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Friday, November 13, 2015

Star Wars Armada - Stats Analysis: Vader vs Screed

Wave 1 gave the Imperial Fleet one of the most popular commanders in the game: Admiral Screed. Wave 2 brings the Imperial Fleet one of the most iconic commanders in Star Wars: Lord Vader. But the debate over "who's better" has been going on ever since Vader's ability text was revealed.

Today, we're going to throw some math at the debate and see what sticks. It's:



(the most exciting of all debate formats)

First, let's start with the card text.

Both cards use different avenues to achieve the same end goal: kill moar stuff. Unlike other commanders who provide improved survivability (Motti/Mon Mothma) or improved flexibility (Tarkin/Garm), Vader and Screed are designed to improve our ability to destroy the enemy fleet - specifically through modifying die rolls.

Screed's impact on die rolls is fairly straight forward. Based on die facings, we know exactly what we will get whenever we flip a Red, Blue, or Black die. Vader, however, is more nuanced - re-rolls can help give us what we want, but also may give us what we don't want. Screed and Vader can be used to help trigger critical effects, though Vader's ability does not guarantee them the way Screed's ability does. Vader, on the other hand, can be used to hunt for Accuracy facings when needed, which is a service Screed cannot provide.

To frame our discussion properly (and in the most general of terms), we will start with an analysis of Raw Damage Output. Ignoring accuracies, critical effects, and all other things, which commander allows us to produce the greatest amount of damage via our die roll. Given this approach, we will also analyze each die color individually as damage outputs vary across each die.

To simplify our analysis, we will also "simulate" Vader's Re-Rolls by using the 'Average Damage' output for each die. While some may not consider this "real math" (discrete probability vs. law of large numbers), it provides a directionally accurate result that we can directly compare to Screed's ability.

To begin, let us start with the Black Die. When re-rolled, Vader produces (on average) 1 damage. When flipped by Screed, the new face produces 2 damage.

Let's assume an initial roll of 4 Black Dice produces the following result:

4 total damage

If we use Vader to re-roll any dice, his ability produces (on average) 4 damage. No net change.

If we use Screed to drop a die and flip one to Hit+Crit, his ability produces 4 damage. No net change.

So in this scenario, we can see there is no difference - in terms of Raw Damage Output - between the two commanders.

Now let's say we roll those same 4 Black Dice and get:

3 total damage

If we use Vader to re-roll any dice, his ability produces 4 damage. An increase of 1 damage from the initial result.

If we use Screed to drop the blank and flip one of the Hits to Hit+Crit, his ability produces 4 damage. Also an increase of 1 damage.

In this scenario, we again see no difference in Raw Damage Output.

Next roll:

2 total damage

Vader's re-rolls give us 4 damage again (we're starting to see a theme here). Screed's drop and flip gives us 4 damage as well. No change in Raw Damage Output.

Next roll:

1 total damage

What do Vader's re-rolls give us? You guessed it - 4 damage. Screed's drop and flip gives us 3 damage - Blank Hit Hit+Crit.

Finally! A difference! If we roll 3 blanks on our initial roll, Vader's ability produces more raw damage.

We can apply this same methodology to all die colors to see the threshold of where the output of Vader's ability surpasses the output of Screed's ability.

For example, rolling 3 Red Dice:

Vader's ability produces (on average) 2.5 damage after modification. Screed's ability produces 2 damage.

If we walk through all of those possibilities, we arrive at the following "Result Matrix", which describes the increase in Raw Damage Output by scenario:

Vader's ability provides a higher damage output with any number of Blank/Accuracy faces on Red and Blue die, and produces a higher damage output only at 3 or more Blank faces on Black die.

Screed's Critical Effects and Vader's Increased Costs

Two of the most effective Critical Effect upgrades in the game - Advanced Concussion Missiles and Assault Proton Torpedoes - both utilize Black Crits to substantially increase damage output.

