*While the Sacramento Kings owner, Vivek Ranadivé is undoubtedly a brilliant business man, his recent proposal to play 4 on 5 defense is flawed, and here’s why.*

### Data can lead you astray

Vivek Ranadivé (Founder / CEO of TIBCO) has an impressive resume, and has recently spent his time analyzing 30 gigs of basketball data to help his team:

Using TIBCO’s technology, Ranadive has applied the same big data-approach to the Kings’ player management. So instead of just drilling down box scores and regular stats, the Kings collect in-game data from six different overhead cameras, and analyze everything from player combination and spacing to shot clock usage and shot selection.

Unfortunately, one of his conclusions is to play 4-on-5 defense, leaving one player to “cherry-pick”. Not sure what software he’s been using, but any middle-school math, will tell you that’s a bad idea.

### Doing the (simple) math to debunk the 4 on 5 theory

The basic premise behind Ranadivé’s theory is that missed shots by the opponent will lead to uncontested shots by the Kings. What he fails to account for is that the opponents will perform better against fewer defenders, and that getting defensive rebounds, and making outlet passes, also need to be accounted for.

#### 1) The offense is 20% more effective

In playing 4 on 5, you effectively have 0.8 of a defender per every offensive player, which we can assume gives the offense a 20% boost (1/0.8).

Looking at stats from the 2013 – 2014 season, the average NBA field goal % is **.454**, while from behind the 3-point line it’s **.360**. Therefore the adjusted field goal % becomes **.545** and **.432** respectively.

Then, weighting these percentages on the stat that there are approximately 4 2-point shots taken for every 1 3-pointer, we get an overall probability of **.522** that the average shot is made. In turn, this yields a value of **1.13** as the expected points per shot attempt.

#### 2) The defense has to get the rebound, throw an outlet, and then score

For the Kings to score, you must assume that their opponent misses AND the Kings get the defensive rebound AND make an outlet pass AND make the resulting shot.

So, if there is a **.522** chance of a made shot, that gives us a **.478** for a missed shot.

Then, the baseline offensive rebound % in the NBA is **.255**, but again we have to adjust that by 20% to account for there only being 4 defenders, to give **.306**, or a defensive rebound % of **.694**.

If we then assume that the probability of making a successful length of the court pass to the “cherry-picker” is 80%, and then let’s give the chance of the resulting shot attempt, given a successful outlet, of 99%.

#### Your opponent will outscore you by more than double

Multiplying out all of those probabilities of each event occurring give us a value of **.263**, or an expected value of **.52** points per defensive miss; while the offense is expected to make **1.13** per attempt.

Of course this doesn’t account for lots of things, like defensive turnovers (harder with 4 guys), or other anomalies, but some quick back-of-the-envelope math can tell you that the NBA isn’t like coaching his daughter’s basketball team. That said, if he wants to try his theory out when playing my Raptors, then be my guest.

Unlike baseball, basketball has challenges that make some analytics unreliable. That said, if Ranadivé serious about this stuff, perhaps attending next year’s MIT Sloan Sports Analytics Conference, should be in his future.

Hey Rishi,

I enjoyed your analysis breaking down the numbers/simple math behind why this idea wouldn’t work. This was the only serious analysis of the cherry picker/4-on-5 idea that I could find. As far as I can tell, the internet is in complete and utter agreement that this idea is imbecilic. Now that Mike Malone has been fired and rumors are circulating that Ranadivé will force Tyrone Corbin to try out this idea, I decided to examine it more closely.

Your math only accounted for the Kings getting “cherry-picker” baskets off defensive rebounds of opponent MISSES. But what about opponent MAKES? When the Phoenix Suns ran their Seven Seconds Or Less offense under Mike D’Antoni, they got out and ran after both opponent misses and makes. That’s partly why their offensive rating was so high and they were able to score in such prolific fashion.

But let’s say that the Kings are able to figure out a way of inbounding full-court bombs to the cherry picker (a la Grant Hill-Christian Laettner). These passes would be inherently more difficult than outlet passes from defensive rebounds to the cherry picker (a la Kevin Love — what you dubbed “length of court passes”) … but wouldn’t they yield some uncontested dunks for the Kings as well?

Let’s assume the probability of the Kings completing such plays — that is, inbounding full-court passes to the cherry picker — to be just 60% (accounting for a) the increased difficulty of the pass, and b) the chance of the opponent defenders being able to get back to contest). Using your above probabilities of .522 for opponent made shots, times 60% chance of success, and you end up with .63 points per opponent made shot.

Added to the .52 points per defensive rebound that you calculated yields 1.15 points per possession — higher than the opponent’s expected 1.13 points per possession that you calculated. And that’s before accounting for things like opponent turnovers, and for the fact that the Kings could practice those full-court passes to increase their chance of success from 60% to, say, 80% (in which case their expected points per possession would be 1.35).

Surely I am missing something here, because everyone else seems to be in agreement that it is a terrible idea. Could someone please explain?

v