Introducing the “Overall Shooting Percentage” Metric
By Jack Van Deventer • August 18, 2021
Introduction: Shooting precision is a huge part of basketball. A team’s probability of winning increases dramatically with shooting efficiency. But what is the best way to monitor shooting accuracy using a single metric, given that shots may be worth 1, 2, or 3 points? This paper introduces Overall Shooting Percentage (OS%) as a more accurate representation of shooting effectiveness in basketball.
Current Options for Shooting Percentage are Inadequate. There are 3 commonly used shooting metrics: Field Goal Percentage (FG%), Effective Field Goal Percentage (eFG%), and True Shooting Percentage (TS%). FG% fails to consider the balance of 2-point and 3-point shots, and it leaves free throws out entirely. eFG% is an excellent metric for shots from the field but again, it fails to consider free throws. TS% is an attempt to consider free throws together with 2- and 3-point shots, but TS% fails to use real free throw data and instead substitutes a “magic number” multiplier of 0.44 in its formula as a generalized approximation. Failure to use actual data is a notable weakness. (Wikipedia and others are right to issue cautions.) Given these limitations, coaches currently lack shooting efficiency insights by which to optimize team performance. Overall Shooting Percentage (OS%) was developed at BasketballScience.Net to meet this need.
Factors to Consider in an Overall Shooting Metric
Weighting by Point Value - Since basketball shots can be worth 1, 2, or 3 points, we want to weight them accordingly. It would be nice if we could just add the percentages for free throws, 2-point shots, and 3-point shots and then divide by 3, but it’s not that easy. Proper weighting requires that we consider the proportions of each shot value (shots made and shots attempted for each of 3 shot types). This is critical for achieving an accurate metric.
Functional Equivalence in Shooting – Additionally, we need to recognize and accommodate the point disparity between 2- and 3-point shots, in particular. If my team takes 30 2-point shots and makes 15 of them, then my team has scored 30 points by shooting with 50% accuracy. On the other hand, if my team takes 30 3-point shots and makes 10 of them, I likewise have scored 30 points but this time on only 33.3% shooting. A common technique in basketball is to use the “2-point percentage” as the standard for judging shooting precision. To make 3-point percentage similar, we make an adjustment by multiplying the 3-point percentage by 1.5. So, 33.3% x 1.5 = 50%. This is a way of saying that 33.3% shooting from 3-point range is functionally equivalent (in terms of point production) to 50% shooting from 2-point range.
The Basic Concept
For each shot type (free throw, 2-point, 3-point) I want to get the ratio of each such that I divide points scored by the “potential points scored” for each type. Doing this provides the proper weighting by shot value. This is NOT the final formula, but the concept looks like this:
Conceptual Calculation = (PTS1 + PTS2 + PTS3) / (FTA*1 + 2PA*2 + 3PA*3)
Where PTS1 = points from free throws, PTS2 = points from 2-point shots, and PTS3 = points from 3-point shots.
FTA = number of free throw attempts, 2PA = number of 2-point shot attempts, and 3PA = number of 3-point shot attempts.
The Final Formula for Overall Shooting Percentage (OS%)
In the conceptual calculation above, I’ll make a simple change to achieve functional equivalence for 2- and 3-point shots:
If I multiply “3PA” in the denominator by 2/3, this is mathematically the same as multiplying 1.5 times the 3P%. (I’ll spare you the math here, but it really is the same.) The nearly complete (but not fully simplified) formula, looks like this:
OS% interim = PTS / (FTA*1 + 2PA*2 + 3PA*3*2/3)
I’ll simplify the equation, and the FINAL FORMULA now looks like this:
OS% = PTS / (2 * FGA + FTA)
Where PTS = total points, FTA = number of free throw attempts, and FGA = number of field goal attempts (2- and 3-point attempts).
The algebra to get here is complex, yet the end result is a rather simple formula. It achieves the proper weighting by shot type and accomplishes the functional equivalence so that 3-point percentage is adjusted to the 2-point percentage scale as discussed above.
An Example Using Overall Shooting Percentage
A team shoots the following:
10 of 30 from 3-point range: 30 points.
18 of 30 from 2-point range: 36 points.
14 of 20 from the free throw line: 14 points.
OS% = (30 + 36 + 14) / (2 * (30 + 30) + 20) = 80 / 140 = 57.1%
Explaining the Math in Chart Form
The formula above is all you need for calculating the Overall Shooting Percentage. The narrative below is designed to shed light on the mathematical principles involved.
See the table below. For each of the 3 shot types, I want to add up the 2 right-most columns, (1) Points Made and (2) Points Possible, where the latter is the number of points if I had made 100% of my shots. Note that in Column D I use “adjusted” shot attempts. The only difference between Columns C and D is that for 3-point attempts, I’ve multiplied 3‑point shot attempts by 2/3 to create the “2-point percentage” standard.
I get my OS% by taking 80/140 = 57.1%.
Graphical Presentation of the Math
The following chart visually illustrates the contributions to the OS% from shooting 3-point shots, 2-point shots, and free‑throws. It uses the values from the table above.
Notes:
1. 3PM = number of 3-point shots made, 2PM = number of 2-point shots made, FTM = number of free throws made.
2. The slope of each line segment (orange dashed lines) corresponds exactly to shooting percentages for 3-pointers (50%), 2-pointers (60%), and free throws (70%).
3. Notice how the chart shows the “weighting” impact by shot type point value.
4. The computational goal is to identify the upper-right endpoint, representing the overall slope for all 3 shot types. Imagine a line extending from the origin (0, 0) to the end point (140, 80). This line’s slope is the OS%, the Y-value divided by the X-value = 80/140 = 57.1%.
5. For confirmation, the Overall Shooting Percentage calculation is as follows, with a slight algebraic rearrangement that mirrors the graphical process above:
Observations
Overall Shooting Percentage (OS%) uses the exact same weighting of 2- and 3-point shots as the very popular Effective Field Goal Percentage (eFG%) metric. Therefore, in the case of an OS% calculation (e.g., for an individual player) where there are no free throw attempts, the results will be identical to the eFG%. This is by design. OS% is mathematically an extension of eFG% that includes free throws (if and when they exist).
Testing shows that OS% calculations are generally higher than eFG% calculations. This makes sense because OS% includes free throw percentages which are normally higher than field goal percentages, even if they make up a smaller percentage of total points in the overall score. Also, as with eFG%, it is possible for a player who makes a very high percentage of 3-point shots (e.g., 5 of 5) to have a shooting percentage greater than 100%. Again, this is by design and results from the fact that 3-point shooting percentage is multiplied by 1.5, as per the discussion above.
Lastly, True Shooting Percentage (TS%) scores are often higher than OS%, and this is an anomaly resulting from the questionable approximation of the 0.44 multiplier in TS% metric.
Competitive Advantage of OS%
Here’s a chart that summarizes the advantages of OS% and the limitations of the alternatives.
Conclusion
The Overall Shooting Percentage (OS%) calculation is a metric that is simple, precise, and honest. It is an improvement over existing metrics by encompassing all shot types in their proper proportions. Additionally, OS% has the advantage of using actual game data. These features enable coaches, players, and even Fantasy Basketball participants to have shooting insights into the game that lead to increased victories on the court.
At BasketballScience.Net we generate advanced statistical assessments of teams, opponents, and players.
Those analytics include Overall Shooting Percentage.
