Citation or Behold (Redux)
5000 Quatloos
✭✭✭✭✭
in The Bridge
Buried in a recent thread was a discussion on the benefits of going for a 45,000 honor Behold vs a 50,000 honor Citation. Good discussion, and among the factors was whether the 10% honor "discount" was worth it given skill creep and better crew not being in the Portal yet.
So, here's some math, although the bottom line is it will depend on your current crew manifest, play style, time since the last portal update, and risk tolerance level....
For a 10% discount to "make sense", there must be a <=10% chance of your Behold giving you all crew you don't want or need, either because they are poor, or because you've already FF them.
OK, here we go. Verification of my statistics are welcome ...
Defining some variables (not all will be used):
My Crew:
FY = # My 5* Crew, Not FF, In Portal
FN = # My 5* Crew, Not FF, Not in Portal
CY = # My 5* Crew, FF, In Portal
CN = # My 5* Crew, FF, Not In Portal
Everything from here on out assumes I would not say no to getting a * on any of my not-FF crew as the outcome of a behold. If you have some crew you wouldn't "waste" a cite on ever, just reduce FY by their number.
N = Total Legendary in Game (something like 224 as of today)
NN = Total Not In Portal (about 67 as of today based on pinned thread here + some late breakers)
NY = Total In Portal = N - NN = 157
Now, your "wants". Depends on how deep you want your bench. I calculated this by sorting the wiki for each Skill by Base Skill, and counting anyone above my 5th best existing crew as a "want". You might do the same for Combined Average, throw in a couple of elusive Gauntleteers, etc. The more you want, the more it will tilt towards Behold. The better your Legendary crew gets over time, the lower your Wants will be using that rubric.
WY = # 5* crew "wanted", and in Portal (consult the pinned thread in the Bridge)
WN = # 5* crew "wanted", and not in Portal
OK, getting close:
A = Number in portal I want or need fuses for = FY + WY
B = Number in portal I don't want or need = NY - A
And now on to chances, I'll do it in two parts to be concise:
a = Probability a Behold slot result is wanted or needed = A / NY
p = Probability I get a want/need in at least one of 2 of the Behold slots = (a + a - a*a)
P = Probability I get a want/need in at least one of 3 of the Behold slots = (p + a - p*a)
Darn = Chance the Behold yields an undesirable outcome = 1 - P
If Darn > 10%, I am "better off" going for the Citation
If Darn < 10%, I am "better off" going for the Behold
And now, with some real numbers ... for my crew/wants:
FY = 43 (fusing, in portal)
FN = 14 (fusing, not in portal)
CY = 5 (FF, in portal)
CN = 6 (FF, not in portal)
WY = 41 (wanted, in portal)
WN = 34 (wanted, not in portal. Sigh, shows how bad skill creep is)
A = 84 (in portal and wanted or needed to fuse)
B = 73 (in portal and not wanted or needed)
a = 53.5% (chance of a single slot in Behold being "good")
p = 78.4% (chance of either of two slots being "good")
P = 89.9% (chance of any of three slots being "good")
Darn = 10.1%
Thank you to the magic of "or" probabilities.
So on paper, taking the "10% Behold" discount seems competitive for me right now. But of my 43 in fusion (half of my "wants"), there are probably a few I shouldn't go out of my way to fuse, so it's probably lower. Besides, I will surely roll a "Darn" the first time I try this strategy, because that's how the universe works, and I still have 14 FN's (crew that need fusing that aren't in the portal, some of which are power crew). But on the upside, I have a very good chance of not being disappointed in a 10-pack 5* Behold.
Now the interesting bit: If I adjust the numbers assuming a similar number of 5*'s are added to the Portal in the next update as were in the August update (and almost all of the August adds were worth pursuing, the upside of skill creep), then:
P = 95%
Darn = 5%
So, there's a pretty good case (for my crew) that the *first* (or maybe first and second) Honor spends right after the next Portal update would be better as 45,000 Beholds rather than 50,000 cites. It all depends on your risk tolerance level around that 2-3 weeks' saved Honor!
So, here's some math, although the bottom line is it will depend on your current crew manifest, play style, time since the last portal update, and risk tolerance level....
For a 10% discount to "make sense", there must be a <=10% chance of your Behold giving you all crew you don't want or need, either because they are poor, or because you've already FF them.
OK, here we go. Verification of my statistics are welcome ...
Defining some variables (not all will be used):
My Crew:
FY = # My 5* Crew, Not FF, In Portal
FN = # My 5* Crew, Not FF, Not in Portal
CY = # My 5* Crew, FF, In Portal
CN = # My 5* Crew, FF, Not In Portal
Everything from here on out assumes I would not say no to getting a * on any of my not-FF crew as the outcome of a behold. If you have some crew you wouldn't "waste" a cite on ever, just reduce FY by their number.
N = Total Legendary in Game (something like 224 as of today)
NN = Total Not In Portal (about 67 as of today based on pinned thread here + some late breakers)
NY = Total In Portal = N - NN = 157
Now, your "wants". Depends on how deep you want your bench. I calculated this by sorting the wiki for each Skill by Base Skill, and counting anyone above my 5th best existing crew as a "want". You might do the same for Combined Average, throw in a couple of elusive Gauntleteers, etc. The more you want, the more it will tilt towards Behold. The better your Legendary crew gets over time, the lower your Wants will be using that rubric.
