Assuming league recovery post-COVID-19, an expansion team (or more) in the NBA feels like more of a “when” than an “if”. Growing team valuations, marketable superstars, and worldwide interest has turned basketball into the sport of the future, and there are plenty of places that could use a squad (looking at you, Seattle).
Creating an expansion team, though, is extremely complicated. Not only need there be an agreed-upon set of rules for which players are available in a potential expansion draft, but the new team itself must make difficult decisions about which players are worth the call, considering both production and cost. We’re deciding how to maximize one variable given a ceiling on another variable – a perfect job for constrained optimization.
To decide on the player pool, there’s no single perfect metric, but I’ve decided to use a maximum of minutes played in the 2019-2020 season. A player who hasn’t played x number of minutes can be construed as more expendable to a team (with obvious exceptions due to injuries, etc.), and this rule allows us to make decisions based on how good we think a player is, which may be higher or lower than their current team’s conception of them. This season’s total minutes leader (so far) is Tobias Harris of the Philadelphia 76ers, with 2,245.5 minutes played. For the first run through, I’ll set the maximum minutes played under which you are “draft eligible” as half that number (1,122.75).
This season’s salary cap was just over $109 million – it’s hard to know what will happen next year, so I’m assuming a “safe” projection of an even $100 million for my hypothetical expansion team salary total. Using 2020-2021 player contracts, I can then run through nearly infinite combinations of 15-man rosters that would fit under that hypothetical cap in 2021 (note: for players not under contract in 2021, I’m assuming 2021 salary to be equal to 2020 salary as an imperfect solution)
So, we have our salary constraint – now we must maximize our value such that the constraint is satisfied. But how? There are plenty of scenarios we could map out using the eye test, but I’m interested in seeing what we get when we let the numbers speak for themselves. For our variable to maximize, I’m choosing to utilize perhaps the best player value metric available, Jacob Goldstein’s PIPM (player impact plus-minus). Its derivative “Wins Added” metric is a perfect place to start in terms of maximizing under our salary constraint.
What other constraints do we need? There needs to be a certain degree of nuance when it comes to player fit, as we don’t want 15 centers, although the current NBA is as positionless as ever, which gives less meaning to the classic 1-5 designations. I’ll set out to maximize wins added under the salary cap for a team with 3 centers, 6 “guards”, and 6 “forwards”.
Alright! Now that the settings are out of the way, we’re ready to optimize! Using Michel Berkelaar’s lpSolve() R package, I uploaded all of the eligible players’ (under our total minutes limit) salary, position, and wins added data. Ladies and gentlemen, or optimal expansion team:
| PLAYER | POSITION | WINS ADDED | SALARY |
| Derrick Favors | C | 3.4 | $ 17,650,000 |
| JaVale McGee | C | 3.2 | $ 4,200,000 |
| Nerlens Noel | C | 2.0 | $ 1,882,867 |
| Paul Millsap | F | 3.3 | $ 30,350,000 |
| Jonathan Isaac | F | 2.5 | $ 7,362,565 |
| Brandon Clarke | F | 2.3 | $ 2,602,920 |
| Chris Boucher | F | 1.5 | $ 1,588,231 |
| Ersan Ilyasova | F | 1.5 | $ 7,000,000 |
| Rondae Hollis-Jefferson | F | 1.3 | $ 2,500,000 |
| George Hill | G | 3.0 | $ 9,590,602 |
| De’Anthony Melton | G | 2.9 | $ 1,416,852 |
| Isaac Bonga | G | 2.0 | $ 1,663,861 |
| Alex Caruso | G | 2.0 | $ 2,750,000 |
| Terence Davis | G | 2.0 | $ 1,517,981 |
| Cody Martin | G | 1.6 | $ 1,517,981 |
| 34.5 | $ 93,593,860 |
At first glance, this team looks… actually pretty good! It’s interesting that the model seems to select for a specific type of player; guys that are viewed as “role players” for winning basketball. Our centers are rim-running rim protectors, our forwards can do some combination of defend/rebound/stretch the floor, and our guards can all shoot and lock down the perimeter. It’s fascinating that we see pretty much zero classic “ball-dominant” players, even at the guard position, and a perfect microcosm is the algorithm’s selection of Paul Millsap as the $30 million centerpiece.
