Does a statistic used as a measure becomes invalid after it's reported on? Apologies if this the wrong place to ask. but i'm trying to explain to a director that his Statistics don't show the truth because he is demanding that the stats are what is reported on and staff are measured against. But my explanations don't get through to him.
I remember reading a long time ago that there was a named Law, or Theory, or something to that effect. It explained it perfectly but i can't remember what it is. Does anyone know?
The basis for the Law was: If Statistics that are reported against are then used as a measure of performance, then they stop being effect measures as people quickly learn to make the statistics look accurate to the measure as opposed to what those statistics mean.
I want to change the way that the statistics of my team are viewed.
 A: What you measure is what you get, so be careful what you measure.
In the world of software development people dread releasing software with bugs. Naturally, you'll want to release the software without any bugs, but how do you measure "success".
Number of bugs found? -- Team stops reporting bugs, QA finds nitpicky bugs, Dev gets defensive about the process.
Bugs per line of code? -- Introduce lots of lines of code to rig the count even though the extra lines don't do anything.
Ultimately, having the name to put with the human instinct to game a system will probably not help your situation. People tend to fight unnaturally hard when they're told they're wrong (even if they are indeed wrong), but when you drop telling them wrong and instead show help they tend to work with you.
In this case, try to work with the director. "I don't understand how tracking this helps the team, can you explain it to me? What if we tracked X instead? Can we make this a 1 hour team building event to spitball other ways in which we can achieve your goal?"
Sometimes the mere act of trying to explain it to someone that just keeps asking "Why?" and "How?" will expose flaws and get them receptive to new ideas.
A: You might be thinking of Goodhart's Law. It is named after economist Charles Goodhart and was stated by Marilyn Strathern in the form: "When a measure becomes a target, it ceases to be a good measure." in ‘Improving ratings’: audit in the British University
system.
A: I believe you are thinking of the Hawthorne Effect, which describes a situation in which individuals modify an aspect of their behavior in response to their awareness of being observed. 
Another possibility is Campbell's law, which suggests "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 is very similar to Goodhart's law, suggested by @JW.
I should add, based on the limited information you provided, that just because you report on a measure doesn't necessarily make it invalid.  As an example, if a football coach's performance is measured on Wins and Losses (which are obviously reported on), this measure could be considered valid.  
What matters is whether a loophole exists in which individuals can 'game' the measurement system, making their performance appear better than it actually is.
