Now, I plan on doing some of this testing on Drg tonight so can vary str a bit more. Basically naked except weapon, and all gear except +ws damage(will find something to put in place of those peices from what I have on hand). If the damage increase on weapon skills is close to 1/3 of my Str again, would that be enough to indicate that the minimum increase is close to that for you? As I have seen that as 50sam/23mnk and 23mnk/blu so far when done weaponskill testing. If it shows up on Drg, that would be up to 4 different str values that it has happened with. Will again be doing it on tunnel worms in south gusta, and be using Leg Sweep, TP affects Stun chance, fTP of 1.0, and while it has a STR mod of 100% itself I will establish a baseline Leg Sweep value for both naked and with gear before using boost, like I have with the others. I don't care to find out what the exact % of Str it is adding, but just about everyone else was saying that boost wasn't affecting WS's at all prior to the linked dev posts spurring new testing, and my testing was showing it was. I also have given enough info here so that others could at least repeat the process to verify or disprove if they wanted, and yet to see someone else disprove or verify. I just haven't put in a lot of time to get enough numbers to rule out variation enough to pinpoint things so one could make a formula.
And the 1/3rd str is kinda important, as look at the patch notes Nyarlko posted. With it not being noticed prior, I was guessing that it might be a % based stat mod like Weaponskills normally have, and 33% would be low enough to be missed.
From what I have seen in practice(yet to test the Boost->wait->WS pattern to verify myself) Odds are best method to use boost is waiting as close to its expiration as possible before using a WS or JA, or let it run out for an enhanced auto-attack.
Problem is weighing out if the combination of wait time(and no tp feed to monster), increased TP gain on the hit, and increased damage is worth it. If it multiplies into weapon skills like auto attacks, high base fTP(such as Howling fist and its 8.0), or ones that duplicate fTP for all hits(like Stardiver, not sure if any H2H ones do) may be the best ones to use it with. The mathy stuff is to try and get to the bottom of how to best use it, and with what.