Nylon Calculus: The championship odds of short-lived megastars (CORP)

KANSAS CITY, MO - OCTOBER 13: Joel Embiid #21 of the Philadelphia 76ers in action during the game against the Miami Heat at Sprint Center on October 13, 2017 in Kansas City, Missouri. (Photo by Jamie Squire/Getty Images)
KANSAS CITY, MO - OCTOBER 13: Joel Embiid #21 of the Philadelphia 76ers in action during the game against the Miami Heat at Sprint Center on October 13, 2017 in Kansas City, Missouri. (Photo by Jamie Squire/Getty Images) /
championship odds
KANSAS CITY, MO – OCTOBER 13: Joel Embiid #21 of the Philadelphia 76ers in action during the game against the Miami Heat at Sprint Center on October 13, 2017 in Kansas City, Missouri. (Photo by Jamie Squire/Getty Images) /

Is it worth mortgaging the future for a small, win-now championship window ? Is it worth taking the risk on Joel Embiid over a lower-peak player who doesn’t have Bill Walton’s injury karma? In a prior post, I introduced the concept of Championship Odds over Replacement Player (CORP) as a way to compare players across multiple seasons and answer these kinds of questions.

But first, some background. When I was growing up, there was a silly belief that if Michael Jordan were on a team, that team would win the title. While this is obviously hyperbolic, I always wondered how likely peak Jordan would be to win a title if he were plopped on a random squad. Would he win 50 percent of time? Eighty? So I set out to answer this by conducting a study that looked at how different quality players impacted a team’s odds of winning a championship.

I took five years of game data and approximated the odds of winning a game based on point differentials for the home and away team. Then, I used that data to determine the odds of winning a best-of-seven playoff series, and, based on average opponent in a given round, four of those in a given year. And voila, we could then say how likely a team was to win a title based on its point differential, or SRS.

But that was only half the battle. I still needed to estimate how much someone like Jordan could change one of those differentials with his presence. And that’s a significantly trickier calculation than it sounds.

What does plus-minus data say about player impact?

As I discuss in Chapter 3 of Thinking Basketball, we have a really good idea of how much players can impact the game. In the book, I use a lot of season-to-season or WOWY data to isolate the top-end of a player’s impact. But it’s worth revising here with the quarter-century of plus-minus data we now have.

In 24 years of scaled plus-minus data, every minute-weighted season falls between a minus-3 and plus-8.5, so no player since Jordan’s first retirement has improved a team by 9 points per game according to this measurement (There are players worse than minus-3 per 48 minutes, but they typically don’t play enough, so we’ll use that as a replacement level). It turns out, according to adjusted plus-minus, that most players are right around, or just below, neutral impact. Here is the distribution, by point-per-game impact, based on the data:

If you’re wondering how point differentials translate to wins, a .500 team has a differential of zero (they score the same number of points as they allow), a 50-win team has a 3-point differential and a 60-win team has a 7-point differential.

So if a player like Jordan had, say, an impact of +8 points per game, he would take a 41-win team to 63 wins. Seems reasonable and easy enough. Except what happens when you add Jordan to a 63-win team? As noted in the book, it’s harder to improve better ones because they already have good skill-sets. They don’t — they can’t! — become a plus-16 team, so how much impact does Jordan have then?

Good teams win by becoming great

Before we tackle that question, keep in mind that the majority of teams aren’t “great.” It’s hard to generate a 5-point differential and really hard to generate a 7-point differential. Since the shot clock, only 64 teams have eclipsed the 7-point mark, and only 13 have topped 9. And, since most teams aren’t great (or even very good), adding all-star players to them won’t move the earth.

Almost no teams win titles without a 6-point differential or better, and even those teams don’t fare too well from year to year. Since Jordan returned in 1996, no healthy team has hung a banner with an SRS differential below 5.6 and only one (the ’03 Spurs) was below 6.6. Luck is a factor, but it’s rare to win without crossing this threshold.

