H-index: Any quantitative (or other) measures on how well h-index actually measures scientific productivity?
Besides the convincing argument in Moriarty's comment to the OP there is also a formal argument that the index is particularly meaningless. The Notices of the AMS recently published "Critique of Hirsch's Citation Index: A Combinatorial Fermi Problem" by Alexander Yong, see here http://www.ams.org/notices/201409/rnoti-p1040.pdf

Roughly: The h index is about half the square root of the number of citations... 

More precisely: For an author with N citations to his paper, the h-Index always lies between zero and the square of N. Now assume that these citation are distributed on a number of papers and all partitions occur with equal probability. Then it turns out that the estimated h-Index is then about 0.54 times the square root of N. In the article it is quoted that Hirsch himself has observed that basically all h-Indices he looked at were in the range of 0.45 and 0.58 times the square root of N. Yong also states that, especially for the highly cited people in math, physics, computer science and statistics only very few people have an h-Index above 0.54 times square root of N (and they are never more that 5% above that). The article contains much more data but only for famous mathematicians such as Field's medalists or members of the National Academy of Science and it is really worth a read.