Human obsession with round numbers occupies a curious corner of psychological study. It’s a phenomenon that dates back millennia, with applications in some of the most visible areas of history. If they were called the Nine Commandments, would they occupy quite the same level of historical significance?
Research suggests the answer is no, and also tells us several other fascinating things about the mind’s desire for stability within numerical patterns.
A study at Pace University displayed a pair of digits on a screen, and asked responders to press a button in front of them only if both numbers were even or both numbers were odd, and therefore not if one was even and the other was odd. It took subjects an average of 20 percent longer to press the button when a pair of odd numbers came up compared to a pair of even numbers, suggesting what researcher Terence Hines called “the odd effect” – it literally takes the average human mind longer to process odd numbers.
In the consumer world, the effect shows a little differently. It’s well known within sales industries that prices ending in “.99” have been proven to lead to higher purchasing rates, but a 2015 study gave us more context:
Rounded prices ($100, $10, $5) are processed more fluidly by the brain, leading to more reliance on feelings and emotion within purchasing decisions. Non-rounded prices ($13.99, $199.99), though, are processed less fluidly, and therefore produce a higher subconscious reliance on cognition and reason.
Best of all, though, is the human response when we know we influence these numbers in our lives. A 2010 study found that we will exert ourselves far above normal levels to perform just above a certain round numerical threshold, rather than just below it. Professional baseball players are about four times more likely to finish with a batting average of .300 than an average of .299; high schoolers taking the SAT test are more likely to retake it if they fall just below a round number than if they fall just above one.
There’s no question the human mind carries a distinct, subconscious attachment to the emotional significance of certain numbers. These psychological roots form the basis for superstitions, laws and even life or death in some cultures. They’re deep, and they’re visible everywhere.
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Nowhere in sports is this phenomenon more obvious than with basketball’s triple-double.
The basis for this one goes back about as far as human records exist. The vast majority of human societies (with a few exceptions) have operated using a base-10 numerical system, with most psychologists in general agreement about the source: The number of fingers we have. Yep, it’s that simple.
And on its face, the triple-double is a great way to get that psychological kitten purring. Three numbers all at 10 or higher is much more powerful to the brain than just one or two, and the fact that most triple-doubles represent a distinctly positive team contribution by the player in question just reinforces the association.
Here’s the equally logical reason why our growing obsession with the stat is fundamentally flawed, though: Exactly how positive a contribution they represent is an incredibly variable factor, and there’s even evidence that certain triple-doubles do not represent a cumulative positive.
To prove it, let’s turn to the numbers.
Before John Hollinger was the Executive VP of Basketball Operation for the Memphis Grizzlies, he was a savant-like journalist/analyst who created a number of metrics. The most popular is likely PER (Player Efficiency Rating), but another that has several practical uses is Game Score.
Game Score, still housed on basketball-reference.com, is a stat designed to give a single numerical representation of a player’s statistical productivity in a single game. This is naturally a number that leans heavily toward offensive contributions, since most box score elements track offensive events (and the ones that don’t are limited indicators of defensive contributions). This is fine for triple-doubles, though, since they’re generally far more weighted to the offensive end anyway.
Using Hollinger’s Game Score, we can aggregate the 350 or so “best” NBA games played since 1983-84. Exactly 378 games have been played with a Game Score of 40 or higher, if we’re satisfying our mind’s desire for round numbers. From a statistical standpoint, nearly all of these games would rank among any objective list of the 400 or 500 best games played in this time period by a single player.
Know how many of these 378 games were triple-doubles? Twenty-one. That’s roughly 5.5 percent.
Yes, barely one in 20 of the best statistical performances over the last 30-plus years was a triple-double. These figures hold for more recent timelines. In fact, they even drop below 5 percent since 2000. If you’re ranking each of these games in order of Game Score, you have to scroll down all the way to row 22 to find the first one that was a triple-double.
Okay, so it’s not all so gloomy. Teams featuring a player recording a triple-double win about 75 percent of their games over this same time span. This is a fantastic percentage, without question.
But is an event truly worthy of jaw-dropping amazement when the team in question still loses once every four times? What about if that number drops to 55 percent when the player in question attempts at least 25 shots (it does)? What if it drops well below 50 percent when the player takes at least 25 shots, but makes 40 percent or fewer of them? Is that still a great game deserving of endless platitudes?
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If you’ve made it this far, you can probably see where this is going.
In a season where the triple-double’s Q-score has no doubt skyrocketed, Russell Westbrook has nearly become synonymous with the term. He’s set to average one, and produces the feat more regularly than we’ve ever seen in the modern era.
Let’s get one thing straight right away: This is not an indictment of Russ, or his case for the league’s biggest award. In fact, it’s the exact opposite – an indictment of the obsessive mindset that’s reduced his MVP candidacy to a single, arbitrary statistic.
