The study at Lin Qi's mansion in the suburbs of Boston.
In late September in New England, night rain pattered against the heavy lattice windows. The pine embers in the fireplace burned steadily, and the air was filled with the subtle aroma of roasted pine resin and the scent of hot black coffee.
The Celtics just finished their Europe training tour and returned to Boston three days ago. There is still a short break before the official start of the preseason training camp in early October, but head coach Rick Carlisle has already gotten to work.
At 9:30 p. m., the doorbell rang.
Rick Carlisle took off his rain-soaked coat and hung it on the porch, then, with a thick, dark blue folder tucked under his arm, went into his study.
"Just came from the Auerbach Center?" Lin Qi looked up from behind his desk, pen in hand, with design drawings of Converse's new North America product line spread out in front of him.
"I spent the whole day in a tactical analysis meeting with those young guys in the uniform department." Rick Carlisle pulled out his high-backed chair and sat down, his expression showing the weariness of deep thought. He picked up the black coffee Lin Qi handed him and took a big gulp, his tense brow relaxing slightly.
Rick Carlisle laid the folder in his hand flat on the table.
On top of the folder was a slightly folded paperback book, Michael Lewis's "Moneyball: The Art of Winning Against All Odds," published in May of this year and currently generating heated discussion among sports management across the United States.
Below the book is a 35-page technical report with a bookish title on the cover, "Reshaping Offensive Efficiency Based on the League's Underlying Data System: On Maximizing Spacing and Eliminating Inefficient Shots."
"This report was spearheaded by the Massachusetts Institute of Technology operations research master's student recommended by Jeff ( Sagarin )."
Rick Carlisle tapped his finger on the report cover, his tone calm but his expression complex. "It's not just them. When David Stern hosted the new season's general manager summit in New York, he touted the basic data system you entrusted to the league as an industry benchmark. Mark Cuban of Dallas publicly stated in the Dallas Morning News last week that the future of basketball competition is essentially a competition of algorithms and mathematics. In Houston, several Ivy League youngsters who were just hired as consultants are also trying to sell Shai Gilgeous-Alexander a similar team-building logic. The whole league is talking about Billy Bean of the Oakland Athletics, as if victory can be directly derived simply by distributing the ball according to a formula."
Rick Carlisle turned to page twelve of the report and shoved a half-court shot distribution heatmap in front of Lin Qi.
"Take a look at the data they compiled, Lin."
Rick Carlisle pointed to the coordinates on the chart. "In a large sample of 82 regular season games, the average expected score for a mid-range jump shot between 14 feet and the three-point line is only 0.82 points. However, inside the paint and outside the three-point lines at the corners, due to the higher true shooting percentage and the weighting of three-pointers, the expected score for each shot is over 1.15 points."
Rick Carlisle paused for a moment, then continued.
Their core advice was straightforward: aside from cuts to the basket, fast breaks, and corner threes, the team should significantly reduce Kevin ( Garnett )'s post-up moves in the left and right elbow areas, limit Chris Paul ( Pierce )'s step-back mid-range jumpers on the wings, and concentrate the team's shooting attempts in the paint and on the perimeter. They called this logic 'absolute rationality,' believing that the mid-range shot is the biggest mistake in modern basketball offense.
Rick Carlisle looked up at Lin Qi.
"Lin, this sounds all too familiar to us."
Rick Carlisle rubbed his temples and candidly reflected, "For a long time, I also firmly believed that basketball could ultimately be fully explained by probability theory and the law of large numbers. As long as there are enough rounds in a game, mathematical laws will eliminate all irrationality."
At this point, Rick Carlisle's breathing became slightly heavier.
"However, after the NBA Finals at Staples Center this June, when I looked at that report again, my thinking completely changed. My intuition told me that if we follow the mathematical formula on paper to plan our offense in the new season, we will not only fail to win the championship, but we will also encounter great trouble in the playoffs."
After listening to Rick Carlisle's words, Lin Qi didn't look at the report; he simply put down his teacup, looking quite composed.
" Rick, the fact that you have this question shows that you're starting to move beyond simply believing in data."
Lin Qi leaned back in his chair, his tone calm. "Because you've finally seen the boundaries of statistics in professional sports. We've gained an advantage in the past by relying on data, but that doesn't mean data itself can directly serve as a tactical tool on the field."
Lin Qi stood up and walked to the whiteboard hanging on the other side of the study. There were still a few simple running lines on the whiteboard. He picked up a pen and drew a horizontal line in the center of the whiteboard.
" Michael Lewis wrote a good book, and Billy Bean did an excellent job in baseball. But right now, the entire league's management is making a fundamental mistake: they're trying to apply baseball's statistical logic to basketball."
Lin Qi used chalk to dot several scattered, isolated dots on the horizontal line.
"Baseball is a discrete sport. Each at-bat is an independent, static contest. When the batter steps into the batter's box, the nine defenders can only stand in roughly the prescribed defensive positions. No matter how fast the pitcher's ball is, they cannot disrupt the batter's swing through direct physical Crash. There is no immediate, continuous physical entanglement between offense and defense. Therefore, Billy Bean can calculate on-base percentage and slugging percentage because the defense cannot dynamically adjust to compress the strike zone from a nine-square grid into a single point."
"But basketball is not baseball. Basketball is a highly continuous fluid sport, full of instant confrontation and dynamic game."
"On a basketball court, space is not a fixed geometric shape. It is flexible and can contract or expand at any time as defensive players move, interfere, and rotate in help defense."
"The data analyst who wrote this report only remembered the premise of the law of large numbers, but ignored the limitations of its application scenarios."
The law of large numbers relies on two fundamental assumptions: first, the sample size is large enough; second, the external conditions of the system are in a relatively stable equilibrium state.
"In 82 regular season games, facing opponents of varying skill levels, and against many teams with loose defensive discipline and no targeted rotations, the law of large numbers did indeed come into play. The expected value of open corner three-pointers and cuts to the basket consistently remained above 1.15 points. Relying on this style of play that pursues extreme efficiency, a team with mediocre talent could achieve 55 or even 60 wins in the regular season, playing very attractively under normal defensive conditions."
Lin Qi's voice turned somber.
"But what about the playoffs?"
"When only two teams remain in the world, when the video analysts of both sides have spent two whole weeks studying the dribbling habits, passing preferences, and defensive weaknesses of each of their starting players, when the game enters the high-intensity, do-or-die moments, the large sample size from the regular season simply disappears."
"In the final two or three minutes of the fourth quarter, with the score difference within two or three points, both sides only had a mere five or six offensive possessions to execute. At this microscale, the sample size has shrunk from tens of thousands of possessions to just a few individual events."
Lin Qi walked to the table and looked at Rick Carlisle: "Back then, the expected value of the law of large numbers was practically meaningless..."