In my own games I systematically underestimate the value of reduction, and I go for risky invasions far too often. I guess I need to become more patient :-)
Andy: I've watched a lot of IGS games between high-dan amateurs and I almost never see the classic reduction moves being played. Instead, I see all-out invasions evolving into large complicated fights. Does anyone still believe that Reduction Is Worth As Much As An Invasion? Do the pros still believe in reduction?
Bob McGuigan: Of course the proverb is to be taken with a grain of salt. It does not mean that there is always an erasing move that is just as good as the invasion being considered. It is just intended to indicate that keshi should be considered more often. In fact, many high dan players in server go just invade and fight rather than reduce because reduction often requires delicate strategic and positional judgment, which require time to think. I am sure you would find a lot of reducing moves in pro games. Another thing, I think the description of reducing moves above is too restrictive. Fujisawa Shuko's book Reducing Territorial Frameworks has a lot of good information. In particular it implies that a shallow invasion could be a reducing move. And I think the knight's move cap is often characterized as a reducing move, even though it may be well inside sector lines for a moyo. So some reducing moves might look like or even be invasions of a sort. Something not mentioned above is that deep invasions usually end in gote for the invader while reducing operations usually end in sente for the reducer.
Bill: You also have to remember that a lot of strong amateurs are strong because they have good fighting and reading skills. When, as kyu players, their invasions failed, they often sought the reason in a missed tesuji or lapse in calculating variations --Such errors are easy to find-- , rather than in the idea that the invasion was the wrong thing to do in the first place. As they got better at sabaki and shinogi they became dan players, and even high dan players.
Tapir: Using reductions efficiently is only possible if you estimate the score regularly and precisely.