Recommend
4 
 Thumb up
 Hide
11 Posts

Star Trek: Attack Wing» Forums » Strategy

Subject: STAW Math: Calculating Efficacy with Expected Averages rss

Your Tags: Add tags
Popular Tags: [View All]
Kevin Roberson
United States
Washington
flag msg tools
designer
I'm doing some probability analysis to help calculate the combat efficacy of cards with comparable action economy. Below are my results so far. More to come if people like it.

Terminology:
N: Number of dice in an equation.
AED: Average Expected Damage
AEE: Average Expected Evasion

Default assumptions:
1.) Half the faces on an attack die represent hits. So an attack die adds 0.5 to Average Expected Damage (AED) of an attack.

2.) Three faces of a defense die negate a hit, so addition and removal of defense die adds +3/8 or 0.375 AED if expressed as part of an attack or similar AEE if expressed as part of a defensive action.

3.) In case of a tie for AED, more attack dice is always better and modifying attack dice is better than modifying defense dice. 2 attack dice at battlestations has the same AED as 3 dice, but obviously the latter is better because the upper limit of damage is higher. Any attack that modifies defense dice is less reliable than modifying attack dice because you can’t necessarily count on your opponent to have enough defense dice to modify.

Basic Actions:
Battlestations: BS essentially converts 1/2 of all misses, or 1/4 of all die facings to hits. It therefore adds 1/4 or 0.25 AED per die. It can be used to apply 0.25 AEE as well.

Target Lock: Without being spent on secondary weapons, this represents a 50% chance to convert a miss to a hit, since miss rate is 50% this gives it +1/4N AED. If used with Battlestations its AED is 0.1875N.

Sensor Scan: +0.375 AED flat and only against enemies with defense dice. Given the above I don't think it's jumping the gun to call this useless without specific cards (which we'll discuss in a minute).

Evasive Maneuvers: 0.375 AEE for one attack.

Cloak: We’ll be ignoring this one as it’s more of a tactical choice than anything. 1.5 AEE hardly sums up the pros and cons of cloaking tactically.


Specific Cards: The following will use the above assumptions to list AED effectiveness of specific cards whose efficacy may not otherwise be readily obvious.

Geordi LaForge
Geordi LaForge + Scanning vs.
1 Defense Dice(DD): +0.375. With Battlestations (W/BS): +0.625
2 DD: +0.61 AED W/BS: 0.86 AED
3 DD: +0.76 AED W/BS: 0.95 AED
4 DD: +0.85 AED W/BS: 0.98 AED
5 DD: +0.91 AED W/BS: 0.99 AED
6 DD: +0.94 AED W/BS: 0.99 AED

Geordi's usefulness has a limit at 1, including the original scan, and specifically the amount he adds to your scans is limited to the odds of them rolling a miss on the reroll (+0.625 without BS, 0.375 with), so despite how it looks, he's actually doing more for you if they don't have battlestations. But none of this really matters, if you're attacking with 4 dice, the Battlestations action gives you +1 AED which is more than Geordi can ever say. The only ship that should even think about blowing 4 points on Geordi is the Excelsior.

Spock: essentially tosses +0.375 AED on top of the Battlestations ability at the cost of not being able to use it for defense. He's useless against the Borg. I can think of better things to do with 5 points unless used in tandem with the Excelsior or Janeway. One upside, though, is it gives Battlestations to Anti-Matter mines.

Dimitri Valtane: The math on this guy gets fairly complicated to work out on a case by case basis. In addition to scanning, his benefit is equal to 0.5X+Y without battlestations, and 0.75X +1.5Y with battlestations where X is the odds of exactly 1 missed die and Y is the odds of 2 or more misses. However, since the most benefit he can grant is 2 rerolls, this means he has a limit of +1 AED without battlestations, +1.5 AED with. He approaches this limit remarkably slowly, too. This is somewhat distressing as it means for most purposes having Valtane is not significantly different from not having him when compared with battlestations and/or target lock. I really only see two uses for him:
1.) Combine him with something else that makes scanning better like Janeway, The Excelsior, Spock or Geordi. Only one card can trigger off a single token, but the trigger occurs during the modify dice step and you can choose the better of two triggers after seeing the attack roll. And with Janeway you could get two separate triggers.
2.) Defusing Feedback Pulse when using torpedoes against the borg by rerolling your hits. Normally you would just do this with a target lock and regular fire, but on a torp boat that’s not really an option.

