my prior analysis, Focus should be more effective than Evade at preventing damage from multiple attacks. The difference shouldn’t be huge, but it should be noticeable; I calculated that with three attacks, a Focus token should be worth about 1.2 Evade tokens.

Judging from his prior comments–and he’s welcome to defend himself or correct me if I’m wrong–but Theorist expected Focus to perform worse than Evade because it provides a more consistently effective defense.

The Test

Here are the tables that illustrate the results after each of the three X-wing shots. These are cumulative values, so each row represents the state of the TIE fighter after it’s been shot 1, 2, and 3 times. Mean Damage is the expected number of damage cards dealt to the TIE fighter, Spent Token is the fraction of simulated fighters that have spent their Evade or Focus, and Survival is the number of simulated fighters that are still alive.

First, the ship with Focus:

3 Attack + Target Lock, firing three times at 3 Agility + Focus.

And the same ship with Evade instead:

3 Attack + Target Lock, firing three times at 3 Agility + Evade.

And here’s the result of all three shots, in graph form. Each chart represents the distribution of damage for the corresponding simulation run.

Distribution of damage vs. Focus. Click to enlarge.

Distribution of damage vs. Evade. Click to enlarge.

Conclusions

It takes three shots for Focus to catch up to Evade in effectiveness, rather than the two shots I predicted. I was definitely wrong there. However, Focus does catch up, which is still an interesting result in itself. Additionally, though, look at the survival rates listed in the table–they’re effectively equal to each other right down the line.

Essentially, the results are ambiguous: Evade is a little better than Focus for the first attack, and it’s a lot better than Focus after the second attack, and by the third attack Focus starts pulling ahead. However, the difference between the two tokens is never so big that choosing one over the other is going to get you killed.

I suspect Theorist was right about the factors working against Focus here. The theoretical value of 1.3 Evades per Focus is only useful when you roll eyeballs and there are multiple hit results that need to be canceled–and it looks like that simply doesn’t happen very often. That is, it’s fairly rare that Focus can be used to cancel more than one damage result, so in practice it’s harder to spend than Evade but has a similar effect.

I’m still somewhat encouraged by the simulation, though. BGG user Piqsid, whose post kicked off this whole idea, posted a smart followup earlier this week:

I don’t think our goal should be to prove that Focus is better than evade. It might be, but it doesn’t need to be. It only needs to be at least the same…

All I want to do is show that Focus is likely to be just as good as evade for defense. I am much more concerned about offense.

I like his point here, and agree with it. There are a number of tactical reasons to use Focus rather than Evade, most of which revolve around the value of offense over defense in X-wing (and I think Theorist would agree…) Given that fact, the question we’re really interested in is whether it’s substantially worse than Evade on defense, and you can consult the simulation results for the answer.

However, I want to guard against over-generalizing from these results. This scenario (3 Attack + action, against 3 Agility + action) is an important test case for Imperial squads, but keep in mind that if your attacker isn’t as effective–fewer dice, or no token to buff the attack–Focus is probably less valuable than it appears here. Similarly, if your ship has better Agility than I’ve assumed–you’re at Range 3 or have a Stealth Device–Focus is better than it looks here.

Last Words

So the bottom line from the previous post needs to be amended. If you’re feeling defensively minded and your TIE or A-wing expects only one or two incoming attacks, Evade provides the best possible defense.

However, if you expect to receive at least three strong attacks in a round, you should Focus regardless of other tactical considerations; in that case, Focus is stronger on offense and at least equal on defense.

Finally, if you’re in exactly one firing arc, seriously consider Focusing anyway. It has a small impact on the damage you’re likely to receive and almost no practical impact on your long-term survivability, and either you get to spend your Focus on defense (in which case it can’t be any worse than Evade) or you’ll be able to hit back much harder when it’s your turn to fire.