I had occasion to post this quote in another thread recently:
"Science is facts; just as houses are made of stones, so is science made of facts; but a pile of stones is not a house and a collection of facts is not necessarily science."
- Henri Poincaré
The issue is which facts (or "numbers") are important and relevant to YOU getting the good beer you want, and which are less so. Obviously, the resulting beer is one's own, and so the results will be strictly self-inflicted, but I believe that some measurements are important enough that I go to some pains to take them.
YES.
1. Weigh out my grain bill
2. Take temperatures of my preheat, strike, and sparge water.
3. Refractometer conversion reading.
4. Refractometer preboil reading.
5. Refractometer post-boil OG reading.
6. Establish temperature of chilled wort prior to pitching.
7. Hydrometer reading of fermented beer.
NO.
1. Efficiency- of no concern to me as a homebrewer making 5 gallon batches. If I were a commercial brewer, I would absolutely be taking these measurements. As it is, if I'm hitting the correct OG- works for me.
2. Fermentation temperatures- Again, of no concern to me. I brew only ales, and my basement is in the low '60s pretty much year-round. This may be of great concern to folks in other situations.