john, I see your point. Putnam scores may or may not help depending on how our performance compares to the students at the places we apply to - just as with any other piece of our application
You're correct, it'd be around the 90th percentile of people with nonzero scores. But you'd still be in the top 10 percent of the best math majors in the country.
Actually, demographic data on who is taking the Putnam would be really interesting. For example, how many students who are taking the Putnam go on to graduate school, and how many graduate students in math took the Putnam as an undergraduate? How representative are the students taking the Putnam of all undergraduate math majors in the US? Or how does the set of students taking the Putnam compare to the set of students taking the math subject GRE?
The most brilliant math majors I know personally do not bother to take the Putnam, but that's a very limited sample size. On the other hand, given how popular the Putnam is at Harvard and MIT, there are bound to be some very high achieving students in the exam pool.