I am not a fan of using a player's plus/minus as a barometer of their play on the ice. However, many coaches, players and fans disagree -- and that is OK, but the metric is far from perfect.
I decided to set up a simulation to show just how inconsistent the metric can be. I created a player who has absolutely no impact on the game. For both his team and his opponent, there is an 8 percent chance of scoring a goal on a shot during even-strength. I am assuming that this player is on the ice for 11 even-strength minutes per game and will be on the ice for six shots for and six against*. I ran the simulation for 1000 82-game seasons, and as you can see, the metric is full of statistical noise.
If the plus-minus statistic were truly fair there would be nothing but zeroes on the chart because like I said, this player has absolutely no statistical impact on the game. Instead, this player is just as likely to be plus-10 or better in a season as he is minus-10 or worse.
Sure, there is noise in any statistic, but this chart shows that the amount of noise in plus-minus is unacceptable. Imagine the narratives that would be written about this same player: how he was too slow, not scoring enough, etc. Some may even feel that the player should be a healthy scratch, when in reality it is simply randomness creating the numbers.
* All bits and bytes appearing in this work are fictitious. Any resemblance to real persons, living or dead, that may or may not rhyme with Pike Panoobell is purely intentional.