An attempt to calculate the multiplier of Super Saiyan forms

[Desassina]

I use these multiplier ranges for each transformation:

SSJ1 - [50, 100[
SSJ2 - [100, 400[
SSJ3 - [400, 3200[

SSJ3 ending at 3200 is explained by those ranges' logic: the entry number is multiplied by 2 to the power of the transformation's number to define its limit. Notice how it goes from 2 to 4 and 8. Theoretically, SSJ4 would start at 3200, but that's only my headcanon.

[dbgtFO]

I don't believe in multipliers as in forever staying the same. As the Saiyans grew more powerful, they eventually reached a point, where their forms were too detrimental and so dialed it back a bit to draw out the same power in a lesser, but more balanced form. Ideally with enough training their base forms should hold exactly the same power Super Saiyan forms give them, but without the drawbacks like Ultimate Gohan. As such I view Super Saiyan forms just as shortcuts to greater power. The transformation occurs, as a side-effect to the power being beyond what their bodies are capable of, thus inducing a change. Thus I also believe a Saiyan won't become a Super Saiyan after achieveing the same power in base(Gohan in BoG and Super be damned!).

The following multipliers only apply to the specific story parts.

Super Saiyan Stage I: 50x - from Freeza Arc to early Android Arc.
Super Saiyan Stage II: 60x - when used by Vegeta and Trunks. Their base forms have increased incredibly, but as soon as they went beyond SS, they didn't train it, so their SSS I multiplier is now 30x. When Goku used it in the RoSaT, he got a 75x boost.
Super Saiyan Stage III: 100x - Super Saiyan taken to its limit, though of course hugely unbalanced.
Super Saiyan FP: 100x - same boost as SSS III, but without the drawbacks, as they went back to SSS I and started all over.
Super Saiyan 2: 2x SSFP - except in the case of Gotenks.
Super Saiyan 3: 4x SS2 - once again not applicable to Gotenks.

[apex_pretador]

I don't believe in multipliers as in forever staying the same. As the Saiyans grew more powerful, they eventually reached a point, where their forms were too detrimental and so dialed it back a bit to draw out the same power in a lesser, but more balanced form. Ideally with enough training their base forms should hold exactly the same power Super Saiyan forms give them, but without the drawbacks like Ultimate Gohan. As such I view Super Saiyan forms just as shortcuts to greater power. The transformation occurs, as a side-effect to the power being beyond what their bodies are capable of, thus inducing a change. Thus I also believe a Saiyan won't become a Super Saiyan after achieveing the same power in base(Gohan in BoG and Super be damned!).

The following multipliers only apply to the specific story parts.

Super Saiyan Stage I: 50x - from Freeza Arc to early Android Arc.
Super Saiyan Stage II: 60x - when used by Vegeta and Trunks. Their base forms have increased incredibly, but as soon as they went beyond SS, they didn't train it, so their SSS I multiplier is now 30x. When Goku used it in the RoSaT, he got a 75x boost.
Super Saiyan Stage III: 100x - Super Saiyan taken to its limit, though of course hugely unbalanced.
Super Saiyan FP: 100x - same boost as SSS III, but without the drawbacks, as they went back to SSS I and started all over.
Super Saiyan 2: 2x SSFP - except in the case of Gotenks.
Super Saiyan 3: 4x SS2 - once again not applicable to Gotenks.

I agree with this

[Desassina]

Saiyans could reach their previous SSJ power level at base, like Piccolo got surpassed by them in the Buu saga, which means that something had increased before the multiplier (their base power). Not so obvious is the fact that Freeza was still stronger than a base Saiyan, so now we're in need of a range that we could define as their "base", and that's why 40 times their power could be a possibility.

Static multipliers would be their comfort zone, like cars decelerate, but won't go past their current gear when you stop hitting the accelerator. To achieve a new transformation, their power output increases before they can stick to it, like cars accelerate before changing gears. The higher the rotations per minute, the more fuel is wasted, and so Saiyans would lose their stamina by sticking to an uncomfortable multiplier for long.

[Darkprince410]

Saiyans could reach their previous SSJ power level at base, like Piccolo got surpassed by them in the Buu saga, which means that something had increased before the multiplier (their base power). Not so obvious is the fact that Freeza was still stronger than a base Saiyan, so now we're in need of a range that we could define as their "base", and that's why 40 times their power could be a possibility.

There's no clear evidence that Piccolo was ever surpassed by their base forms, as the one individual who gave us that information (Dabra) proved to be completely inept in terms of ki sensing. Remember, despite sensing that "extraordinary" power from Goku and the others, he still thought that Pui Pui would be more than a match for them, and was completely shocked by how quickly he was taken out. So Dabra's ability to seemingly sense their strength despite them being suppressed really doesn't hold much weight at all if he's that significantly off base.

With Beerus though, there's nothing contradicting his assessment of Goku's strength in comparison to Freeza's, thus Goku's base being below Freeza is really the only substantial information we have on the matter.

[Desassina]

Evidence, substantial... What a court case, huh? Piccolo was said to be worthless, so that's where I stand.

[Tectorman]

Evidence, substantial... What a court case, huh? Piccolo was said to be worthless, so that's where I stand.

Of course he was worthless. He's half-former-God, and Babidi outright stated that the Supreme Kai's power could not contribute to Buu. Piccolo being worthless doesn't have to have anything to do with how powerful he is and could instead be a reference to his power being too tainted/pure to be useful.

[Desassina]

However, when Dabura and Babidi spoke of Kaioshin's energy, they didn't go the leaps and bounds of including Piccolo for his lineage. There were three people whose energy was marvelous, and the rest was just trash.

[Tectorman]

"Useless to them" is "useless to them". Regardless of the particular reason why. Those characters not going to the bother of specifying why (and really, in context, why would they?) doesn't make it not a thing.

[Darkprince410]

Evidence, substantial... What a court case, huh? Piccolo was said to be worthless, so that's where I stand.

However, when Dabura and Babidi spoke of Kaioshin's energy, they didn't go the leaps and bounds of including Piccolo for his lineage. There were three people whose energy was marvelous, and the rest was just trash.

Said to be worthless by someone who proved later to be completely inept at determining strength levels. That's like listening to and putting value in an individual critiquing paintings, only to find out said person is both color blind and suffering from severe astigmatism, yet doesn't wear any kind of corrective lens. His value at critiquing ends up being questionable if what means he's using to critique things ends up being so unreliable, which is exactly the case with Dabra.

[Desassina]

The faster argument isn't one whose information has yet to appear, because Kaioshin's energy being useless has an interpreted meaning, so making a complex theory about it is bound to leave questions. For example, if Piccolo was a deity by half, was the other one read instead? Since Ki is made of all sorts of Ki, and because Gods can't be sensed, then Piccolo was only showing portions of it, and could be stronger. That's something we know in hindsight though, and couldn't probably imagine at the time it was written and published. Also, characters aren't inept, but they underestimate sometimes.