Sulu: Adds 1.75 - 0.75^N AEE with a minimum N of 2. So for most uncloaked ships this lands between 1.19 and 1.51 AEE, or 1.675 upper range for cloaking ships. At first glance this is incredible. But it has one fatal flaw that I’ve noticed: it’s too good. Stay with me here, if you have 2 ships on the field, the ship with Sulu is simply going to be the last target. Sulu is a waste of an action in a round in which his ship isn’t being fired on unless the goal was to get the other ship targeted. For this reason, I’d carefully consider the following alternative in most multiship builds:

Worf (Defiant Version): Pretty straight forward, -1 AED to one enemy’s attacks, 1.5 if they use battlestations or a target lock. Though note that if they use battlestations, it increases the odds that they’ll save BS for defense, hurting your next attack. And since he requires range 1, the enemy probably gets another die anyway. At first glance this isn’t that good compared with Sulu. But the neat thing about Worf is he’s one of very few cards that can directly cover allied ships. His defense bonus cannot be ignored by simply switching targets which makes him much better against the Borg than most defensive upgrades since the borg have free range of any target they choose most of the time.

Worf(starter), Attack Pattern Delta and Bioneural Circuitry: Unfortunately the above assumptions do a very bad job of addressing these. Strictly speaking their benefit is equal to 1/4 your total AED. That’s the odds of rolling under the average (50%) multiplied by the average of the difference between the old roll and the new one. But the reasons for a reroll being desirable go well beyond rolling just below the average and the risk of rolling lower than your first roll makes it a dubious call. Their action economy is also much worse than the cards being evaluated above, and other disable cards for that matter, because you don’t know when or if you’re ever going to use them again when you decide to enable them.

Boheeka: Boheeka’s AED is 1 - 0.75^N on top of Battlestations. This means at 2 attack dice he’s already better than Spock AND lets you keep your battlestations token for defense if you choose. At 2 points, 3 cross faction, this is one of the best crew upgrades in the game, hands down. Boheeka is so good, he could eat Spock for breakfast and still have enough room for a Dimitri Valtane snack before lunch. Boheeka's name is actually a phonetic version of the acronym BOHICA which stands for Bend Over, Here It Comes Again. In Star Trek (2009), the Red Matter was, in fact, Boheeka’s blood. Q knows how they extracted it. In an early draft of Star Trek: Nemisis, The Scimitar’s ultimate weapon was revealed in the following exchange:

Geordi: When the Scimitar decloaked there was a momentary spike in the tertiary EM band. You’re not going to believe this. It’s Boheeka.

Picard: I thought Boheeka was theoretical.

Geordi: Which is why our initial scans didn’t pick it up. But he’s got it, Captain.

Picard: As I remember, Boheeka research was banned in the Federation because of its biogenic properties.

Beverly: I can’t overestimate the danger of Boheeka, Jean Luc. A microscopic amount could kill every living thing on this ship in a matter of seconds.

This draft was dropped because test audiences didn't find it plausible that Boheeka would require the seven minute activation sequence needed for the movie’s climax.
7 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Jonas Albrecht
United States
Illinois
flag msg tools
mbmbmbmb
Boheeka does indeed own. He's certainly the best crew member the Dominion has to offer.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Jared Voshall
United States
Missouri
flag msg tools
Avatar
mbmbmbmbmb
Having done a similar analysis with the various Torpedoes in another thread, I definitely like seeing this sort of analysis take place. As a followup question - do you feel that these upgrades are worth their point cost, or would you prefer to see a higher discrepency between the cost of the ships and the cost of the upgrades - or even split the two into two separate pools with a differing number of points?
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Kevin Roberson
United States
Washington
flag msg tools
designer
Ships and more crew should definitely be mutually exclusive under the current build of the game. Were I designing the game from the ground up, I'd investigate the idea of having an upgrade pool be a ship stat instead of the current upgrade tray, but I'm sure Wizkids thought of and rejected this in early development.

Regarding cost, it's obvious that if we use Boheeka as an indicator (2 points for 0.9ish AED) every other upgrade of similar action efficiency is too expensive. I'm especially skeptical of anything that costs 5 points. Tuvok and Spock especially simply don't give 5 points worth of benefit for what they do.

