Quantitative and Qualitative Values
I’ve been working hard to get clear on the differences between quantitative and qualitative values lately.
Here’s an example:
If I want to improve my GPA, that’s basically a math problem. I should take easy classes. No need to do more than the bare minimum for an A.
If I want to improve my education, that’s much more complicated, because good education can’t be captured by a single metric. A good education traffics in a ton of different values: crystallized knowledge, practiced skills, intellectual virtues, transformative experiences…
(Notice that trying to optimize my GPA actually seems antithetical to my education...weird!)
GPA is a quantitative value.
And when we consider value as a quantity, we reason in the language of math. To be effective calculators, we have to ask: How big can we make this number?
Education is a qualitative value.
But when we consider value as a quality, we reason in the language of criticism. (As in art criticism, not mean-spiritedness.) To be wise judges, we have to ask: How alive can we be to our many different values and how they interact?
Okay, that’s a pretty good first pass. But what’s the relationship between quantitative and qualitative values? Is one just better than the other?
Not exactly. But to dive in, you’ll be shocked to hear that I wanna take a trip to the Naismith Memorial Basketball Hall of Fame.
We start out with a deeply qualitative question: How would you tell the history of basketball? Well I guess you have to start with James B. Naismith who hangs up the first peach basket and eventually make your way to LeBron James and Nikola Jokic. But we don’t have to talk about every last benchwarmer, do we? We just want to grab all the players (and coaches, and referees, and announcers, and commissioners…) who are essential to that story. So now it’s 1959 and you’re going, wait a minute. We need a way to remember the truly great figures in the history of basketball, the best of the best, like 6-foot-10 George Mikan who became a bruising big man and five-time champ instead of a Catholic priest. We gotta make a Hall of Fame class. And that means we need to ask a slightly different question: Who do we need to discuss if we’re going to tell the history of basketball? Notice that this question, while still deeply qualitative, does begin to sort everyone into one of two camps: You’re either in the Hall of Fame, or you’re not. There’s still a deeply qualitative threshold, but we are pushed towards more binary thinking. But after decades of seeing how Hall of Fame voters evaluate players’ careers, we can put together a statistical model to answer the following question: Do this guy’s statistics and awards look like a Hall of Fame résumé? And we can rank players based on the “Hall of Fame probability” our model spits out:
Here’s the full list. Well, we finally settled it: Kareem is the Greatest of All Time (GOAT), as settled by the implicit correlations between the selections of anonymous Hall of Fame voters over the years and players’ statistical achievements and accolades (as massaged by our inevitable choices as statistical modelers). So what do we do with this number? Well, I’ve already hinted at the fact that choices about how to make this model are not themselves quantitative questions. Check out this quote from basketball-reference explaining how the model was built:
Our player pool includes players who have played a minimum of 400 NBA games and were retired by the end of the 2004-05 season, so that they've had several years to be considered. We excluded players that spent significant time in the ABA. As well, from the list of current Hall of Famers we excluded players with fewer than 50 Win Shares. The reasoning here is that the media and likely voters are more attuned to statistical output, however refined, than they were through the 1980s. There are players that have been inducted in the past that aren't necessarily predictive of future inductions.
So this model is much more quantitative than where we started, but it isn’t quantitative through-and-through, and it really couldn’t be. After all, “indispensability to the history of basketball” isn’t quantitatively measurable or maximizable, any more than “shiftiness” is on the court, or “shrillness” is at a jazz concert. That’s just not how our words work. And we don’t really want them to work that way, either. Our words capture value in deeply qualitative terms that quantitative analysis couldn’t replace without gross distortion. Let me be clear: This Hall of Fame probability is a very cool metric. But even if the quantified language is nice to have in addition, its interest depends on its qualitative value for us. Three quick case studies to make this clear:
Dwight Howard (99.73% HoF probability)
8x All-NBA center Dwight Howard’s statistical case for the Hall of Fame is bulletproof. Even if Shaq is the real Superman, Dwight’s the only truly dominant American big we’ve seen come through in the twenty-first century. He won three defensive Player of the Year awards in a row, and in 2009 he made the Finals by knocking off LeBron (who was having arguably the most statistically dominant playoff series ever). But then Dwight wanted his coach fired, and things got really awkward in the media. And then he got chronically hurt. And then he wanted out of different teams again and again and again. He ended up winning a ring with the Lakers in 2020 once he matured a little and accepted being a role player. But voters still think of him as a bad locker room presence, and they kept him off the NBA’s 75th Anniversary Team. Note that those concerns from voters are basically qualitative in nature. But 99.73% reminds us just how strong Dwight’s case for the Hall is, even if the media has thoroughly turned against him. Does he really only have a 1 in 400 chance of being snubbed again? I don’t know—he might have to wait a while. But for all his flaws and limitations, hopefully we can eventually come to terms with how great Dwight Howard really was. In Dwight’s case, it’s nice to begin his case for the Hall from that statistical baseline.
Blake Griffin (54.81% HoF probability)
Does 5x All-NBA power forward Blake Griffin belong in the Hall? Best known for coming up short in the playoffs with the Clippers and being forced to (sort of) jump over the hood of a Kia Optima in the dunk contest, Blake is the most violent slam dunker of all time. Repeated apologies to Pau Gasol’s face (skip to 4:30):
So does Griffin belong? Well statistically, it’s nice to know his résumé is basically a push. So set playoff expectations and meltdowns aside. The question becomes: What’s Blake’s impact on the development and trajectory of the game? Here the quantitative Hall of Fame probability can help us set aside less interesting questions (Is six all-star appearances really enough?) and refocus on more pressing ones (Could we really tell the story of the 2010s without watching this hyperathletic power forward have to develop increasingly diverse perimeter skills?)
Andre Iguodala (12.69% HoF probability)
So he probably shouldn’t have won Finals MVP, and he was only a one-time All-Star. But it was Iguodala whose selflessness and two-way versatility unlocked the Death Lineup (and eventually, the Hampton Five) that powered the Golden State Warriors at their peak. Iguodala was at the heart of arguably the most unstoppable teams of all time. Death Beam aside, I doubt he’ll make the Hall, but I do think Andre Iguodala has a real case! And of course that case goes beyond his statistics. We don’t want an algorithm to determine who goes into the Hall anyway. But the numbers can help us have more considered conversations. And that’s what we’ve seen: The quantitative value of Hall of Fame probability can drive a whole lot of really rich qualitative conversations about what we value in telling the history of basketball. But the number on its own doesn’t really matter; it’s only interesting insofar as it reflects and informs these deeper, qualitative conversations. Of course, there are plenty of other players to discuss: Kyrie Irving (93.45%), Joe Johnson (50.56%), Derrick Rose (10.52%)… It’s a cool list! Go check it out.