Plus-Minus and the Hot-Hand Fever: Why One Brilliant Night Proves Nothing

During a regular-season game, a bench player entered at the 18th minute, scored just 4 points, and left the floor with a plus-minus of +21. Less than ten minutes later, social media called it a “masterstroke” by the coach. I reopened my log file. In the 14 minutes he was on the floor, opponents shot 6 of 19, or 31.6%. In the 34 minutes he sat, opponents shot 38 of 71, or 53.5%. A gap of nearly 22 percentage points in the opponent’s shooting success. It sounds like ironclad evidence. But I have one unbreakable rule: before believing a number, ask how many repetitions produced it. Numbers do not lie, but they do not tell stories either. First, a little definition. The plus-minus measures the team’s point differential when a player is on the floor versus when he sits. It is one of the most quoted and most misunderstood numbers in modern basketball. At the level of a single game, it is shaped by at least four factors the player himself does not control: who is beside him, who is opposite him, the pace of the game, and plain luck on uncontested shots. Added together, you get a number that looks scientific but is really a blend of many variables. This is why I always separate two concepts: signal and noise. A sample of 19 opponent shots is noise. A season of more than two thousand minutes can be signal. But fans, and part of the media, read noise as if it were signal, then turn it into a story. In a six-month regular season, dozens of such stories are born every night, and most are forgotten before the next game tips off. The problem is not that the number is wrong. The problem is that we assign it a meaning larger than it can bear. A coach sees +21 and thinks he has found a formula. An analyst sees the same number and asks: if we repeated this a hundred times, how often would the result hold? The difference between those two readings is the entire content of this piece. Start with simple math. Suppose a team’s true shooting success rate is 35% on every attempt. Over 19 attempts, the average number of makes is 6.65. The standard deviation of this distribution is about 2.08. That means a two-shot deviation from the mean is a perfectly ordinary statistical result. When opponents shoot 6 of 19 instead of 7 of 19, no miracle occurs. The “genius” social media celebrates sits entirely within the natural range of probability. This is what I always say in meetings with a team: every coach talks about feel. I have no feel; I have standard deviation. Standard deviation does not deny intuition, it only shows intuition its own limits. One shot going in or out proves nothing. A hundred shots begin to say something. A season, with thousands of shots, is what lets me dare to bet. But there is a deeper layer here, and this is the part that forced me to rewrite my own beliefs. In 2026, three researchers published a conclusion that made the sports world believe the “hot hand” did not exist: players did not shoot better after making a shot. For more than thirty years, that conclusion was passed down as truth. In 2026, two researchers showed that the 2026 study itself contained a methodological flaw: its sample was selected in a way that quietly created bias. Once the sampling was corrected, evidence for the hot hand returned. In other words, an entire generation of hot-hand denial rested on a badly chosen sample. Data is a monastery: the less noise, the more clearly you hear something trying to speak. But a monastery can also echo the voice of the person chanting, if that person never checks how the sample was chosen. I learned this lesson the most expensive way: by believing a conclusion only because it was repeated many times. So what do I do with plus-minus? I do not throw it away; I shrink it. In my model, every player starts at an average assumption, no one better than anyone else. Every minute played is a small piece of evidence, and small evidence is only allowed to move the assumption a short distance. It takes thousands of minutes for a player to separate from the average in a trustworthy way. This sounds dry, but it mirrors how people actually learn: slowly, needing many repetitions, always doubting the first impression. With that approach, I often place two tables side by side. The first is a single game’s plus-minus. The second is the adjusted plus-minus for the whole season. They often tell opposite stories. The player who shone for one night usually slides to the middle of the table once the sample widens. The player fans call “invisible” climbs, because he does the small things that need no ball in his hands: screening, rotating, holding defensive position. Take an example large enough to talk about. In the 2026-16 season, according to official NBA data, the Golden State Warriors finished 73-9, an all-time league record. Stephen Curry made 402 three-pointers that season, a figure with no precedent. But what interests me is not the 402. It is this: watching game by game, you see the nights Curry shot 3 of 11 and the public said he was “slumping.” Widen the sample, and those nights are just noise around an unusually high mean. People look at one game to judge; I look at a whole season to understand. When a young coach tells me, “He just had the night of his life,” I smile. I touch the future with a keyboard. A night of a lifetime, in my language, is one data point. It may be the start of a trend, or it may be a coin landing heads. Only time and repetition can adjudicate. The regular season is the ideal environment for understanding why small samples deceive us, because it is long. Six months, more than eighty games, dense travel, back-to-back nights when the legs stop obeying. Under those conditions, a single game’s numbers are shaped by fitness and travel as much as by talent. I once collected data and found that teams’ three-point rates dropped markedly in the second game of a two-night set. A coach who looks only at that game will misjudge his player, then adjust the lineup on a distorted signal. The experience of 2026 taught me that context matters as much as technique. When the stands were empty, home-court advantage partly vanished, and numbers that seemed fixed had to be reread from scratch. Basketball is the same: a player who shoots well at home may simply be enjoying a familiar floor, the lighting, and the crowd, not a leap in skill. Ignore context, and you mistake a favorable condition for an ability. The counter-intuitive angle lies here: the analytics community tends to mock coaches’ intuition, yet that same community sometimes reads small samples exactly like the coaches it criticizes. It swaps the word “feel” for the word “data,” but keeps the habit of concluding too fast. I do not deny intuition; I only require it to declare its own confidence level. A coach who says “he’s got a hot hand” is not necessarily wrong. The error is turning a single observation into a rule that applies to every following game. And an analyst who says “the hot hand doesn’t exist” can also be wrong, as the history of 2026 itself proved. The blind spot belongs to neither side. It lies in both sides being reluctant to say the hardest sentence: “I don’t have enough data to know.” What I want you to carry away is not absolute skepticism, but disciplined skepticism. Absolute skepticism will make you miss real signals, which are rare and quiet. Disciplined skepticism will make you wait for enough sample before acting. In a long season, the person who waits at the right moment usually beats the person who acts at the right moment for the wrong reason. Tonight, when you watch a game and see someone shine, ask yourself: is this signal or noise. If it is noise, do not build a story around it. If it is signal, wait a few more games before believing. The next stretch of the season will answer for every commentary. And if a team changes its tactics on the strength of one such night, I will reopen my log file to see what actually happened.