Hitting the Mark: The Search for Basketball's Ideal Shot Equation
The landscape of basketball has been reshaped over the decades by the evolving strategy surrounding the 3-point shot. Since its inception, the 3-pointer has grown from a novelty into a cornerstone of offensive game plans, fundamentally altering the way the game is played at all levels. The chart below bears witness to this transformation, tracing a clear upward trajectory in the volume of 3-point attempts per game over NBA seasons.
This trend has been alredy well documented and numerous articles can be found on the internet. In the spirit of adding to this body of knowledge, we delve deeper into the theory and practice behind the rise of the long-range game.
Our exploration will dissect the elements that contribute to a winning formula in the modern era of basketball. By understanding the key factors influencing winning percentage, analyzing the shot mix—particularly the distribution between 2-pointers and 3-pointers—and trying to find the optimal mix, we aim to distill the essence of success in today’s game. It's clear that the sheer number of 3-point attempts (3PA) has a significant impact on team strategy and game outcomes however, as we will explore, the type of 3-point attempts may be even more crucial. Teams like the Houston Rockets and Golden State Warriors have not only championed the 3-point shot but have also revolutionized its strategic implementation, highlighting the critical role of shot selection and placement in securing victories.
As we continue to contribute to the ongoing conversation, we'll unpack these components, demonstrating how the 3-point shot is not just a trend but a vital piece of the puzzle in the quest for basketball excellence.
Understanding the Key Factors Influencing Winning Percentage
In our quest to unravel the mysteries of what drives success in the NBA, a thorough statistical analysis was conducted, focusing on the correlation between various team statistics and their winning percentage (WIN%) over the last 10 seasons. The findings are intriguing and offer some expected as well as some surprising insights.
As anticipated, there are strong positive correlations between WIN% and certain key statistics. Scoring more points (PTS) has a moderate positive correlation (0.38) with winning, highlighting the straightforward but crucial role of offense in securing victories. Defensive rebounds (DREB) show a stronger correlation (0.42), underscoring the importance of controlling the defensive glass to limit opponents' scoring opportunities. However, it's worth noting that offensive rebounds (OREB) show a negative correlation (-0.10) with WIN%, which might seem counterintuitive initially but could be indicative of teams missing more shots and thus having more opportunities for offensive rebounds.
The Paradox of Field Goal Attempts: Quality Over Quantity
A fascinating aspect of our analysis is the relationship between WIN% and the number of field goal attempts (FGA). Contrary to what one might expect, there is a slight negative correlation (-0.05) between the number of FGAs and WIN%. This suggests that merely increasing the number of 2pts shots taken does not necessarily lead to more wins. It underscores the importance of shot quality over quantity.
The Rising Significance of the Three-Point Shot
In contrast to the general field goal attempts, the number of three-point attempts (3PA) has a positive correlation (0.14) with WIN%. This finding aligns with the contemporary trend in basketball where the three-point shot is increasingly recognized as a crucial element of modern offenses.
The Paramount Importance of Shooting Efficiency
Most notably, the strongest correlation with WIN% comes from shooting efficiency, both from the field (FG%) and from beyond the arc (3P%). FG% has a correlation of 0.57, and 3P% is even higher at 0.59. These statistics reinforce the critical nature of not just taking shots, but making them. Efficient shooting, therefore, is paramount to a team's success.
Given the above findings, understanding the most effective shooting areas and the ideal balance between two-pointers and three-pointers will offer deeper insights into crafting winning basketball strategies. In the following sections, we’ll continue to dissect the intricacies of basketball analytics to uncover the formula for success in the NBA.
Analyzing the Shot Mix (2-Point vs. 3-Point Distribution)
The heatmap visualization below offers us a nuanced understanding of the relationship between shot distribution and winning percentage. While our initial focus was on the raw number of shot attempts (FGA and 3PA), our further analysis reveals that the volume of shots (TOT_SHOTS) has an almost negligible impact on winning, with a correlation close to zero. This finding challenges the conventional wisdom that more shooting opportunities inherently lead to more victories.
The data decisively points to the composition of shots being more influential on a team's success than the volume of shots taken. Teams with a higher proportion of three-point attempts out of their total shots (3P%_TOT_SHOTS) have a positive correlation with winning percentage, suggesting that a strategic focus on three-point shooting is more beneficial for winning games. In contrast, a greater percentage of two-point attempts (FG%_TOT_SHOTS) correlates negatively with success, indicating a strategic pivot in basketball towards the higher value of three-pointers over the traditional two-point shots.
Finding the Optimal Mix
The below heatmap provides a compelling visual representation that underscores the significance of expected values (EV) in our quest to determine the optimal shot mix for NBA teams.
EV = (FG% × FG Shot Proportion × 2) + (3P% × 3PT Shot Proportion ×3)
The concept of EV is pivotal because it encapsulates not just the likelihood of a shot being made, but also its point value. This dual consideration is crucial for understanding which shots are most conducive to winning games.
Analyzing the heatmap, it's evident that the expected value of 3-point shots (3P_EV) has a stronger correlation (0.32) with winning percentage (WIN%) compared to the expected value of 2-point shots (FG_EV), which shows a lower correlation (0.24). The total expected value (TOT_EV), a synthesis of the two, shows an even more robust correlation (0.62) with WIN%, suggesting that a balanced approach that optimizes both 2-point and 3-point attempts can be particularly effective for teams looking to enhance their winning prospects.