WY = # 5* crew "wanted", and in Portal (consult the pinned thread in the Bridge)
WN = # 5* crew "wanted", and not in Portal
OK, getting close:
A = Number in portal I want or need fuses for = FY + WY
B = Number in portal I don't want or need = NY - A
And now on to chances, I'll do it in two parts to be concise:
a = Probability a Behold slot result is wanted or needed = A / NY
p = Probability I get a want/need in at least one of 2 of the Behold slots = (a + a - a*a)
P = Probability I get a want/need in at least one of 3 of the Behold slots = (p + a - p*a)
Darn = Chance the Behold yields an undesirable outcome = 1 - P
If Darn > 10%, I am "better off" going for the Citation
If Darn < 10%, I am "better off" going for the Behold
And now, with some real numbers ... for my crew/wants:
FY = 43 (fusing, in portal)
FN = 14 (fusing, not in portal)
CY = 5 (FF, in portal)
CN = 6 (FF, not in portal)
WY = 41 (wanted, in portal)
WN = 34 (wanted, not in portal. Sigh, shows how bad skill creep is)
A = 84 (in portal and wanted or needed to fuse)
B = 73 (in portal and not wanted or needed)
a = 53.5% (chance of a single slot in Behold being "good")
p = 78.4% (chance of either of two slots being "good")
P = 89.9% (chance of any of three slots being "good")
Darn = 10.1%
Thank you to the magic of "or" probabilities.
So on paper, taking the "10% Behold" discount seems competitive for me right now. But of my 43 in fusion (half of my "wants"), there are probably a few I shouldn't go out of my way to fuse, so it's probably lower. Besides, I will surely roll a "Darn" the first time I try this strategy, because that's how the universe works, and I still have 14 FN's (crew that need fusing that aren't in the portal, some of which are power crew). But on the upside, I have a very good chance of not being disappointed in a 10-pack 5* Behold.
Now the interesting bit: If I adjust the numbers assuming a similar number of 5*'s are added to the Portal in the next update as were in the August update (and almost all of the August adds were worth pursuing, the upside of skill creep), then:
P = 95%
Darn = 5%
So, there's a pretty good case (for my crew) that the *first* (or maybe first and second) Honor spends right after the next Portal update would be better as 45,000 Beholds rather than 50,000 cites. It all depends on your risk tolerance level around that 2-3 weeks' saved Honor!
Accepted. Mark them, Galt.
7
Comments
Curse you. Infographic request noted and queued :-)
To test my theory, I bought a 10-pack today and sure enough, I pulled Arachnia, Shinzon and Suus Mahna Sarek, none of whom were on my want list. Like I said, guaranteed that I would pull the "Darn" category first time out of the gate! But I have no complaints about Kung Fu Sarek, a reasonable all-arounder who may see some future Event play.
First, nice analysis. I may work the math for my own situation at some point, but for now I'm comfortable with my perceived risk level (as I noted before).
Second, I personally would have been happy to get your behold. I might have considered Arachnia (for art and Janeway depth; don't have this variant), but since my Sarek is at 2/5, the choice would have been easy. In a vacuum, I think your choice was good - SM Sarek will be bonus in several events, especially with another round of Discovery pending.
Third, I purchased my 9th honor-behold yesterday. Choices were Captain Sisko (4/5), Dr. Soong (1/5), and Ushaan Shran (0/5). Although I had no pressing need for a FF Captain Sisko, I have him now. He is now my 3rd best CMD base and 5th best CMD base+roll. I would rate this as my 7th best honor-behold out of the 9 that I've done. So even though I wasn't yearning to FF this card, I'm still quite satisfied with this specific result and the ongoing honor-behold process.
To each his/her own.
But using your calculations my “darn” probability is 20%.
And, most importantly, going through the list of crew in the portal I realized that right now there are only 17 crew that I want and do not have stars on yet. So a citation is definitely more sensible in my case.
But you know what would be cool? Slot machine Beholds. Watch those precious gems spin by and then ... triple Shinzon's. Which reminds me, assuming that triple Shinzon's are not possible (are they?), the math above was done "with replacement", so is a tiny tiny smidge off.
And if you GOT triple Shinzons, would you get the grand prize of all 3 *s for him in one shot? I think you should!
Hey, you’re on to something here!! What better incentive to purchase an honor hall behold over a citation?
[Quickly re-checks the wiki before speaking]: Would a 3* even be worth the crew slot? His only point for existing appears to be ship stats; no number of *s redeem his skill scores. (And even at that - has anyone ever seen him in the Arena? Exceptional captaining was not exactly his forte, so maybe we should have seen that one coming).
Poor Shinzon. Tom Hardy deserved so much better both in the movie and the game. I really wanted to want that card until I peeked under the hood.
Hey, on the upside I lucked out and pulled a 3rd Temporal Chakotay * today from a ranked reward free pull. Woo-hoo! TC was halfway down my citation priority list so would have languished forever there if not for the "freebie". Low-Darn Beholds ARE actually fun.
Now only three more years of data gathering to validate whether the theory actually works or not!
Unlocked Da Vinci, Assimilated La Forge and now Honey Bare Dax. of course I have spent 12 Citations in between these but they have been on important imortalisations.
Mirror Picard, Cornwell, Surak, Ru'Afo, BR Bashir, Guinan (+4), Interfaced La Forge (+3)
As long as there are still a couple of legendaries I am wanting to unlock I will probably continue on begolds for a while.