I wonder whether Yuumi W scales with the stats it itself gives. I know of a way to test it, but don't have anyone to test it with in a custom game, and the ability doesn't explicitly mention it (unlike Vladimir passive, which does explicitly state it does not self-scale), and the wiki has no info on it either.
If anyone would be interested in testing it for me that would be greatly appreciated ^^. What follows are instructions on how to test it:
1. start a custom game with two players on the same team. Player A should take Yuumi, and player B any ap champion (AP makes it easier to calculate since it has a 1:1 ratio with adaptive force) note: both players should avoid taking ap buffing runes and/or champions, as wheter these do or do not work in the Yuumi W may influence the result of this test.
2. farm for few minutes in order to get an amount of ap large enough to notice a difference (about 100 on both players is enough if Yuumi has maxed their w, 400 on both is just barely enough if Yuumi has only a single point in w). note: Both players should avoid taking any ap buffing effects, such as baron, rabbadon's deathcap, or Archangel's, as wheter these do or do not work in the Yuumi w may influence the result of this test.
3. detach Yuumi and write down the amount of AP both Yuumi and the other player have
4. attach Yuumi and write down the amount of AP both Yuumi and the other player have
5. go to this calculation I have prepared: https://www.desmos.com/calculator/inrx7tycg9 (desmos is an online calculator).
6. in the calulator, set A1 to the amount of AP Yuumi had while detached, B1 to the amount of AP the ally had detached, and S to the scaling on Yuumi's w (ie 5 if you have on point, 21 if you maxed it)
7. scroll down in the calculator. There should be variables named A2, B2, A3, and B3. Compare the amount of AP Yuumi had attached to A2 and A3, and do the same for the other player with B2 and B3. If both are closer to (A/B)2, it means Yuumi's w does not self-scale. If Both are closer to (A/B)3, it means Yuumi's w does self scale. If the test is inconclusive, it is most likely the result of a rounding error (ie you need more ap/points in Yuumi w)