# San Antonio Spurs: Finding the analytically perfect rotation

#### By Luke Swiatek

## Methodology

The goal of this article is not necessarily to find the rotation timeline that is wisest for a team to play, but to find the rotation timeline that gives a team the best shot at winning games; think of it like a playoff rotation. For example, it might make sense for the Orlando Magic to play Mohamed Bamba over Nikola Vucevic, but if Vucevic is better now, so that’s who this analysis will recommend.

With that in mind, here are the steps that will be followed:

**Step 1: Make some rules**

Setting up a few guiding principles will make the next step much easier. Most of them will probably relate to staggering starters’ minutes, or keeping certain groups of players together. An example for the Golden State Warriors might be “always make sure two All-Stars are on the floor.”

Additionally, it is very unlikely that a team will have more than a 10-man rotation, if that. Obviously, rotations are shortened in the playoffs, and these are playoff rotations after all. I’ll generally exclude players that haven’t played a ton of games or are clearly at the end of the bench.

We’ll also restrict the number of minutes each player plays to a reasonable level. For example, LeBron James *could* play every minute in the playoffs if he wanted to, but we’ll probably top him out at 36 minutes, or maybe 40 if we’re feeling dangerous.

For my own sanity, I only use even numbers for players and try not to have them play in shifts shorter than four minutes (which is probably sound coaching advice anyway, considering how much of a rhythm sport basketball is). It’s highly unlikely I’d have a player play a shift longer than 12 minutes, unless it was broken up by halftime.

**Step 2: Use the rules to make the timeline**

Here, all the rules will be combined to create a full 48-minute rotation. This is where the guess-and-check comes in, since it would be incredibly difficult to start with the best lineups and try to fit them in a rotation, especially because then one needs to control for sample size and other concerns. Instead, the guiding rules will be followed based on the eye test, and the analytics will follow later.

On this slide, there will also be a basic discussion of the thinking that went into each decision, beyond what was already discussed in step 1.

**Step 3: Analyze it**

Once the dice have been cast, it’s time to see what’s been rolled. I’ll look at each individual lineup selected, and check out their plus/minus stats per 48 minutes. To find the entire rotation’s stats, I’ll weigh each lineup’s plus/minus based on how much they actually play in the rotation. I’ll report the individual stats for each lineup, as well as the aggregate.

The reason for this weighing is because of the way the stats are standardized. If a lineup has a per 48 minutes plus/minus of 10 points, that just means they outscore other teams by 10 points per 48 minutes. So if they only play 24 minutes, which is half of 48, then they should be expected to outscore the other team by five points in those minutes.

Each lineup will receive what I’ll call the “aggregate plus/minus,” which is just the lineup’s regular plusd/minus adjusted for how much they’ll be playing in the rotation. Then I’ll add all of these lineup’s plus/minuses together, to receive one final plus/minus for the whole rotation.

Here’s a simplified example. Imagine that I said a team should play its starters together for 32 minutes and its backups together for 16 minutes, so there were only two lineups. Let’s say the starters have a plus/minus of +6.0 and the backups have a plus/minus of -4.5.

The aggregate plus/minus for the starters would be +6.0 * 32 / 48 = +4.0. This makes sense; the starters play two-thirds of the game, so their plus/minus in those minutes should be two-thirds of what it would be over a full 48 minutes. The aggregate plus/minus for the bench would be -4.5 * 16 / 48 = -1.5. The same logic applies.

So to find the rotation’s plus/minus, I’d just add 4.0 and -1.5, and receive an answer of +2.5. Hopefully, this number will be as high as possible! Also, if for some reason I concoct a lineup that has never been played before, I’ll average the five players’ per 48 minutes plus/minus. It’s imperfect, but we work with what we have. Let’s dive in.