It’s not Westbrook himself who brought on the obsession, either. The guy was getting sick of it three full months ago. Does he stat-chase sometimes? Absolutely. So does virtually every star (virtually every player) in the league. Does it mean he’s more focused on it than he should be? Almost certainly not.
Everyone discussing it sure is, though. Nearly every big feature written about Westbrook this season features the term in the title or the lede. A Google News search for “triple-double” yields about as many first-page results for Russ as all other players combined, depending on which day you type it in. NBATV is currently airing a show called The Art of the Triple Double, surely in no small part due to Westbrook’s charge at history.
This is selling Westbrook woefully short. Defining his ridiculous season based on such a lazy, easy crutch ignores all the more complex ways he’s dominating.
For starters, another half-dozen healthy games will give Russ a case for having completed the most physically taxing season in NBA history – and surely one of the most exhausting in the annals of modern team sports.
Before this year, just 18 guys had finished a full season using at least 35 percent of team possessions while on the floor, per basketball-reference.com. Under half managed to do so while missing fewer than 10 games, and Russ would become just the third – joining Michael Jordan and Kobe Bryant – to play all 82 while pulling this off.
He’d do it while setting the NBA record for usage percentage. He’ll have run nearly 200 miles during NBA gameplay since the beginning of the season, per SportVU figures extrapolated at his current averages.
Through this lens, his effectiveness-to-volume ratio is pure insanity. Just five of those 18 guys through history with uber-high usage figures managed a better team winning percentage than Westbrook’s Thunder are on track to post, and that’s without considering supporting casts or a cupcake schedule over the final few weeks of the year.
If you absolutely must find meaning in triple-doubles, find it in a similar team theme. Remember those figures we cited above, showing how much worse the team record in triple-doubles gets when the guy in question is chucking mercilessly?
Not with Russ. Other guys through history have won 55 percent of their triple-double games with at least 25 shots attempted; Westbrook has won 75 percent of such games this season. Many of these aren’t just chucking for chucking’s sake – the Thunder needed those ridiculously burdensome performances. Oklahoma City wins games where Russ manages a triple-double at a significantly higher rate than the league throughout history.
If you’re obsessed with unique historical numbers, all of this is barely scratching the surface. We could double the length of this article simply listing the various, volume-related statistical crevices in which Westbrook is either all alone or in short, illustrious company.
In the interest of transparency: If this pen filled out an MVP ballot, Russ wouldn’t currently occupy the top spot. He might be as low as fourth.
Anyone with a serious objection to Westbrook winning, though, either hates fun or roots for the Cavs, Spurs or Rockets. There isn’t enough separation between the top four guys, especially not when parsing out who deserves an award the NBA intentionally defines ambiguously to stoke the fire on debates like these.
If he does win, though, here’s hoping it’s due to more than a deep-seated obsession with round numbers. Ask any smart statistician, and they’ll tell you: You can prove virtually anything if you manipulate the data the right way. Using the right statistical thresholds, anyone with internet access can find several examples of how LeBron James, Kawhi Leonard and James Harden are posting historically unique seasons this year.
Westbrook deserves it as much as any of these guys, but not because his uniqueness conforms more to your brain’s natural tendencies than the others. Count this as a plea that those with a vote come April think a little better of their base nature, and look a little deeper.
Middleton, Bucks Aiming To ‘Lock In’ As Season Comes To Close
Spencer Davies catches up with Milwaukee Bucks swingman Khris Middleton in a Basketball Insiders exclusive.
Basketball Insiders had the chance to chat with Khris Middleton about the direction of the Milwaukee Bucks as the season comes to a close.
You guys won three out of four before you came into Cleveland. What was working during that stretch?
Just being us. Doing it with our defense, playing fast-paced offense. Just trying to keep teams off the three-point line. We haven’t done that. We didn’t do that [Monday] or two games ago, but it’s something we’ve just gotta get back to.
With the offense—it seems like it’s inconsistent. What do you think that’s got to do with mostly?
Just trying to do it by ourselves sometimes. Standing, keeping the ball on one side of the floor. We’re a better team when we play in a fast pace. And then also in the half court, when we move the ball from side-to-side it just opens the paint for everybody and there’s a lot more space.
For you, on both ends you’ve been ultra-aggressive here in the last couple weeks or so, does that have to do with you feeling better or is it just a mindset?
I’ve been healthy all year. Right now, it’s the end of the season. Gotta make a push. Everybody’s gotta lock in. Have to be confident, have to be aggressive. Have to do my job and that’s to shoot the ball well and to defend.
Have you changed anything with your jumper? Looking at the past couple months back-to-back, your perimeter shooting was below 32 percent. In March it’s above 45 percent.