However, note that the salaries actually sum up to a good amount below $100 million. Let’s see what our team would be if we made more “star” players eligible by raising the minutes maximum from half to two-thirds the leader (1122.75 to 1497):
| PLAYER | POSITION | WINS ADDED | SALARY |
| Mitchell Robinson | C | 4.1 | $ 1,663,861 |
| Daniel Theis | C | 4.0 | $ 5,000,000 |
| Ivica Zubac | C | 3.6 | $ 7,000,000 |
| Christian Wood | F | 4.6 | $ 1,645,357 |
| Paul George | F | 4.4 | $ 35,450,412 |
| John Collins | F | 2.9 | $ 4,137,302 |
| Jonathan Isaac | F | 2.5 | $ 7,362,565 |
| Brandon Clarke | F | 2.3 | $ 2,602,920 |
| Marquese Chriss | F | 2.0 | $ 1,824,003 |
| Donte DiVincenzo | G | 4.6 | $ 3,044,160 |
| Patrick Beverley | G | 4.4 | $ 13,333,333 |
| Derrick White | G | 3.3 | $ 3,516,284 |
| Damion Lee | G | 3.1 | $ 1,762,796 |
| Kris Dunn | G | 3.1 | $ 7,091,457 |
| De’Anthony Melton | G | 2.9 | $ 1,416,852 |
| 51.8 | $ 96,851,302 |
There are plenty of usual suspects, like De’Anthony Melton, Brandon Clarke, and Jonathan Isaac, but this looks like a far more complete team. It’s interesting that the optimization shifts dollars away from the center position (Derrick Favors makes almost $18M on our first team) even though the overall salary increases. Oh, and shout out to Mitchell Robinson.
A photo of Mitchell Robinson.
The two big fish this team reels in are Paul George and Patrick Beverley from the Los Angeles Clippers. It’s a lot harder to see a scenario where a guy at PG’s level, though, is drafted to an expansion team, and out of Los Angeles no less. I tried another optimization with PG excluded to see where the model decided to allocate the extra money:
| PLAYER | POSITION | WINS ADDED | SALARY |
| Joel Embiid | C | 5.0 | $ 29,542,010 |
| Mitchell Robinson | C | 4.1 | $ 1,663,861 |
| Daniel Theis | C | 4.0 | $ 5,000,000 |
| Christian Wood | F | 4.6 | $ 1,645,357 |
| John Collins | F | 2.9 | $ 4,137,302 |
| Jonathan Isaac | F | 2.5 | $ 7,362,565 |
| Brandon Clarke | F | 2.3 | $ 2,602,920 |
| Trey Lyles | F | 2.2 | $ 5,500,000 |
| Marquese Chriss | F | 2.0 | $ 1,824,003 |
| Donte DiVincenzo | G | 4.6 | $ 3,044,160 |
| Patrick Beverley | G | 4.4 | $ 13,333,333 |
| Derrick White | G | 3.3 | $ 3,516,284 |
| Kris Dunn | G | 3.1 | $ 7,091,457 |
| Damion Lee | G | 3.1 | $ 1,762,796 |
| De’Aaron Fox | G | 3.0 | $ 8,099,627 |
| 51.1 | $ 96,125,675 |
Trust the process! Although the overall wins added total is lower (considering the PG team was the optimal solution to our given constraints, we couldn’t expect any additional constraint – in this case the removal of PG from the player pool – to increase the wins added), I might actually like this team a bit better. Embiid is a worthy star, and we add some more offense on the perimeter with De’Aaron Fox. Oh, and we still have Mitchell Robinson.
