When a measure becomes a target, it ceases to be a good measure.
Improving Ratings, Audit In The British University System, 1997, Marilyn Strathern
Monetary Relationships: A View from Threadneedle Street. Papers in Monetary Economics (Reserve Bank of Australia), 1975, Charles Goodhart
The original 1975 quote from economist Charles Goodhart actually looks like this:
Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.
The more direct rephrasing is attributed to Marilyn Strathern in 1997.
But even another aphorism, called the Campbell's law, puts it in a more dramatic way:
The more any quantitative social indicator is used for social decision-making, the more subject it will be to corruption pressures and the more apt it will be to distort and corrupt the social processes it is intended to monitor.
Campbell's law was used to criticize the high-stakes testing in U.S. classrooms, where teaching for the test can be applied to guide the teaching practices, even discarding more beneficial ones. Note that the term beneficial would be again subject to debate; and if another indicator is chosen, then that indicator would be subject to Goodhart's law again.
A similar thing could happen if an educational institution chooses to get rid of lower-grade students, in order to keep a high position in a rank of top graded schools.