Ok, would be giving futher Impute for sterm clarification
Firstly, will be going over the previous basis to make em crystal clear
I'll be using the scan for Jiriaya's jutsu but just gonna extract the explanation from it
Fire Style: Flame Bombs
Chakra is used to create oil in the caster's mouth, which is then ignited using the Fire Style technique as it is spit out
Fire Style: Giant Flame Bombs
After filling his mouth with oil created Inside his own body from sage jutsu chakra, the caster sprays the oil out as he ignites it with a Fire Style technique technique. The flames are more than ten times as large as Flame Bombs
From this both work basically with the exact same mechanics where oil is created and both are light up by a simple same Fire Style technique just like a match stick, but one is 10x+ greater than the other
So what changed?
One utilises normal chakra while the other utilises sage chakra
Note that the quantity of oil was never said to increase not the quantity of chakra increased, or even any form of unconventional manipulation was applied
The only change that occurred was the use of Sage Chakra gotten from his SM and more than 10x increase came about, this more than 10x narratively correlates to how SM is a better version of ST >>> CM was stated and depicted
Now back to how the only change was the use of Sage Chakra, this is heavily solidifying Sage chakra has a 10x+
Quality over normal chakra and note it's not about Quantity
In other words,
100 normal Chakra is worth 10 Sage Chakra
Presuming his normal Fire Bomb contains 5 strands of chakra to create the oil his sage fire bomb would still require 5 strands of sage chakra to create the oil but that 5 strands from SM is 10x greater than the 5 from normal chakra
So what's the implication of all this?
Statistics Amplification (Shinobi are capable of enhancing their physical capabilities with the use of chakra)
Based on the layed out mechanics I've given, Naruto without SM does the normal low ranking amp and increases from 1 - 2m/s
But when he amps in sage with the exact same amount of chakra and same mechanics he is going to move from 1 - 20m/s
It's a simple application
Then by simply entering SM the user's Physical Capabilities are passively restructured from normal chakra to Sage Chakra giving him the 10x increase
The reasons and workings for CM not affecting stats while ST and SM affecting all stats has previously been emphasized on
I think
@ssgengar and
@GokuSparkle points correlates with this as they've been main reasonable contributors