You're using a corollary to the LoTT, not the Law itself (very nicely explained by Aryabhata). The corollary says:
it is usually right to compete to the level equal to your trump fit.
[2 level with 8 trumps, 3 level with 9, 4 level with 10]
The math is pretty extensive, and it's all in Larry's books, but you don't have to care. Sure, there are adjustments, sure there are auctions where the length of the opponents' fit isn't confirmed, sure there are auctions where they're not playing in their best fit; if you know all of that, great, use it! But if you don't, competing to the level of your fit will be right more often than not.
Note, though, the word "compete". With game-going values, don't stop in 2 just because you only have a 4=4 or 5=3 major fit (obviously). With enough for slam, same deal. But on the hands where both sides have somewhere between 16 and 24 HCP, and they can both reasonably be in the auction, blindly accepting the push to the Law level (and giving up after) is no worse than reasonable.
Larry Cohen's partner at the time he was writing his books on the LoTT was Marty Bergen, and he was a proponent of pushing the opponents around a lot, and using the Law to determine "safety". From him, we get:
- Bergen raises: "if we have 9 trumps, get to the 3 level before the opponents get a chance to say anything and we might win the competitive auction before it starts."
- definitely "preemptive raises in competition" - 1H-X-3H on "nothing and 4 hearts"; again, trying to win the competitive battle before the opponents can show their suits.
- Law-safe raises of weak 2s and preempts (partner opens 2H, you raise to 3 with effectively any hand with 3 hearts, because 6+3=9). Note that the Bergen-Cohen partnership played this differently, preempting effectively one card lighter (and with much weaker suits) than standard, "expecting" 3-card support from partner. Don't try this if you can't play like Bergen or Cohen!
- when they've found an 8-card fit, try very hard to not let them play at the 2 level. Larry once said on vugraph, "I'd rather be -1100 than -110"; because much more often than not, especially at matchpoint scoring, there's a better score for you somewhere else. Sure. sometimes, you're hooped, and you go for sticks and wheels. Apologize to partner, and get 'em next time.
All this is common to the point of being elementary now, but was revolutionary in the 1980s.
Finally, note that the LoTT degrades the higher the trick count. When both sides have 10-card fits, the chance total tricks is exactly 20 (or even one trick away) is much lower than when total trumps are 16, 17, or 18 (the most common cases).