Battle Advantage StandardS, or B.a.s.s. Values is simply the average amount of shield and cards a certain field formation or skill can force out. Let's say you have a completely vanilla set up like:
Three situations can occur due to triggers, if we assume that the opponent must guard every attack, has no Perfect Guards. If you pull no triggers, you can expect to force out a minimum of 35K shield in total, in the form of 4 cards. If you pull 1 trigger, this rises to a minimum of 40K shield, and 5 cards. Finally, if you were to pull double triggers, this attack formation can rise up to 45K shield, and 6 cards.
Right about here however, a major derp occurs. What do you say about how strong this attack formation is? You can rule out Double Triggers since it's so unlikely for it to happen, but now you're left with either no triggers or a single trigger, both of which equally likely to happen. Normally, most people automatically default to assuming you pull 1 trigger, and base how powerful a certain attack or skill is off this. Normally the story ends here, as pulling 1 trigger sounds reasonable enough and it still gives you a general idea of how strong your forces are. That is, until you run into some problems, problems like these:
Goku and Death Army Lady both respond to Grade 3 Drive Checks, CEO Amaterasu basically doubles your chances of checking double triggers, and Dark Rex gives you a second Twin Drive entirely. Do you just continue to use single triggers to base your claims off? Do you just mention off hand 'oh, right, this unit also happens to do x if y'? The problem with oversimplifying things into just a single trigger check like that is that when cards can manipulate your Drive Check outcomes, the entire premise of the oversimplification falls apart.
Here's where B.a.s.s. values come in. For the 16-16-16 field above, we still have 35K 4 cards for no triggers, 40K 5 cards for 1 trigger, and 45K 6 cards for 2 triggers. Next, we find the probability of each event happening. Bit of math later, there is a 22/49 chance of 0 triggers, 22/49 chance to pull 1 trigger, and 5/49 chance to pull 2. The next step is a little more complicated, but it simply goes to pick either the amount of shield or the amount of cards to focus on. Going with the amount of cards, 4 cards will be forced out 22/49 of the time, 5 will be forced out 22/49 of the time, and 6 will be forced out 5/49 of the time. Basically, it should look like this:
multiplying the output of the attack by the probability of that certain event happening. Finally, just add these all up for 228/49. This is the average amount of cards that the vanilla set up can force out, about 4.7 cards per turn. Repeating the process shows that 1875/49K shield is forced out, approximately 38.3K shield per turn. This means that the b.a.s.s. value of those vanilla columns is 1875/49K shield, 228/49 cards (38.3K shield, 4.7 cards) per turn, the average amount this field set up will force out.
Of course, these numbers have to be readjusted as field formations get stronger or power gets spread out or Asura Kaiser is also restanding units for more attacks and such. However, proper use of these B.a.s.s. values can prove valuable in properly scaling and measuring exactly how powerful certain attacks really are, since they can cope to how Grade 3 checkers work, how Amaterasu manipulates the deck, and can work with restanding/attacking Vanguards. With it, real and tangible values of how attacking units work can be found, greater allowing a player to really understand the potency (or potential lack) of their attacks and attackers.