Most, if not all of you must be quite familiar with various statistics for measuring usage on the offensive end, as well as efficiency statistics. Most commonly used are *Usage %* (Stats.NBA.com) and *Usage Rate* (ESPN, Hollinger) on one hand, and *Efficiency* and *PER* (ESPN, Hollinger) on the other. *Offensive Efficiency* and *Offensive Real Plus-Minus* could also be applied for measuring players’ contributions on the offensive end. We, on the other hand, have aimed to develop offensive statistics which would take into account more than already established indicators, yet would measure only direct involvement of a certain player and not the efficiency of the whole team when that player is on the floor. In this blog post we are presenting new “usage” indicator, *Involvement Rate (INV Rate)*.

In the last few years, NBA statistics websites introduced newly developed statistics, which enable us to go even deeper into player’s offensive (as well as defensive) involvement and contributions. Secondary assists, potential assists, screen assists or assisted points are just some of them. In our previous blog post we tried to dissect MVP contender’s offensive games and to do that we had to take into account those newly introduced statistics as well. And while doing that we got an idea to develop our own, expanded, in a way more sophisticated indicators.

When we talk about how much a certain player is used on the offensive end, we have to include Usage in the conversation. Simple statistics *Usage %*, which is based on player’s and team’s field goals, free throws and turnovers, is a standard way of showing player’s usage. However, when a player is more of a passer than a scorer, think Rajon Rondo, his offensive usage is underestimated. That is why *Usage Rate* in theory presents a bigger picture, since player’s assists are also included in the formula, and team pace (number of possessions) is taken into account. But there are also other offensive statistics which could present an even bigger picture, which would at the same time narrow the gap between guards and power forwards /centers, especially for those who do less scoring and passing, but are involved in more hustle plays (e.g. offensive rebounding, screen assists). This newly developed indicator is called *Involvement Rate* and is basically a ratio of the number of possession events of a player (FGA, FTA, OREB, AST, TOV etc.) and the number of possessions when that player is on the floor. It is, however, not a percentage, since there are more than one potential possession events per possession, e.g. FGA+OREB+TOV in one extended possession. In fact, in the regular season 2016/2017 there were exactly 1.837 events/possession. The individual statistics used in the *Involvement Rate* formula are:

- FGA – Field Goals Attempted
- FTP – Free Throw Possessions (FTP = FTA * 0.44)
- AST – Assists
- 2
^{nd}AST – Secondary Assists - FTAST – Free Throw Assists
- OPAST – Other Potential Assists (Potential Assists minus Assists)
- SAST – Screen Assists
- OREB – Offensive Rebounds
- TOV – Turnovers
- MP – Player Minutes Played
- TeamMP – Team Minutes Played
- PACE – Pace Factor, the number of possessions a team uses per game.

The I*nvolvement Rate* formula in the end looks like this:

**INV Rate = 100*(FGA+FTA*0.44+AST+2ndAST+FTAST+OPAST+SAST+OREB+TOV)/(MP/TeamMP*PACE)**

The formula is offensive possession based, as possession events in the first parentheses either end or extend a possession. Widely used estimation of free throw possessions, FTA*0.44, is also included. To establish how many possession a player spent on the floor in a game on average, given that we are not provided with the exact number, we simply divide player minutes played with his team minutes played and multiply the coefficient with all team offensive possessions average.

Now we will show *Involvement Rate* statistics for 10 NBA players, all of them qualified in 2016/2017 (condition 500+ minutes played in the whole season, n=355), intentionally selected at different levels of involvement on offense. We purposely selected two players at each of the basketball positions: PG, SG, SF, PF and C.

Russell Westbrook stands out with his enormous *Involvement Rate *value, more than twice as high as the average *Involvement Rate* for qualified players: mean 35.44, standard deviation 9.52. Dwayne Wade was actually in the top 40 (9th decile) in *Involvement rate*, yet there is a bigger difference between him and Westbrook than between him and Andre Robertson, a typical perimeter defensively oriented player with the 4^{th} lowest *INV Rate* out of all 355 qualified players. Involvement Rate 80.0 actually means that a player on average records 8 possession events in 10 played possessions, while he can technically record more than 1 possession event in a single possession.

Last but not least, since* Involvement Rate* measures a similar dimension of offensive game as *Usage Rate*, we would like to illustrate the relationship between those two statistics. The scatterplot below presents *Usage Rate* and *Involvement Rate* 2016/2017 regular season averages for the 10 selected players.

The relationship between *Usage* and *Involvement Rates* seems quite linear in the first sight for those 10 players, yet a closer look at the middle of the pack reveals that there is less relationship between *Usage* and *INV Rates*. E.g. in the case of our two Power Forwards, Serge Ibaka has a little higher* Usage Rate* than Draymond Green, yet the *Involvement Rate* of the second is almost 10 points higher. It is true that more analysis is required to investigate the relationship between those two indicators, however this partial results already show that our new statistics *Involvement Rate* is not a substitute, rather it represents added value to existing Usage statistics.

In the next two blog posts we will present two other newly developed statistics: (1) *Direct Offensive Contributions (DOC)* and (2) *Direct Offensive Efficiency (DOE)*, which are more or less related to *Involvement Rate*. Stick around!

From where did you get the FTAST,SAST,OPAST,2ndAST, and other statistics?

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Those stats and much more is available at:

https://stats.nba.com/players/passing/

https://stats.nba.com/players/hustle/

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