I posted something similar to this last year as well. I've written a full article, but I'll post the data and some quick conclusions (though sharing the data is more the point) here for anyone who just wants that. The article has explanations and fuller discussion/conclusions in it, if interested.
A common approach in stats for several sports, most predominantly hockey but also catching on with basketball of late, is to judge player's impacts on their teammates. This is done by looking at each player's performance with and without each of their teammates on the floor (known as WOWY’s, or With or Without You stats). What we'll do is look at the team's net rating (point differential per 100 possessions) while these players are on the floor together (and apart) to judge that impact.First, the "with" data set — how the team performs with certain pairings of players on the floor. The following chart shows each player with significant playing time so far on the left column, and the players they have been paired with along the top row. The numbers in the chart are the team's on-court net rating with that pairing on the floor — colour coded from very good (green) through average for the team (yellow) to terrible (red). The values for players “with” themselves is simply the player’s overall on-court net rating.
To really get an idea of who is actually impacting each others’ play though, we also need to look at how each player does away from each teammate. The following chart shows the same thing as the above chart, but without each teammate instead of with them.
But what we really want is the net impact each player has on each teammate. So we find the difference between the player’s performance with each teammate and his performance without that teammate, and we get the following results.
1. Play Siakam next to JV, Carroll, DD or Lowry as little as possible, but definitely never with more than one at the same time, let alone with all of them (and ideally literally zero minutes ever with Carroll or Valanciunas). Find him time with the bench units if Sullinger is still unable to play basketball (although I should note: the one player Sullinger has a positive “with” value beside is Nogueira, so if you have to use him, use him exclusively as the bench PF in Siakam’s place).
2. Start Patterson, and don’t stop. He really unlocks the other starters’ games, and the bench unit’s productivity seems far less reliant on his presence.
3. Play Joseph as little as possible with DeRozan and Valanciunas. DeRozan is hard to avoid (maybe try some no-star bench units for short stretches to see if they survive — it’s not like the DeRozan plus bench unit is holding its own, anyway), but never put JV out there with Joseph, and certainly not with both Joseph and DeRozan. Save his time for playing with the starters, who should also be the closers, by the way, since Joseph has struggled so much all year.