I love three things: cryptos, data, and basketball. In fact, my username "shocker" was my nickname on my basketball team in high school.

With the wrap up of the basketball season, I noticed a few things, most notably was that 3pt. shots are increasing! I fired up Tableau, SQL, and python and dove deep!

NBA players make split-second decisions. Time is a limited resource and each play must be crafted to maximize score opportunity. One of these key choices is between a comfortable 2pt. shot versus a difficult 3pt. basket. Currently, three pointers roughly account for one-third of total shots, but grow in importance as the game advances.

Number of 2pt. and 3pt. shots completed and missed by quarter

However, is this the optimal mix of shots for a team to maximize their points? When should a player forgo a 2pt. basket for a 3pt. attempt? There are several team-specific variables and factors that come into play such as player skill, timing, and risk tolerance. Generally, this decision should be driven by comparing the potential distance to the closest defender.

Number of 2pt. and 3pt. shots completed and missed by quarter

Shot margin is the likelihood that an attempted shot will score. As expected, the shot margin is higher for two pointers than three pointers. The shot margin also increases as the distance of the closest defender increases. However, this distance affects the shot margin of three pointers 20% greater than two pointers. Distance to defender is a much bigger factor for completing 3 point shots.

Description of shot margin model and calculation of expected value

Shot Margin Model - 3 Pointers:
    Slope (SIII): 0.011045
    Y-intercept (YIII): 0.285967
    R-square: 0.259866
    P-value:  0.0001

Shot Margin Model - 2 Pointers:
    Slope (SII): 0.009215
    Y-intercept (YII): 0.455385
    R-square: 0.148147
    P-value: 0.0001

Expected Value of a Shot: Point value * Shot Margin

A 2 pointer shot is inefficient if:

    the expected value of a 3 pointer shot 
        (driven by the potential distance to defender from the 3pt. shooter >- DIII) 
        
    exceeds
    
    the expected value of the 2 pointer shot 
        (driven by the current player's relative distance to the closest defender >- DII)  

Generally, if:

    3 * (SIII * DIII + YIII) > 2 * (SIII * DIII + YIII)
    The player should pass to the 3pt. shooterelement here instead.

A player for simplicity has two decisions when inside the 3pt. line: he can shoot from where he is currently standing or he can pass to a 3pt. shooter. Using the above as a decision model, scenarios can be originated where the current distance to defender and the potential distance to defender for the 3pt. shooter are taken as inputs and used to produce a shoot/pass decision. A player can use this model to determine if he should shoot or pass depending on how much distance the team can put between the 3pt shooter and the closest defender.

Decision matrix of a 2pt. shooter on whether he should attempt the 2pt shot or pass it to a 3pt. player

A player should pass the ball to a 3pt shooter if the current distance to the closest defender and the potential distance to the closest defender of a 3pt. shooter places the decision in the Pass area of the chart. Over half of the 2pt. shots are attempted when a defender is 2-4ft. from the player. If the player can pass to a 3pt. player in such a way that it creates a greater than 3ft. gap between the 3pt. shooter and his closest defender, then that player should pass. Generally speaking, a player should only give up a 2pt. shot for a 3pt. shot if he is confident that the play will allow the 3pt. shooter to be atleast 5ft. away from the closest defender.

Strategy: On average, pass the ball to a 3pt. shooter if the potential distance between the 3pt. shooter and the closest defender exceeds 5ft. Perform plays where this can happen.

Average point gain for passing to a 3pt. player within the 2pt. sweet spot

Simplified estimate of expected gain from following this strategy

The expected point gain from following this strategy increases as the gap between the 3pt. shooter and his closest defender increases. In other words, if the team can craft plays that allows the distance between the 3pt. shooter and his closest defender to reach 5ft, the average expected gain is 0.02 to 0.08 points per play (assuming that the 2pt. player is currently in his sweet spot which occurs the majority of the time). Since over 70% of 3pt. attempts occur between 3-7ft, this is a realistic goal.

There are, on average, 104 2pt. attempts in a game.
                
70% of 2pt. shots occur when the distance of the closest defender is less than 4ft

For half of those shots, 
    the player can pass the ball to a 3pt. shooter and can create a distance to defender of 5ft. 
For a quarter of these shots, 
    the player can pass the ball to a 3pt. shooter and create a distance to defender of 6ft. 
Finally, for the last quarter of these shots, 
    the player can pass the ball to a 3pt. shooter and create a distance to defender of 7ft.

The average gain of passing the ball from a 2pt. player in his median sweet spot (3ft) to 
a 3pt. shooter, 
    where the distance to the closest defender is 5ft, is 0.06
    where the distance to the closest defender is 5ft, is 0.09 
    where the distance to the closest defender is 5ft, is 0.13 

Expected Gain per Game = [104 * 70%] * 50% * 0.06 + [104 * 70%] * 25% * 0.09 + [104 * 70%] * 25% * 0.13

Expected Gain per Game = 6.2 points

Note: Conservative estimate. This is the expected gain if 
    (1) the strategy is only followed by 70% of 2pt. non-dunk plays 
        (not followed by 2pt. players whose distance exceeds 4ft),
    (2) the strategy only goes one-way from 2pt. shooters to 3pt. shooters 
        (expected gain would increase if 3pt. shooters employed the strategy),
    (3) there is no increase in shot margin of 3pt. shots 
        (it is expected that more 3pt. practice would increase margin), and
    (4) the 2pt. plays occur at the median sweet spot of 3ft 
        (whereas many plays occur when the defender is at 0-3ft)

The simplified expected gain (see Note above) from following this strategy is an addition of 6 points. This is a conservative estimate as it does not imply this strategy is used in 100% of the situations (2pt. shooters where defender distance exceeds 4ft and passing from 3pt. shooters to 2pt. shooters), assumes that 70% of 2pt. shooters can always reach a defender distance of atleast 3ft, and there is no improvement in 3pt shot margins.

Is this strategy relevant if it only produces a simplified yield of 6 points? Approximately 30% of the 2015-16 NBA playoff games had a point differential of 6 or less.