So for example, pro basketball player knows they are measured by their accuracy. However, when a player optimizes his accuracy, that does not compromise the effectiveness of that metric.
To use your basketball example, say you have a player that takes a shot every time they get close enough to the basket, scoring 60% of them. You decide to measure accuracy. They get more conservative with when they take shots, so now half the time they run out of shot clock (resulting in a turnover) and the other half of the time they take a shot and score with 100% accuracy.
Their accuracy went from 60% to 100%, but the fraction of time possession results in scoring went from 60% to 50%.
The issue there is that you don't _really_ care about accuracy per se. What you care about is contribution to the score differential vs the opposing team. But that's hard to quantify, so people come up with various metrics that correlate to such contribution (shooting accuracy, rebound percentage, etc, etc), along with relative weights for these metrics. In fact, the weights depend on the exact team you're playing, who your current teammates are, etc.
In any case, it's actually fairly rare to be able to directly measure the thing you care about, especially in the social sciences, not least because a lot of the things we care about ("success in life", "college preparedness", "job satisfaction", "knowledge and understanding of the material covered by this class") are fairly difficult to quantify. So instead one ends up measuring various correlates and hoping that either people don't adjust their behavior too much to degrade the correlation before you're done measuring or that your measurement process attempts to account for such adjustments.
And another friend of mine works at a big software company (SAP, Oracle, those sorts of companies) in sales. Basically he has to generate leads, pass them on, and if they're closed he hits his target. So what most people do is they call the manager and suck up to him, and ask him to register a closed sale's lead as one of his. A lot of these sales are simply recurring sales, or sales closed when a customer called the company, as opposed to closed after a cold-call led to a lead. Long story short, you've got people hitting their targets without generating any leads or sales, making $40k a year and moving into the same closing function two years later without ever having done anything.
The idea seems pretty straightforward, once you create a metric, people will game it. And it seems a single person designing the system (the metrics, the governance of the metrics) over time continuously gets outsmarted by the hundreds or even thousands of people that are incentivized to find the loophole in the design of that individual.
On another note... If a metric is being used properly, it might not seem like it's working. For example... Harvard saw that GMATs didn't correlate with their MBA's success, so they dropped it as admission criteria. Years later they checked the GMAT scores for the classes where they weren't required. What happened? GMATs correlated to performance. What's the cause? Earlier on they were properly weighting in. (Higher GPA? GMAT doesn't matter much. Lower GPA? It matter mores. Grad degree in stats? Lower undergrad GPA and GMAT don't matter as much, etc.) If you're weighting it properly, the importance won't show. (In essence, a 780 is the right marginal score to let one person in, a 680 on another)
All that said, in a way, the perfect measure is an unfair one, because you don't know what you're being measured on so you can't change it.