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(1/8) Measuring academic impact is tricky. The h-index (the largest integer such that the person has h papers with at least h citations) is one standard and widely popular metric. Another metric is the total # of citations N. In theory at least, they’re related: h ≈ 0.5 * √N
(2/8) The result follows a standard combinatorics argument for large N, described by A. Yong in the Notices of the American Mathematical Society in 2014. This rule thumb is quite surprisingly accurate, even for modest N values -at least for mathematicians
http://www.ams.org/notices/201409/rnoti-p1040.pdf
http://www.ams.org/notices/201409/rnoti-p1040.pdf
(3/8) I wanted to see for myself, so I used data from scholar and looked for a fit. The data is from late Sept. 2019. To simplify the fit, whenever m scholars had the same h index, I averaged their # citations.) The fit is pretty great.
https://docs.google.com/spreadsheets/d/1vxTP6LTSl3W1_RvUAwABCSR0jn7P1xYPg8z5V4TFSLc/edit?usp=sharing
https://docs.google.com/spreadsheets/d/1vxTP6LTSl3W1_RvUAwABCSR0jn7P1xYPg8z5V4TFSLc/edit?usp=sharing
(4/8) Other fields and smaller N values have also been tested, and the results are quite consistent (R^2=0.96). So as a general model, h ≈ 0.5 * √N is quite reasonable. The question is, what do we learn from this model and how do we interpret it?
https://thebibliomagician.wordpress.com/2018/03/23/is-it-time-to-bury-the-h-index/
https://thebibliomagician.wordpress.com/2018/03/23/is-it-time-to-bury-the-h-index/
(5/8) To the extent that this model is valid, reasonable comparisons between scholars could be made, so long as they fit well with the model. But for many highly cited researchers in the sciences, mathematics, and statistics, the model h=0.5*√N over-estimates their h index. Why?
(6/8) Many reasons. Some are benign: a single highly cited book. Others, less so -- like the "Matthew Effect" of accumulated advantage, described by the great economist Robert K. Merton. Basically, the more cited you are, the more citations you'll get. https://science.sciencemag.org/content/159/3810/56
(7/8) The Matthew Effect naturally applies to grant funding too. That's why it's critically important to generously funding early-career researchers.
https://www.nature.com/articles/d41586-018-04958-9
https://www.nature.com/articles/d41586-018-04958-9
(8/8) Intellectual impact isn't the same as a high h-index. There is certainly a correlation, but that's all. So publish lots of (good) papers. With time, citations, h-index, impact , and funding will follow. Subject to peer review, of course. 
