Nylon Calculus: Conjunction and disjunction bias in the NBA draft

One of the keys to improving decision-making in front offices is understanding the biases that impact how we perceive value. Here, we break down a major pair of biases and how they could impact the way teams scout the NBA Draft.

Projecting the NBA Draft is, at its core, a probability exercise. Players have variable outcomes with a band of possibilities, and their landing spot along that band of possibilities is impacted by an innumerably large number of factors, both controllable and uncontrollable. As a result, in order to improve the draft process, we have to have a fundamental understanding of probability, and more importantly, how humans evaluate probability. Spoiler: we suck at it.

There’s a series of known fundamental biases in handling probability in behavioral economics. Some, like the endowment effect, are already known in basketball: Teams tend to value their own assets more highly than assets that aren’t their own. In fact, we know that the trade that sent Kyle Lowry to Toronto was explicitly made because the Rockets were aware of the endowment effect, per Michael Lewis’s famous feature on Daryl Morey.

But a pair of those biases that are less often mentioned, despite possibly being the most relevant to the scouting process, is conjunction and disjunction bias. Put simply, humans tend to overestimate the probability of a set of events all happening, and we tend to underestimate the probability of any one of a set of events happening.

How do conjunction and disjunction bias apply to the NBA Draft?

For example, say you have a prospect that needs all of traits A, B, and C to develop in order to succeed, and those traits develop independently, with probabilities a, b, and c. If that’s the case, then that prospect will succeed a*b*c percent of the time. If a, b, and c are all 50 percent, then that prospect succeeds a paltry 12.5 percent of the time, even though none of the individual traits are exceedingly likely to fail on their own.

Or say you have a prospect that will succeed if any of traits D, E, and F develop, and all of those traits develop independently with probabilities d, e, and f. If that’s the case, then that prospect will succeed a + b + c – ab – ac – bc + abc = 87.5 percent of the time.

Now, that model is a drastic oversimplification for illustration’s sake. Development is not necessarily independent, and the probabilities are not usually 50/50. But the general principle will absolutely hold across any set of assumptions: When multiple things need to go right, the probabilities get really low really fast. When you only need one thing to go right, it’s likely that something will.

And fortunately for this writing, this class has a pair of players at its top that slides neatly into this kind of thinking in LaMelo Ball and Anthony Edwards.

LaMelo Ball needs a bunch of things to go right. He needs to learn how to finish through contact. He needs for his jump shot to be usable. He needs to be an average off-ball defender so that he can be hidden. He needs to improve his burst. And if any of those traits is missing, he’s probably not a good player, and it’s highly likely that some of those traits will be missing given that he ranges from bad to exceptionally bad at all of them currently.

Anthony Edwards, by comparison, only needs one of a few things to go right. This idea has been discussed in places like the Prep2Pro podcast, but essentially, if Edwards is a high-level pull-up shooter, he will be a successful NBA player. If Edwards learns to consistently use his excellent first step, he will be a successful NBA player. If Edwards learns how to consistently make the right decision within the offense, he will be a successful NBA player. He only needs one to be successful, and even though the probabilities of each of those aren’t exceptionally high when taken in disjunction, his success becomes likely.

If, then, those two are viewed without adjustment for bias as having approximately equal odds of success, it makes sense to view Ball more weakly and Edwards more strongly. If conjunction bias tells us that we’re likely to overestimate the probability of multiple things all being true, then LaMelo’s odds of success are likely overestimated. If disjunction bias tells us that we’re likely to underestimate the probability of any one thing out of multiple being true, then Anthony Edwards’ odds of success are likely underestimated.

But it doesn’t have to be those two guys or even at the top of the draft. Think about a guy like Georgios Kalaitzakis, who has the potential to be a 6-foot-7 point guard that’s a capable handler, passer, shooter, and defender. What he could be is incredibly valuable. Except there’s the problem that he has to do every single one of those in order to be successful, and the odds that he does all of them, when none of those traits are guaranteed given his inconsistency, are lower than we would naturally tend to think.

Or think about a guy like Vernon Carey. For Carey to be a relatively successful NBA player, he only needs one path out of multiple to hit. If he gets the drop coverage defense to a passable level, he’s probably an NBA player. If he expands the 3-point volume to be a credible threat, he’s probably an NBA player. If he’s enough of a passer that he can be a credible change-of-pace plodding big, that’s valuable to at least some teams. And with that many paths to success, the odds are probably more favorable that one of them will happen than we tend to instinctively think.

Now, this kind of analysis isn’t absolutely rigorous or perfectly informative. A guy like Kalaitzakis might have a 10 percent chance of being that truly valuable player, but the version of a valuable player he can be is just worth so much more than the player that Vernon Carey becomes 90 percent of the time, that it’s worth selecting Kalaitzakis earlier anyway. This effect could be mitigated by only applying the reasoning to prospects viewed similarly or not applying it in comparison based reasoning.

Further, not every player is even clear how they should be classified. Take Patrick Williams for example. He might need to become all three of a great team defender, a good off the dribble playmaker, and an above-average shooter in order to succeed. But maybe he only really needs one of those and any one will do. So is his probability of success being biased upwards or downwards?

But what this can do is inform how we advocate for players. It’s important to understand that multiple paths to success is valuable. It’s also important to understand that making large leaps in anticipating improvement or success against uncertainty across multiple areas is not necessarily strategically correct. So while it can’t be taken as an absolute, since the player with more paths to success isn’t automatically more valuable, it must form a piece of the analysis for any prospect because otherwise, the analysis comes out with error.