Vegas intuits this every offseason and during the trade deadline. When flawed teams make moves, they need to combine star players to qualify as bona fide contenders. That player doesn’t have to be Kobe Bryant, but adding an all-star like Pau Gasol to a team that already has Kobe Bryant could be game-changing. However, adding Pau Gasol back to his lowly Grizzlies team would be about as landscape-altering as Jimmy Butler going to the Wolves this year or DeMarcus Cousins going to New Orleans or…please don’t make me continue.

The point is, most teams win by stacking stars, and all of those stars are important, even though some are far more important than others.

The importance of the secondary star

With the exception of the few megastars that can take middling or borderline-playoff teams to championship heights, most players accrue CORP points by positively impacting good teams. In other words, dragging hopeless teams to 35 or 40 wins is useless if the player can’t improve a 50-win team by a comparable degree. Lifting marginal teams to 55-wins won’t bring many championships either.

Counterintuitively, this means that “first options” aren’t quite as earth-shattering as we might think. While many people rightfully believe “there’s no way Klay Thompson could lead a team to a title in 2015,” they overlook the equally important counterbalance: It’s unlikely Steph Curry could have led that team to the title without Klay Thompson!

Indeed, the same can be said about most, if not all, title teams — stripping them of their second or even third (!) best player erodes their odds of winning the title. (Remember, supporting casts are integral to winning.) You want Klay Thompson on your team, even if you wouldn’t want Klay Thompson to be the best player on your team.

Comparing high peaks to steady longevity

Now let’s return to that really tricky part of the calculation. How much does a player like Jordan improve a 60-win team that already has a 7-point differential? This was where the portability (or scalability) curve originated that’s discussed in Thinking Basketball — it’s a method to approximate how well players hold their value on better and better teams. (It’s really not possible to ballpark championship odds like this without accounting for some kind of scaling curve, because so much of a player’s value-add comes from improving better and better teams.)

So, if we assume a player loses some impact as his team improves, what does the CORP curve look like? Taking a standard scaling curve, the historical distribution of teams, and the odds of playing on any of those random teams, we’re left with the following results. I’ve added in the frequencies of these seasons based on the aforementioned scaled APM distribution (from 1994-2017) to connect per-game impact to qualitative benchmarks like All-Star or All-NBA:

(Super nerdy note: The original “normal” scaling curve was impact_per_game * 1.5 ^ [1- e^(team_SRS/10)]. However, a curve centered slightly below zero is probably more realistic.)

First, note how a competent starter adds some value. This is important and often overlooked, as was the case in a 2013 538 article by Nate Silver, in which he quickly cooked up a CORP calculator but assumed the odds of a typical player winning was one in thirty. This reduces the NBA to a roulette wheel, drowning out the skill with luck. But bench players on the 2018 Bulls don’t have the same odds as winning a title as bench players on the Warriors! The Bulls are bad because they give more minutes to negative impact players, per the distribution above. Thus, the odds of a replacement player winning a title is actually closer to 1.3 percent than 3.3 percent, because only so many replacement players can exist on a good team before they aren’t good anymore.

Next, there is indeed a superlinear difference between All-Stars and the supernovae of the league. Solid MVP-level players providing around15-18 percent CORP, are on order of three times more valuable than a fringe all-star. .

Perhaps the most interesting point of comparison is between a borderline top-10 player and a top-5 player. We historically view these as having massive gaps, but the curve is not that steep yet. The typical 12th-best player in the league adds about 9 percent CORP, while the fourth-best adds about 14 percent. Historically good seasons, like those above 6.0, can be three to four times as valuable as a typical 12th-best player.

Next: Was the Rockets' clutch defense meaningful or a mirage?

Now we can finally resolve my childhood curiosity. Since the best seasons seem to peak around plus-8, it’s unlikely that Jordan would have been more than 40 percent likely to win a title if placed on a random team. And as far as the Embiids of the world go, the equivalent of four “weak-MVP” seasons (13-16 percent CORP) is about eight fringe all-star ones, and the equivalent of two transcendent years is about eight top-10 seasons.

Let’s keep our fingers crossed for Embiid to last longer than Walton.

Ben Taylor is a behavioral scientist and the founder of Backpicks.com. His book, “Thinking Basketball,” is available on Amazon.