The stronger correlation for 3P_EV is rooted in the formula itself, which factors in the higher point value of 3-point shots (worth 3 points versus 2 for a FG), the shooting percentage from the 3-point line (3P%), and the distribution of 3-point shots within the team's overall shot selection. Given that 3P% is not dramatically lower than FG% for 2-point shots, the additional point gained from 3-pointers makes them statistically more rewarding. This insight suggests that teams should consider increasing their proportion of 3-point attempts within their offensive strategy to leverage the higher point value.
It's important to note that if we were to solve this optimization problem (optimal mix between FG and 3P) under the assumption of constant field goal percentage (FG%) and three-point percentage (3P%), the logical outcome would be a 100% allocation to three-point shots. This is because, as previously demonstrated, three-pointers inherently possess a higher expected value (EV) than two-pointers.
However, basketball is not a game of absolutes, and such an extreme allocation is impossible in reality. The distribution should be increased only to the extent that it doesn't substantially diminish the 3-point shooting percentage. The trade-off is beneficial as long as the increase in 3-point attempts doesn't lead to a decrease in 3P% that would outweigh the additional point gained per shot.
To address this challenge and provide actionable insights, we turned to historical data. By analyzing the shot distributions and performance metrics of successful teams over the years (WIN% above .500), we uncovered a compelling trend. Teams that strategically balanced their shot selection, allocating a proportion of their attempts to three-pointers falling within the 25% to 30% range, were more likely to achieve higher average total expected values (TOT_EV). This 'sweet spot' in the shot distribution reflects the real-world complexity of basketball strategy, where optimizing the mix of two-pointers and three-pointers can lead to a trend of enhanced performance.
As we've established that an optimal shot distribution falls within the 25% to 30% range for three-pointers, and recognized the practical limitation of not being able to allocate 100% of shots to three-pointers therefore, to further enhance a team's performance, the focus shifts to improving field goal percentage (FG%) and three-point percentage (3P%). The fundamental question becomes: What types of field goals (FG) and three-pointers (3P) are more likely to result in higher percentages, and how can coaches design systems that lead to these types of shots?
The Number of 3PA Matters, but the Type Might Be Even More Important
The excerpt from Kirk Goldsberry's book "SprawlBall" discusses the transformation of NBA shot selection analysis due to advanced cartography and spatial analytics. His meticulous analysis dovetails with our own above findings, the success rate of jump shots diminishes only modestly with increasing distance from the hoop. Despite only a slight variance in shooting percentages between extended 2-pointers and 3-pointers, the latter garners a significantly higher point yield (50% reward).
Source: How Mapping Shots In The NBA Changed It Forever by Kirk Goldsberry
Building upon this framework, it's advisable for teams to prioritize corner 3-pointers and layups due to their superior expected value (points per shot). Strategically, teams should implement systems that enhance the frequency of these high-value shots.
Plays like well-timed cuts to the basket can increase chances for successful layups and shots with points per shot (PPS) of theoretically more than 1.20 according on the above shots map. Hence, it is not surprising to see that cuts yield the highest points per possession (1.303 on average) among all play types so far. Since the beginning of the current NBA season, cuts are used as low as 4.6% (Portland) and as high as 9.9% (Golden State) of the time (total possessions). In addition to not rely on cuts, Portland exhibits the 23rd 3P% in the league (out of 30) despite being among the first 14 teams attempting the most 3-pointers per game.
As discussed before, even if Portand attempt a relatively higher number of 3-pointers, the poor 3P% combined with a very little reliance on cuts to the basket potentially leading to shots with high EV, can be the reason why only Memphis score less points per game on average than the Trailblazers this season (108.1, 29th).
Tactics
Basketball Immersion has conducted a concise yet insightful video breakdown showcasing how the Shanghai Sharks execute plays to create open three-point opportunities for Jimmer Fredette, a shot with a high expected value (EV). The offensive system is designed to set Fredette up for a swift three-pointer, targeting either a wing position following an initial screen or a corner shot. Of particular note in this analysis is the system's built-in response to defensive overplay. If a defender anticipates the move and obstructs Fredette’s route to the screen, the play adapts seamlessly. Fredette counters by using the screen to execute a sharp cut to the basket instead, converting the defender’s denial into an opportunity for an easy layup, which carries an even higher EV. By integrating such tactics, teams can exploit the most economically sound areas of the court, as underscored by our analysis and Goldsberry's work.
In summary, in examining the strategic evolution of basketball, our analysis confirms the increasing importance of the 3-point shot, evidenced by the rising trend in attempts over the years. Our study delves into the winning percentage's relationship with shot types, revealing that while volume matters, the efficiency and expected value (EV) of shots, especially 3-pointers, are crucial. We highlight the ‘sweet spot’ for the balance between 2- and 3-point shots, noting the higher EV of corner 3s and 2s in the restricted area. This insight into shot selection and efficiency offers teams actionable strategies to enhance their performance in the evolving game of basketball.
Disclaimer: The essence of data analysis is not to capture the entirety of the story but to piece together a narrative from the data fragments at hand. While the data utilized herein is robust and comprehensive, it's not exhaustive. Every statistical representation has its constraints. Our aim is to utilize accessible data judiciously, aiming for an honest and insightful interpretation, recognizing that there are always more layers to the story.