h-rate
Originaly defined by Hirsch (2005), this metric is also known as the m-quotient, m-ratio index, age-normalized h-index, and Carbon h-factor. It measures the rate at which the h-index has increased over the career of a researcher. It is calculated simply as:
$$m=\frac{h}{Y-Y_{0}+1},$$where \(h\) is the h-index in year \(Y\) and \(Y_{0}\) is the year of the researcher's first publication (the denominator of this equation is the academic age of the researcher).
The above estimation is essentially just the slope of the line from the start of a researcher's career (0 publications, 0 citations) through the most recent estimate of their h-index.
History
| Year | m |
|---|---|
| 1997 | 1.0000 |
| 1998 | 1.5000 |
| 1999 | 1.0000 |
| 2000 | 1.2500 |
| 2001 | 1.2000 |
| 2002 | 1.1667 |
| 2003 | 1.4286 |
| 2004 | 1.5000 |
| 2005 | 1.5556 |
| 2006 | 1.6000 |
| 2007 | 1.7273 |
| 2008 | 1.7500 |
| 2009 | 1.8462 |
| 2010 | 1.7857 |
| 2011 | 1.8667 |
| 2012 | 2.0000 |
| 2013 | 1.9412 |
| 2014 | 1.8889 |
| 2015 | 1.8421 |
| 2016 | 1.7500 |
| 2017 | 1.7619 |
| 2018 | 1.6818 |
| 2019 | 1.6087 |
| 2020 | 1.5833 |
| 2021 | 1.5600 |
| 2022 | 1.5769 |
| 2023 | 1.5556 |
| 2024 | 1.5000 |