When statisticians first started keeping plus / minus stats for NBA games, I thought we’d uncovered the holy grail of basketball stats. I mean it’s a helpful stat is a sport like hockey where the scoring is so infrequent that a team could go through a dozen line changes and see maybe two changes in the pluses and minuses of its players. How much more information would we be able to cull from an NBA game with its frequent changes in score and minute distribution based (presumably) on ability? Of course we were all disabused of this notion pretty quickly. Too many different line-ups are used. Too many different opponent line-ups are met. From a 5-man unit perspective, it’s very useful, but when looking at an individual, there is too much noise in the numbers to really distill what one player has contributed.
I tried to explain the concept of the plus / minus stat to my wife recently. I told her that a player may play extensive minutes without personally scoring any points or taking any rebounds while still contributing to a win. He can set a good screen to free a teammate for a shot. He can make the pass the leads to an assist or the pass that leads to a free throw. He can box out his man so that a teammate can grab a rebound uncontested. He can run the lane in transition to occupy a defender. If none of these positive actions shows up in a box score, how can we measure them? Winning is one way. A player getting significant minutes on a winning team is probably doing something right. But there are a lot of factors in a win, and one player may be contributing in good ways on a bad team. So we make a measure using only the change in game score while the player is on the court. We ignore his traditional stats. We ignore the final winning and losing of the game. All that matters is whether the player’s team does better or worse while he’s on the floor.
My wife understood, and then I explained the rest. I explained that these plus / minus numbers are as untrustworthy a measure of player value as any other statistic. Tracing one player’s plus / minus ignores the abilities of those he plays with and against. A player might excel when he plays with a great passer or next to a terrific defender and play poorly otherwise. A player may play the majority of minutes against bench players, who are presumably weaker competition than opposing starters.
She suffered through my lecture with admirable patience, as you have if you’re still reading this, but I left something out, something I hadn’t realized before I tried my hand at keeping track of player plus / minus stats. In an individual game, plus / minus numbers can be largely a result of when a player checks in and out of the game. Great plus / minus numbers tend to come when a team makes a big run, and big runs don’t necessarily require great players, they often require turnovers, the sort of gambling defense or undisciplined opponent offense that occurs often enough but at unpredictably times.
I watched Game 5 of the 1997 NBA Finals – Bulls vs Jazz, “The Flu Game” and kept the plus / minus for the four most statistically notable players on each team. Here’s the breakdown:
Chicago Bulls –
Michael Jordan +5 in 44 minutes
Scottie Pippen +3 in 45 minutes
Dennis Rodman -4 in 23 minutes (6 fouls)
Toni Kukoc even in 24 minutes
Karl Malone +7 in 34 minutes
John Stockton -16 in 36 minutes
Jeff Hornacek -5 in 29 minutes
Bryon Russell +9 in 40 minutes
Russell and Malone had the best plus / minus numbers at the end of the game despite the fact that Chicago won it, while John Stockton had a horrible plus / minus in the same game. Confused? Let me explain it. The plus / minus story of this game took place when the second unit for each team played in the first quarter. Stockton and Hornacek sat about 7 minutes into the quarter with the Jazz up 2. In the next several minutes the Jazz hit a few outside shots, took advantage of the Bulls second unit (Kerr in particular), and built their lead up as high as 16. By quarter’s end when Russell and Malone finally went to the bench, the Jazz lead was at 13.
Jordan and 4 white guys (Kerr, Kukoc, Buchler, and Longley) went on a little run, and when Russell and Malone came back, the lead had been cut to 7. So even though Chicago’s comeback continued with Russell and Malone playing big minutes, the two Jazz forwards were already +5 ahead thanks to having been on the court during the first big run Utah made and off the court during the first big run the Bulls made. You could make the argument that this is exactly what plus / minus is trying to measure, but having watched the actual plays I can tell you that Michael hitting tough shots and Kukoc making threes would have happened either way.
To demonstrate how this all works, here’s a narrative breakdown of a couple players’ on court / off court night.
Jordan starts the game +0. Sits with the Bulls down 11 (-11). Re-enters the game with the Bulls down 13. Sits with the Bulls down 4 (+9). Jordan starts the second half with the Bulls down 5. He does not sit again. The game ends with Chicago leading by 2 which means the team was +7 for the second half. So for the game Jordan was -11, +9, and +7 for a grand total of +5.
Malone starts the game +0. Sits with the Jazz up 13 (+13). Re-enters the game with the Jazz up 7. Sits with the Jazz up 5 (-2) at halftime. Starts the second half with the Jazz up 5. Sits with the Jazz up 3 (-2). Re-enters with the Jazz up 4. Sits with the Jazz up 2 (-2). Re-enters with the game tied. The game ends with Utah down 2 (-2). So for the game Malone was +13, -2, -2, and -2 for a grant total of +7.
By those numbers what you see is that the Bulls were 5 points better than the Jazz in the minutes that Michael Jordan played, and the Jazz were 7 points better than the Bulls in the minutes that Karl Malone played. However, the reality behind those numbers is that the Jazz had one good run in the beginning of the game and then died a slow death while Chicago made a methodical comeback throughout the second half. Karl played the entire first half. Jordan played the entire second half.
To put it bluntly, when the going was easy, and Chicago was out of synch, the Jazz took advantage and built a lead. Once the Bulls got it together and it became a tight contest, each team took away the other’s ability to execute their offense, and Chicago won because it was better at making something out of nothing. The lie of plus / minus is that it doesn’t divulge circumstance, just like any other stat.