As a side note, I have a feeling Wizkids thought Boheeka was balanced by the fact that only 2 races get Battlestations. But since you can flagship it onto any card and/or use Picard who is also certainly worth the point cost, you have a 10-13 point cross faction combo that ups your AED by at least 2, plus other benefits. Compare this with 10 points of other damage upgrades like Spock (.375 AED for 5 points) or Tuvok (0.5 AED for 5 points, action inefficient) and you find this combo to be well worth the points to any faction.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Jared Voshall
United States
Missouri
flag msg tools
Avatar
mbmbmbmbmb
I would approach it from the other directions, and say that a consistant +.75 to average damage is worth 2 points (which would be the equivalent of getting +1 attack on the ship with no restrictions), and Boheeka is definitely quite near that point. As for the rest... Yeah, most upgrades are quite over-costed - and few places are as apparent in that regard as with Torpedoes.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Kevin Roberson
United States
Washington
flag msg tools
designer
I see torpedoes as a way to bring up the base attack of otherwise underpowered ships. One can hardly imagine a Miranda, Gal Gath'thong or Conny seeing play without a torpedo or flagship upgrade.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Erin OConnor
United States
Ohio
flag msg tools
badge
What is your favorite color?
Avatar
mbmbmbmbmb
Turbowombat wrote:
Target Lock: Without being spent on secondary weapons, this represents a 50% chance to convert a hit to a miss, since miss rate is 50% this gives it +1/4N AED. If used with Battlestations its AED is 0.1875N.


The thing about target lock is this:
You choose which dice to re-roll.
So all hits stay hits.
All critical hits stay critical hits.
You just reroll Battle Stations and Miss results.
If you also have a Battle Stations token you just need to reroll misses.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Kevin Roberson
United States
Washington
flag msg tools
designer
Echo2Omega wrote:


The thing about target lock is this:
You choose which dice to re-roll.
So all hits stay hits.
All critical hits stay critical hits.
You just reroll Battle Stations and Miss results.
If you also have a Battle Stations token you just need to reroll misses.


All this is factored in. The math works as follows:

Without battlestations the odds of a miss are 50% per die. Of those misses, 50% of them will be converted to hits. IE half of half the time it will roll a hit that it otherwise wouldn't have. .5*.5*N= .25N AED

With battlestations, a given die will miss 25% of the time. Of that 25%, 75% will be converted to hits. IE 0.25*0.75*N 0.1875N AED.

Though if you were pointing out the typo "miss to a hit" thanks. Fixed.
1 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Jared Voshall
United States
Missouri
flag msg tools
Avatar
mbmbmbmbmb
Turbowombat wrote:
I see torpedoes as a way to bring up the base attack of otherwise underpowered ships. One can hardly imagine a Miranda, Gal Gath'thong or Conny seeing play without a torpedo or flagship upgrade.


I'm not entirely certain about that (and am not really sure what you're referring to as a 'Conny'). The Miranda Class, in particular, has a low cost and wide firing arc, making it a great support ship, even if you don't put torpedoes on it (granted, it won't do a lot of damage - but it'll likely be ignored for most of the game, and can whittle down the mega-hull, 0 agility ships surprisingly quickly). The Gal'Gathong is also the cheapest combat competitive ship that can also cloak, so it also has a place in the game.

And even in that ideal situation, the torpedoes aren't worth the points to take them, since they replace rather than augment the ship's attack value - even a 2-die attack ship is only looking at a 1.18 AED boost on the turns it fires, which (IMO) equates to a point cost of 1.58 - for the Federation torpedoes that give the free BS conversion. The 5 point torpedoes are further off, only scoring a point cost of 2.35 out of 5 for their on-shot effect - and that's not accounting for the loss of attack on the turns that you're re-enabling them.

...

I'm sorry. This is one of the things in the game that I feel rather strongly about, and any time it's brought up, I feel compelled to point out this particular failing. I want torpedoes to be awesome, for them to be worth taking and using (especially in regards to the big ships, which are strictly worse than just firing their primary weapons). As it is now, they're a nice trick, and can build up some of the weaker ships a little bit, but have many better alternatives to take that are much more effective.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Kevin Roberson
United States
Washington
flag msg tools
designer
Conny = Constitution class. Slang from Star Trek Online, sorry. Round these parts it's better known as Tinyprise.
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Will Sanchez
United States
Clermont
Florida
flag msg tools
Avatar
mbmbmbmbmb
Also to further bash on Geordi, with a scan token, there are a lot of ships in this game that roll 0 defense dice makign geordi even more useless.

All hail Hypno-heeka!
 
 Thumb up
 tip
 Hide
  • [+] Dice rolls
Front Page | Welcome | Contact | Privacy Policy | Terms of Service | Advertise | Support BGG | Feeds RSS
Geekdo, BoardGameGeek, the Geekdo logo, and the BoardGameGeek logo are trademarks of BoardGameGeek, LLC.