The scene: A call centre, doing IT support. Big company, sold a lot of computers at retail, so we took a lot of calls. Probably around 50 of us, all in one big open-plan office.
Head office wanted lots of customers helped quickly. And our phone system could report lots of data. So they told the managers of the call centre that they wanted average call duration to go down, and number of calls taken to go up. That would mean more customers were being helped, and we were wasting less of their time and ours while doing it.
Except once you're measuring a statistic and trying to change it, that' might not be the result you get.
There was one phone in the place that wasn't part of the phone system - just a plain old phone mounted to the wall at the back of the building. so every time it was quiet, and there weren't more calls coming in than we could deal with, one of the supervisors would go to that phone, and repeatedly speed-dial the main phone line. Every time someone answered, they'd say "It's just me" and hang up.
So every bit of quiet time suddenly had a whole lot of very short calls.
The average call duration went down. The number of calls taken went up. The managers got to proudly report their improvement in the stats, as requested. Head office was happy, they had achieved something.
Customers saw no change at all, and we all had a bit of extra mindless work to do.