I feel like I got a lot of great looks earlier this year. They just weren’t falling. Right now, they’re falling for me, so I have the same mindset that I had when I was missing and that’s to keep on shooting. At some point, they’re gonna go down for me.
Is knowing that every game at this point means more an extra motivator for you guys?
Definitely. We’re basically in the playoffs right now. We’re in a playoff series right now where we have to win games, we have to close out games, in order to get the seeding and to stay in the playoffs. Each game and each possession means something to us right now.
Is it disappointing to be in the position the team is in right now, or are you looking at it as, ‘If we get there, we’re going to be alright’?
I mean, we wish we were in a better position. But where we’re at right now, we’re fine with it. We want to make that last push to get higher in the seeding.
Lots of changes have gone on here. Eric Bledsoe came in two weeks into the season. You had the coaching change and lineup changes. Jabari Parker’s been getting situated before the postseason. How difficult does that make it for you guys to build consistency?
Yeah, it was tough at first. But I think early on we had to adjust on the fly. We didn’t have too many practices. There was a stretch where we were able to get in the film room, get on the court, and practice with each other more.
Now it’s just at a point where we’re adding a lot of new guys off the bench where we have to do the same things—learn on the fly, watch film. We’re not on the court as much now, but we just have to do a great job of buying in to our system, try to get to know each other.
Does this team feel like it has unfinished business based on what happened last year?
Definitely. Last year, we felt like we let one go. Toronto’s a great team. They’re having a hell of a season this year, but I feel like we let one go. This year’s a new year—a little add of extra motivation. We’ve been in the playoff position before, so hopefully, we learn from it when we go into it this year.
Would you welcome that rematch?
I mean, we welcome anybody man. We showed that we compete with any team out here. We can’t worry about other teams as much. We just have to be focused on us.
What has to happen for you guys to achieve your full potential?
Lock in. Just play as hard as we can, play unselfish, and do our job out there night-in, night-out.
NBA Daily: Raptors Look To Fine-Tune The Defense
The Toronto Raptors’ defense had a letdown against the Cavaliers, but has been outstanding overall.
The Cleveland Cavaliers and Toronto Raptors engaged in an offensive shootout on Wednesday that could be a playoff preview. The Cavs protected home court with a single-possession, 132-129 victory. Afterward, the Raptors spoke about the types of defensive adjustments the team needs to make as the postseason rapidly approaches.
“That’s how a playoff game would be,” said DeMar DeRozan, who missed a three at the buzzer that could have forced overtime. “This is a team we’ve been playing against the last two years in the postseason. Understanding how we can tighten up things defensively, how to make things tougher for them [is key].
“[It’s] little small things that go a long way, and not just with them … with every team.”
Raptors coach Dwane Casey concurred with DeRozan that fine-tuning of the defense is needed. He also pointed out that, with young contributors such as center Jakob Poeltl and power forward Pascal Siakam on the roster, defensive experience against the league’s best player, LeBron James, is something they will have to gain on the fly.
“I don’t think Jakob Poeltl played against him that much, and Siakam,” said Casey. “This is their first time seeing it. I thought Jak and Pascal did an excellent job, but there are certain situations where they’ve got to read and understand what the other team is trying to do to them.”
Poeltl was outstanding, leading the bench with 17 points and tying for the team lead in rebounds with eight. Casey praised the diversity of his contributions.
“I thought he did an excellent job of rolling, finishing, finding people,” said Casey. “I thought defensively, he did a good job of protecting the paint, going vertical. So I liked what he was giving us, especially his defense against Kevin Love.”
Basketball Insiders previously noted how the Raptors have performed vastly better as a team this season when starting point guard Kyle Lowry is out of the game. Much of that is due to Fred VanVleet’s emergence as one of the NBA’s best reserve point guards. VanVleet scored 16 points with five assists and no turnovers against Cleveland. It’s also a reflection of how good Toronto’s perimeter defense has been up and down the roster.
According to ESPN’s defensive Real Plus-Minus statistic, three of the NBA’s top 15 defensive point guards play for the Raptors. VanVleet ranks seventh while Lowry is 12th and Delon Wright is 14th. Starting small forward OG Anunoby ranks 16th at his position.
The Raptors also rank in the top five in offensive efficiency (third) and defensive efficiency (fifth). Having established an identity as a defensive team, especially on the perimeter, it’s perhaps understandable that Lowry was the one player in the visiting locker room who took the sub-standard defensive showing personally.
“It was a disgraceful display of defense by us and we’ve got to be better than that,” said Lowry. “We’ve got to be more physical. They picked us apart and made a lot of threes. We’ve got to find a way to be a better defensive team.”
Lowry continued the theme of fine-tuning as the regular season winds down.