Of course, our original team still feels a whole lot more realistic; guys like Joel Embiid would be going absolutely nowhere. That got me thinking of another potential solution – what if we capped individual player salaries? We’ll keep the higher minutes cap, but say no individual can be drafted to the expansion franchise with a personal salary above $20 million. Here’s what that would look like:
| PLAYER | POSITION | WINS ADDED | SALARY |
| Mitchell Robinson | C | 4.1 | $ 1,663,861 |
| Daniel Theis | C | 4.0 | $ 5,000,000 |
| Ivica Zubac | C | 3.6 | $ 7,000,000 |
| Christian Wood | F | 4.6 | $ 1,645,357 |
| John Collins | F | 2.9 | $ 4,137,302 |
| Jonathan Isaac | F | 2.5 | $ 7,362,565 |
| Brandon Clarke | F | 2.3 | $ 2,602,920 |
| Trey Lyles | F | 2.2 | $ 5,500,000 |
| Trevor Ariza | F | 2.2 | $ 12,800,000 |
| Donte DiVincenzo | G | 4.6 | $ 3,044,160 |
| Patrick Beverley | G | 4.4 | $ 13,333,333 |
| Derrick White | G | 3.3 | $ 3,516,284 |
| Kris Dunn | G | 3.1 | $ 7,091,457 |
| Damion Lee | G | 3.1 | $ 1,762,796 |
| De’Aaron Fox | G | 3.0 | $ 8,099,627 |
| 49.9 | $ 84,559,662 |
Fascinating! This team looks far better than our original squad with the lower minutes cap (it also has a significantly higher Wins Added total), with more individual offense creation on both the outside (De’Aaron Fox) and inside (John Collins) alongside the usual suspects for plug-and-play role players like Beverley, Clarke, and Isaac. And we still have Mitchell Robinson.
This looks to me like a legitimately possible expansion team – no one’s played huge minutes; no one is making star money.
It’s also worth noting that this team was over $15 million below the allotted salary cap – just because someone’s making more money, doesn’t mean they’ll be more valuable.
This all got me thinking, though – how about a bonus round with no restrictions on minutes or individual salary? Based on essentially PIPM and the salary cap alone, what’s the best team we could possibly construct?
| PLAYER | POSITION | WINS ADDED | SALARY |
| Bam Adebayo | C | 7.5 | $ 5,115,492 |
| Brook Lopez | C | 6.5 | $ 12,697,675 |
| Mitchell Robinson | C | 4.1 | $ 1,663,861 |
| Giannis Antetokounmpo | F | 12.4 | $ 27,528,088 |
| Jayson Tatum | F | 8.9 | $ 9,897,120 |
| Royce O’Neale | F | 5.4 | $ 8,500,000 |
| Dorian Finney-Smith | F | 5.0 | $ 4,000,000 |
| Christian Wood | F | 4.6 | $ 1,645,357 |
| OG Anunoby | F | 4.6 | $ 3,872,215 |
| Luka Doncic | G | 8.1 | $ 8,049,360 |
| Duncan Robinson | G | 7.0 | $ 1,663,861 |
| Trae Young | G | 5.1 | $ 6,571,800 |
| Shai Gilgeous-Alexander | G | 4.9 | $ 4,141,320 |
| Donte DiVincenzo | G | 4.6 | $ 3,044,160 |
| De’Anthony Melton | G | 2.9 | $ 1,416,852 |
| 91.6 | $ 99,807,161 |
Now that’s a squad.
What you’re looking at is essentially the best 15-man roster that $100 million can buy. It’s not surprising to see so many young stars still on their rookie deals, as they’re the best bang-for-your-buck you can get in the NBA. Guys like Luka Doncic, Jayson Tatum, and Trae Young are incredibly valuable assets (as is, still, Mitchell Robinson). It’s pretty funny that the second highest-paid player is Brook Lopez, as good as he is.
So, how can all of this information be utilized in a real-life expansion team scenario? Well, for one, a potential billion-dollar expansion franchise should be doing far deeper analyses than this one – analyzing potential synergies between players, and accounting for more than just the combination of salary and an all-in-one metric, however robust it may be (it is). The team would also have to account for salaries past just one season, and plenty of potential NBA-required constraints (Only one player drafted from each team? Only players with fewer than a specified number of experience years?). Despite these extra considerations, the thought process for a new team should be largely the same – how can we maximize value given our situation? What’s the best way to allocate salary across players of different roles? An expansion team is a blank slate and thereby a major opportunity. I, for one, look forward to the next one.
by Derek Reifer, Northwestern University
follow Derek on Twitter @d_reif
follow Corner Three on Twitter @corner3sports
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