Welcome back to Stats for Dummies: in this eighth episode, we will try to reveal the secrets behind Box Plus Minus and VORP, two statistics that are both interesting and obscure. So, let’s start!
The Box Plus Minus is a creation of Daniel Myers, who wanted to create an instrument with similar characteristics to PER, Win Share, and other “all-in-one” stats, which however had the form of the plus-minus. In other words, the BPM tries to convey all the player’s contributions into a single number that can assume a positive or a negative value. Obviously, it will be positive if these contributions are good, while it will be negative if the player’s performance has not been good enough. That’s why I define it interesting and obscure: from one side, it is easy to understand because of a higher value corresponds to a good player’s performance, but on the other side, the many steps required turn the contributions into a number far away from a simple sum. The Box Plus Minus is, therefore, an excellent indicator of the players’ performance, but you have to know it very well.
The VORP is instead a statistic calculated directly from the BPM: the term is an acronym that stands for Value Over Replacement Player and allows you to report the values of BPM on a single scale. In other words, all BPMs are compared to the replacement player’s Box Plus Minus, that it sets at -2. In this way, you will get the estimate of the level of players’ contribution.
After this brief introduction, let’s go deeper. The Box Plus Minus is a per 100 possessions stat: by correctly performing the calculations you will always get zero as the league average; the value of -2, as already mentioned, will be the replacement player’s BPM, that is the player with contributions closer to the league average. Clearly, it is a statistic that rewards players who produce a lot: once again, players who work more for intangible contributions to the box score are penalized. Therefore I want to restate that players with low BPM values are not necessarily bad ones for their teams.
There are also the offensive variants (Offensive Box Plus Minus, OBPM) and the defensive one (Defensive Box Plus Minus, DBPM): the first is also calculated from the classic box score but differs from the Box Plus Minus because of the coefficients used. The second one is obtained as the difference between the BPM and the OBPM: this implies an important limit for the defensive statistics. The idea of obtaining it from the player’s global contributions less the offensive contributions is more than fair, but the flaw is that Box Plus Minus take into account only defensive rebounds, blocks and steals as defensive contributions. They are not in any way counted, loke for the Defensive Rating, efforts such as the contested shots, the forced turnovers, and committed fouls. All contributions can be partly estimated from the Box Score, but in this case, are not computed.
This flaw is a great defect of the DBPM, but, for the reasons just explained, it is also a defect for the Box Plus Minus. Again, therefore, a player’s defensive impact is widely underestimated. The most reliable statistic to analyze it, if you don’t have the NBA tools, is the Defensive Rating: PER and BPM have a lack from this point of view.
When you want to understand who are the best players in terms of points, assists, and rebounds, you can definitely rely on Box Plus Minus. If you want to classify the players using their BPM it is useful to use the VORP: through a simple formula all the players are classified univocally. It is, therefore, an additional tool that simplifies the reading of this statistic, since it also considers the minutes played. In this way, same or very similar BPMs result in different VORPs.
In conclusion, these two statistics are certainly fascinating in their intent, but they have clear limits for defensive contributions. These statistics are certainly comfortable when you want to classify and evaluate the players’ contributions obtained from the box score, considering several factors that are normally difficult to evaluate.