Yeah, I'm going to partially agree here with Faf.
Probability and expected value are good tools. They seem to have a reasonable application in terms of final standings, and how that relates to draft position via the lottery.
As for the box and ball bet discussed, it has no relevance. You can't really apply that analogy, as the 'negative result' has a disproportionate outcome to the 'positive result'. There's no probability or expected value in the world that would sway me to take that bet. That isn't even remotely the case in the NBA draft lottery. You don't lose your team if you 'lose' the draft lottery, you just get a less nice 'house', or whatever.
But here's the thing with expected value, it requires a fairly comparable progression of results (positive or negative). To truly be effective, you also would need to be working under the assumption this same process will be repeated multiple times, as is the case with any probability based event. It works great for land developers, or other similar enterprises. And while it works here in the simplest of terms, as in, it accurately estimates the value of each initial lottery slot prior to the actual lottery, it does nothing to account for the disparity between possible picks. There isn't exactly a set value for any one draft position, as the quality of the players who might be drafted can vary widely and is difficult to accurately quantify for the sake of computing any sort of meaningful expected value.