“I think we’ve just got to make adjustments on the fly as a team,” said Lowry. “We can score with the best of them, but they outscored us tonight. We got what we wanted offensively. We’re one of the top teams in scoring in the league, but we’re also a good defensive team.”
Lowry was clearly bothered by Toronto’s defensive showing, but Casey downplayed the importance of a single regular-season game.
“We’ve got to take these games and learn from them, and again learn from the situations where we have to be disciplined,” said Casey. “It’s not a huge thing. It’s situations where we are that we’ve got to learn from and be disciplined and not maybe take this step and over-help here. Because a team like that and a passer like James will make you pay.”
While the Raptors continue to gain experience and dial in the fine defensive details, Casey was insistent that his players should not hang their heads over falling short against Cleveland.
“Hopefully our guys understand that we’re right there,” said Casey.
The Raptors host the Brooklyn Nets tonight to open a three-game home stand that includes visits from the Clippers Sunday and the Nuggets Tuesday. After that, Toronto visits the Celtics March 31 followed by a return to Cleveland April 3 and a home game against Boston the next night. With three games in a row against the other two top-three teams in the East, the schedule presents plenty of opportunities for the Raptors to add defensive polish before the playoffs begin.
NBA Daily: Jaylen Brown Set To Return For Celtics
The Celtics finally got some good news on Thursday. Jaylen Brown’s return is imminent.
Finally, some good news for the Boston Celtics.
Jaylen Brown is set to return to action.
Brown has been M.I.A. since sustaining a concussion during the team’s 117-109 victory over the Minnesota Timberwolves back on March 8, but has traveled with the team to Portland and is expecting to return to the lineup on Sunday when the Celtics do battle with the Sacramento Kings.
As the Celts gear up for a playoff run, which they hope will result in them ending LeBron James’ reign atop the Eastern Conference, they’ve picked the wrong time to run into injury issues. Along with Brown, both Kyrie Irving and Marcus Smart have each been conspicuous by their absences, and the team could certainly use all of their pieces as they attempt to enter the postseason on a high note.
Fortunately for Boston, with the Toronto Raptors leading them by 4.5 games in the standings and the Celts ahead of the Cleveland Cavaliers by a comfortable six games, Brad Stevens’ team is enjoying the rare situation of having a playoff seed that appears to be somewhat locked in.
Still, with the team only able to go as far as its young rotation will carry it, Brown addressed the media on Thursday.
“I’m feeling a lot better. I’m just trying to hurry up and get back,” Brown said, as quoted by Celtics.com.
“I’m tired of not playing.”
Stevens is probably tired of him not playing, too.
As we head into the month of April, playoff-bound teams and conference contenders begin to think about playing into June, while the cellar-dwellers and pretenders begin to look toward the draft lottery and free agency.
What’s funny is that in the midst of the Raptors and their rise out East, the Celtics and their dominance has become a bit of a forgotten storyline. When Gordon Hayward went down on opening night, the neophytes from the Northeast were thought to be a decent team in the making whose ceiling probably wasn’t anywhere near that of the Cavs, the Raptors and perhaps even the Washington Wizards.
Yet through it all, with the impressive growth of Jaylen Brown, impressive rookie Jayson Tatum and the rise of Irving as a franchise’s lynchpin, the Celtics stormed out the games to the tune of a a 17-3 record. What made the strong start even more impressive was the fact that the team won 16 straight games after beginning the season 0-2.
Although they weren’t able to keep up that pace, they began the month of February having gone 37-15 and turned a great many into believers. With their spry legs, team-first playing style and capable leader in Irving, the Celtics, it was thought, were a true contender in the Eastern Conference — if not the favorite.
Since then, and after experiencing injuries to some of its key cogs, the team has gone just 11-8.
In the interim, it seems that many have forgotten about the team that tantalized the Eastern Conference in the early goings of the season.
Brown’s return, in one important respect, will signify a return to Boston’s prior self.
With Marcus Smart having recently undergone surgery to repair a torn tendon in his right thumb, he is expected to be out another five weeks or so, meaning that he’ll likely miss the beginning of the postseason.
As for Irving, although reports say that his ailing knee has no structural damage, everything the Celtics hope to accomplish begins and ends with him. FOX Sports 1’s Chris Broussard believes that it’s no slam dunk that Irving returns to action this season, but he’s in the minority. This team has simply come too far to not give themselves every opportunity to compete at the highest level, so long as doing so doesn’t jeopardize the long term health of any of the franchise’s cornerstones.
Make no mistake about it, the Celtics are far from a finished product. With their nucleus intact and flexibility preserved, they will have another offseason with which to tinker with their rotation pieces and plug away at building a champion.
But here and now, with what they’ve got, the Celtics are much closer than any of us thought they would be at this point.
And on Sunday, when Jaylen Brown rejoins his team in the lineup, to the delight of the Boston faithful, the Celtics will be that much closer.