Stations of the Court, part 4: Streaks
I made 13 consecutive shots today. I was in the middle of my ritual, starting the sequence in which I make a basketball move to my right (head fake, ball fake, shoulder fake - chef’s choice), then pivot left, elevate, and shoot. I started as usual in the low post position, and moved through my usual progression, and all the way around without a miss. Holy smokes, eight in a row - never done that before! Without pausing I started the next sequence, in which I fake left, then pivot right and shoot. Another make, then another, and another. I made both free throws, too, but my high post shot rimmed out, and the streak was over.
This is extremely unusual. I have done this routine in various forms for many years, and never managed a streak longer than six. To make 13 is stunning, because you are dealing with an exponentiating series. If you make 50% of your shots, it’s pretty common to make three in a row: 0.5 x 0.5 x 0.5 = 0.125. But one of those next ten attempts will kill you. The chances of making 13 in a row, before you take the first shot, are 0.5^13, or about one in ten thousand.
That’s a rough approximation. Astute readers will note that my shots vary in difficulty. So I have estimated my shooting percentage from each spot, then charted the probability of a streak from the first shot of the ritual to the last. As you can see from the chart (note log scale), the odds of making the first shot are about 60% (I’m good at the one), but after that the exponentiation gets kind of rough. The probability of a streak of 13 from the start still about one in ten thousand:
The odds of making all 48 shots without a miss? About one in 92 trillion, so careful betting on that one:
So what happened there? Did I get hot, or was it just my lucky day? I’m not sure myself.
The answer’s more complicated than we used to think. Until fairly recently, statisticians viewed the hot hand as a cognitive illusion. It’s a big world and there are a lot of basketball players, they reasoned, so unusual things will happen fairly routinely. Someone was going to make 13 consecutive baskets today, it just turned out to be me. Wikipedia has a nice article on this, including a good discussion of the canonical 1985 paper by Gilovich, Tversky, and Vallone, which concluded that shooting streaks in basketball were basically down to chance.
But modern research is questioning that view. Not before time, because it’s obviously wrong. If you assume, as most analysts do, that the underlying frequency distribution never changes, then of course all variation will be attributable to random chance. But that’s crazy. Steph Curry’s going to score fewer points if Kawhi Leonard is guarding him, and more if I’m guarding him. He’s going to feel better some days, and worse on others. The underlying distribution is changing all the time.
The great J.R. Smith, who wrapped up a 16-year NBA career in 2020, was one of the great streak shooters. His career statistics are good, but not exceptionally so: he launched about seven three point attempts per 36 minutes, making 37% of them (Steph Curry: 9, 43%). But there were times when Smith entered the zone, and viewing this I cannot fault his teammates for passing him the ball:
The ultimate avatar of the hot hand is Klay Thompson, who once got so hot that his teammates refused to shoot, passing him the ball on every possession. This resulted in Thompson scoring 37 points in 12 minutes, the most by a player in a quarter in the history of the Association:
Thompson made 13 consecutive shots (same as me!) during this adventure, nine of them three-pointers. “Get Klay Thompson the ball” cried announcer Bob Fitzgerald, and the Warriors, unburdened by fears of mean regression or cognitive error, obliged.
I would be the first to acknowledge that this sort of thing doesn’t happen very often, and that Thompson benefited from a lucky bounce or two. But I suspect it would be difficult to find members of the Kings who would accept that these events were due primarily to cognitive social bias. Witchcraft? Possibly. Extraterrestial genetics? Plausible. But no one who witnessed that quarter would accepts that Klay Thompson was “just lucky”.
The dark side of the streak is the slump. In 2019 Baltimore Orioles first baseman Chris Davis broke out of the worst batting slump in Major League history, an 0-54 that spanned parts of two seasons. Statisticians may differ, but professional baseball players will tell you that while luck plays a role in a slump, it also affects the batter’s abilities. It preys on his mind and saps his confidence. Distractions increase: Your own fans boo. Well-intentioned friends and relatives offer batting tips. Reporters (it’s their job) ask for fresh insights after each futile outing.
Breaking out entails more than just waiting for your luck to turn. In many cases, a psychological adjustment is required. "You have to embrace it at some point,'" Davis said, shortly before his drought ended. When he finally broke the string he asked for the game ball, and got it. After all, he had defeated the toughest opponent in the game: himself.
Slumps are lonely. The world loves a winner, but its view of the slumping athlete is more complicated. We react in contradictory ways – disappointment and distancing, but also sympathy and support. As we struggle with our own response, the athlete is on an island. He is the only one who truly has to live with the consequences. Everyone is replaceable in pro sports. If the athlete is going to fail we’ll be sad, but there will be others.
The professional golfer is the epitome of loneliness. Standing at the tee, everyone is even, the score reads zero. There’s no pitcher trying to trick you, no athletic defenders trying to block your shot. It’s just you and the ball, and you face exactly the same conditions - course, wind, and weather - as everybody else. The only variable that matters is your performance.
There are certainly some interesting situations to study. My middle-aged heart thrills to memory of 46 year-old Jack Nicklaus storming down the last ten holes at Augusta, breaking out of the pack with a flurry of birdies, and an eagle thrown in for good measure:
Source: Wikipedia
And, as that was happening: Seve Ballesteros and Greg Norman self-destructing, allowing Nicklaus to win outright.
The average golf hole is designed to give the player an even chance - a scratch golfer should be able to make par, a birdie on a good day, a bogey on a bad one. That underlying fairness is the essence of the game. They do make the holes tougher in pro tournaments, rewarding players who can manage difficult risks, and punishing those prone to overconfidence. But even in professional tournaments a given hole offers a normal spectrum of outcomes, with due rewards for risks successfully taken.
And then there is the Road Hole.
The 17th at St. Andrews, the infamous ‘Road Hole’ - Image Source
The penultimate stop on the Old Course at St. Andrews, the par four Road Hole yields far more bogies than birdies. Writing in 1984, The Washington Post’s Thomas Boswell called it “the hardest hole on earth.” After the difficult tee shot and approach, one faces Scylla and Charybdis. There is the all-devouring Road Bunker in front, and behind the green there is an actual road, backed by a stone fence. According to Boswell,
[p]itching over the Road Hole bunker is an advanced form of golf torture. Dump it in the trap and you may have to playout sideways. Go a few feet past the pin and you slip down a sharp hill and onto the stony road itself.
The bunker is also known as “The Sands of Nakajima”, in memory of the Japanese golfer who in 1977, following a nice drive and approach, met with catastrophe. Boswell’s account:
Nakajima's first putt took a left-hand turn and trickled into the Road Bunker. Fearing that he might blast over the green, over the road and over a low stone wall out of bounds (a realistic possibility), Nakajima swung too tenderly. And left the ball in the bunker. Twice.
His third blast escaped the sand. His chip reached the green. Two little putts and a quintuple bogey. Easy.
I have experienced my own version of the Road Hole in my workouts, although unlike the golfer at St. Andrews, I never know when I might encounter it. I’ll be going along and suddenly my ability to put the ball in the basket completely deserts me, my attempts as scattered as they were on my first day of basketball camp in 1973. I miss, one, two, three, four shots, and start to wonder what the hell is wrong. I slow down. I check my form. I remind myself to maintain good eye discipline (back of the rim, nowhere else) and footwork (feet shoulder-width apart). I focus on my follow-through. All of this usually makes things worse. More often than not, I end up chasing the ball the length of the court and crawling into the bushes to retrieve it.
On the way back my mind often wanders. Sometimes I’ll casually bring the ball up and, with hardly a thought, throw it in the basket. That makes one. A new streak - and the rest of my life - begins.