Screed guarantees these upgrades will be used, versus an increased chance to trigger with Vader. The impact of that guarantee cannot be underestimated, allowing the player to make better roll modification decisions - especially in a dual-arc fire scenario.

That being said, Vader's ability clearly provides a greater increase in Raw Damage than Screed - but at what cost? And at what real benefit?

Since Screed's costs are built into the die roll, we can simplify our analysis by looking at the change to Vader. Picking Vader over Screed first costs us 10 fleet points. The abstract cost in Defense Tokens, means we probably want to save his ability for when we really need it. When "do we Need that re-roll" versus "do we Need that Defense Token" means Vader's choice will not come down to pure mathematics.

But we can sure try!

Swinging back to look at Black Dice, Vader's ability only pays off when 3 or more Blanks are rolled. How often does this occur?

If we're looking at shots out the side of a Gladiator I, 4 Black Dice produce a result with 3 Blanks only 5.1% of the time - is Vader really worth it if Screed is just as good 95% of the time?

Having a Black Crit Effect upgrade on that Glad I swings the meter in favor of Screed even more - not to mention the fact that he saves me a Defense Token and 10 fleet points!

Decision Point

If I'm running a list with lots of Black Dice and any number of Black Crit Effect upgrades, Screed is still my #1 choice.

However, Screed is a relatively poor choice for an Imperial Fleet that rolls mostly Red and Blue dice. If I decide to plop 3 ISD IIs or 4 VSD IIs on the table, Vader is clearly a better commander if I'm looking to maximize my damage output (not to mention the ISD has an extra defense token to spend towards re-rolls). Vader might have to compete with Motti for the commander role in those lists, but that's another story!

The biggest service that Vader provides to any list is a 'normalization' of your attack rolls. Rolling up in an ISD II and dropping 3 Blanks + 3 Accuracies on 8 dice is nothing short of disappointing. While the chance of rolling 2 damage on 8 dice is relatively low, including Vader in your list makes it virtually impossible. Vader also allows you to search for Accuracy faces if you really need to get around a Brace or Redirect. Interestingly enough, they're only found on Red or Blue dice - Screed maintains control over his Black dice!

In the debate between Vader and Screed, the answer is likely not whether one is better than the other - it is that they are better suited to command different types of fleets. Focus your fleet build to take advantage of one or the other and you will be far more successful in utilizing either commander.

If you can't make up your mind, go Motti instead!


Nicolas Roland said...

Interesting as always. ;-)
Keep up the good work !
As a rookie in Star Wars Armada, this kind of articles are a great way to improve my skills and game mechanics understanding.

Anonymous said...

One thing you might have missed in this is that the expected value of additional damage isn't a linear function. As a ship gets closer to 0 hull, each additional point of damage is more valuable than the previous (with going from 1 to 0 being the most valuable jump).

As an example, firing 3 black dice at a Corvette with no tokens/shields and 4 hull left. If you roll {blank, blank, hit} the mean damage for Screed vs Vader is both 3, but the distributions are very different. The chance that Vader kills the Corvette when rerolling all dice is 34.38% while the chance that Screed kills it is 0%.

A similar exercise with an Assault Frigate with no tokens/shields and 6 hull, and rolling 4 blacks. If you roll all hits, both have an expected damage of 4. Vader's ability allows you to reroll all dice for the same expected damage, but a 11.33% chance of destroying the frigate outright while Screed has a 0% chance.

Vader is much better at taking weakened ships off the board. Whether this outweighs his additional costs is up for debate.

Anonymous said...

Pew pew!

The Riha said...

While I do understand Vader's statistical ability to deal that extra damage, I'm not sure I agree with it from a practical/tactical point of view. If I try to re-roll 4 damage on 4 black dice, I have just as much of a chance to roll 2 damage as I do 6 damage.

I suppose there are scenarios where this re-roll can be the deciding roll between winning and losing, but I personally don't believe those situations occur often enough to warrant the increase in cost - especially if I can buy two Assault Proton Torpedoes for the difference in price!

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