Analytics are now commonplace in sports. Analytics and advanced statistics (whatever that means) are used in front offices and in the media. However, while these new statistics are frequently mentioned, it is rare that anyone explains how these metrics are developed, what they really mean and what their shortcomings might be.

As a starting point for considering advanced basketball analytics we investigate a variety of basketball efficiency statistics. We start with the NBA Efficiency Stat, then we discuss the Player Impact Estimate (PIE) and we finish with John Hollingerâ€™s Player Efficiency Rating (PER). These measures all share the common idea that the way to evaluate players is to somehow combine multiple measures of player performance.We go in depth on the podcast â€“ what follows are a few formulas and notes.

The NBA Efficiency metric is given below. It is a simple metric that basically adds up all the good things a player does and subtracts all the negatives.

Key Benefit: Efficiency is fairly comprehensive as it includes a wide range of player statistics.Key Issue: The weights used to construct the statistic are too simplistic.

The second statistic we evaluate is the Player Impact Estimate or PIE. PIE represents an extension to efficiency as it adjusts for additional factors such as a teamâ€™s overall output and the weights of individual statistics are adjusted.

Key Benefit: The adjustments for team output provides a better tool for player comparisons.Key Issue: the weights still seem arbitrary.

The third statistics we look at, Hollingerâ€™s PER, seems to have become the industry standard. This one is difficult to present because of the complexity of the formula. The link below takes you to the formula. PER is interesting because it represents an attempt to build in the structure of play with multiple adjustments. For instance, rather than just assign a value of 1 efficiency point to a steal, the PER formula uses the value of a possession (based on league averages) to place a value on a steal.

Key Benefit: The formula attempts to capture the structure of the game and makes appropriate adjustments.

Key Issue: The formula is barely comprehensible. This makes the stat a black box that is hard to understand.In summary, these statistics are progressively, fancy ways of adding up simpler statistics. They provide a service by making it possible to compare players across different positions and with players with different styles(the rebounding power forward versus the spot up shooter). For the basketball analyst and front office, the real question should be how these stats be best used and what is the trade-off between simplicity (easy understanding and the ability to adapt) and complexity (the value of increased precision).For the fans, the fundamental issue is to understand what these metrics are and their relative strengths and weaknesses.

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