Baylor forward Jonathan Tchamwa Tchatchoua went down with a knee injury in the first half of Baylor’s last game, and the team announced shortly thereafter that he would miss the remainder of the season.
From @BaylorMBB: Sad news for Everyday Jon. Prayers for a smooth recovery #SicEm | #CultureofJOY @JonathanTchamwa is nicknamed “Everyday Jon” because he gives elite effort everyday! He will work to overcome this injury! We will help him… More importantly, God got Jon! pic.twitter.com/W2LzmL0Hyu— Alvin Brooks III (@Coach_AB3) February 13, 2022
Everyday Jon provides unmeasurable intangibles on and off the court, and simple box score statistics don’t do the Junior justice. That said, I wanted to do a simple exercise to see if it is even possible for Scott Drew to reallocate the team’s minutes to replicate the lost stats.
Jonathan is fifth on the team with 20.8 minutes per game. He’s good for 8.4 points, 6.8 rebounds, 0.7 assists, 0.7 steals, and 0.4 blocks per game with those minutes. How should the remaining players’ minutes change to make up for his absence?
A very tough day if you are @Big12Conference basketball & BaylorMBB fan with the significant knee injury to Jon Tchamwa Tchatchoua. Widely respected among player & coaches. I was putting this out tomorrow on attacking Big 12 pick & roll coverages with Everyday Jon. pic.twitter.com/kJdXavjrGN— Fran Fraschilla (@franfraschilla) February 13, 2022
Reallocating minutes among the remaining players is a straightforward optimization problem. Skip ahead to the next section if you aren’t interested in the details!
First, choose a statistic, e.g., points. The team’s points per game equal:
Points Per Game = (Akinjo Points Per Minute * Akinjo Minutes Per Game) + (Flagler Points Per Minute * Akinjo Minutes Per Game) + ... + (Bonner Points Per Minute * Bonner Minutes Per Game).
If we assume that each player’s points per minute are constant regardless of how many minutes they play (unlikely, for sure, but a useful assumption to get us started), we can remove Tchamwa Tchatchoua’s points and minutes and increase everyone else’s minutes to get as close to the original point value as possible.
Extending this to multiple statistics requires choosing how to combine deviations across statistics. The most common approach is to use the “sum of squared errors”. Take each of the five main stats — points, rebounds, assists, steals, and blocks — and:
- Calculate the difference between the original stat value and the predicted value after reallocating minutes.
- Take the square of each difference (this makes positive and negative differences equal).
- Sum the squared differences.
There are a few constraints I’d like to impose on players’ new minutes:
- The total number of minutes can’t change. With Tchamwa Tchatchoua, Baylor’s current eight-man lineup averages 186.4 minutes per game (pour one out for LJ). Without Tchamwa Tchatchoua, the remaining seven players’ new minutes should also equal 186.4 per game.
- No player can have their minutes decreased. It’s possible that the best way to replace Tchamwa Tchatchoua’s stats is to reduce the minutes of our guards and give even more minutes to the bigs. I don’t see that happening in reality, so I don’t want to allow it here.
- No player can have more minutes than available in a game.
With a clearly defined optimization function (sum of squared errors of points, rebounds, assists, steals, and blocks) and constraints, Excel’s built-in Solver tool can easily find the best solution.
Revised Minutes Per Player
If Jonathan Tchamwa Tchatchoua is out for a long time, Baylor is going to have to figure out how to be successful without either Thamba or JTT on the floor.— Evan Miyakawa (@EvanMiya) February 12, 2022
Before today, the sample size for lineups deployed without them was really small. I'll update this tomorrow as well. pic.twitter.com/v2SMvtgDqg
Jeremy Sochan is the best player to make up for Tchamwa Tchatchoua’s loss. He registers 8.1 points, 6 rebounds, 1.8 assists, 1.3 steals, and 0.7 blocks per game, but his minutes would need to increase from 22.9 per game to a team-leading 35.5 minutes per game!
The second biggest mover is Matthew Mayer, with his minutes per game increasing from 21.6 to 26.9. Mayer adds more scoring than Sochan but has fewer rebounds and assists.
The third (and final) player with a minutes increase is Flo Thamba, who is the most similar to Tchamwa Tchatchoua in terms of assists and steals. Thamba’s minutes would need to increase from 17.9 minutes per game to 20.8.
This new allocation of minutes is expected to produce 69.3 points per game (vs 70.1 from the pre-injury eight-man lineup), 31.9 rebounds per game (vs 33.5), 16.8 assists per game (vs 16.2), 9.7 steals per game (vs 9.3), and 3.7 blocks per game (vs 3.4).
Obviously, the assumption that each player’s productivity would stay the same for any increase in minutes makes this an overly optimistic prediction. What happens if I assume that every 1% increase in minutes leads to a 0.25% decline in productivity?
First, Mayer now sees the biggest increase in minutes per game, up 7 minutes to 28.6. Sochan is second, up 6.4 minutes to 29.3. Kendall Brown now sees an increase in his playing time, from 26.4 to 30.7. Finally, Thamba picks up 3 minutes per game.
Is there evidence that Sochan, Mayer, and Thamba playing more together would work out? According to Evan Miya’s Bayesian Ratings, the lineup of Akinjo, Bonner, Mayer, Sochan, and Thamba is the most efficient lineup Baylor has used this season, among lineups with at least 10 registered possessions.
Note, this lineup has only played 21 possessions together, and one of Baylor’s worst lineups this season also included Mayer, Sochan, and Thamba (Akinjo, Cryer, Mayer, Sochan, and Thamba for 18 possessions). But if there’s anyone who can figure out what to do with this team, it’s Scott Drew.
Hoping for a quick recovery for Jonathan!