A simple minded analysis on whether to take a J or look for something else

Preliminary stuff:

During one of Morey's radio interviews this season, a caller complained about Trevor Ariza launching too many 3s despite shooting in the low 30s on 3 pointers. Morey replied that the volume of Ariza's 3 pt attermpts caused by Morey and Adelman to keep launching these because it is overall a good shot not only because you get 3 pts out of it, but also other things like offensive rebounding, etc.

So, I thought I would try to objectively analyze the decision to shoot Ariza 3. Below is a spreadsheet setting out the results of my calculation. More on it later.

http://spreadsheets.google.com/ccc?key=0Ah9LoXfT1jT2dGttSWNoenJwTDZXdXd5U09YaU0yekE&hl=en

First, please note that this is greatly simplified because I don't have time to dig through all of the game-play data and address all of the issues. It's not intended to adress everything. I just want to illustrate some of the consideration as to whether a player should elect to launch a shot or not. The Rockets have a team of people who get paid to spend time doing the more complete analysis. This is just me entertaining myself.


The Initial Question: Should Trevor chuck the 3?

Anyhow, here's the question I am going to start with: You are Trevor Ariza, standing behind the 3 point line with the basketball. You have a look at the basket which is average in quality (i.e. as open are on the average shot that you take, not super open, and not super-contested): you know you have a 34.5% chance of making the 3 (which is your season average). Also, you know that, because you are relatively open, there is a 0% chance you'll get fouled, and a 0% chance you'll turn it over. Do you go ahead and take the shot, or do something else with it?

The answer, under most circumstances, is "yes you do."

Lets first take a look at the consequences of launching-- that is, how many points can you expect to score on this possession?

Please note that a "possession" ends when the ball gets into the other team's hand and the shock clock begins at 24 for the OPPOSING team. So, if you turn the ball over, the possession is over, but if you shoot and get the offensive rebound, the possession is NOT over. By this definition, both teams would have the same number of possession each game, aside from end of quarter issues.


Here is how the calcualation goes:

34.5% of the time, you get 3 points until the possession ends by the made shot. The other (100-34.5)= 65.5% of the time, either (1) the other team gets the defensive rebound, and you get 0 pts, or (2) your team gets the offensive rebound and gets to try scoring again.

So, the expected Point per Possession if you launch the 3 = 34.5%*3 + (1-34.5%)*(Probability that Rockets get an offensive rebound after the shot misses)*(Rockets expected points scored after an offensive rebound until the end of possession)

For the sake of simplicity, let call the robability that Rockets get an offensive rebound after a missed shot "OReb%" and lets call the Rockets expected point per possession if it gets and offensive rebound "SCP" Also, lets call the expected Point per Possession if you launch the 3 "CPPP." (for "conditional point per shot"_

So, what we have is

CPPP = .345*3 + (1-.345)(OReb%)*(SCP).

So, if you go to the first Tab, titled "34.5% 3 pter (the Ariza)" You'll see at the top of the spreadhset a table setting out what the CPPP is given different values of OReb% and SCP.

For instance, if the OReb% is .12 (Rockets only has 12% chance of recover the missed shot) and the SCP is .80 (Rockets expect to score only .8 points between getting an offensive board and termination of possession), the CPPP is 1.09788. If the OReb% is .24, and the SCP is 1.01, the CPPP is 1.193772. So, as you can see, the CPPP increase, from the 1.09788 to almost 1.32 as each of OREb% and SCP get larger.

Are these numbers good? Generally, yes. But of course it depends on the situation.

Let's say what we have here is an early shot clock situation, Trevor is open, but if he does'nt there's plenty of time to run the offense. Now, the Rockets overall points per possession is about 1.08 (Leaving aside the cheap fast breaks that number is even lower). So, even in a rather terrible case of .12 OReb and 0.80 SCP, it's worth it to launch the 3 if the alternative is to get 1.08 points per possession.

On the other hand, there are situations in which the Rockets might expect to get more if Trevor doesn't shoot. The opponent can suck on D, the opposing D may not be set, etc. Lets say the Rockets are playing last years' Wizards or Kings, who gave up about 1.14 points per possession and that's what we expect to score against these guys on this particular night or on this particular play. Is it still worth it?

Generally yes... you'll notice that most of the values on the top table is more than 1.14. So, as long as you have a somewhat decent OReb% on this particular shot (Rockets overall is 30%, not sure what it is after missed 3s generally) and a decent opportunity to score after getting a rebound (again, not sure what this number is, but shouldn't differ that greatly from their overall 1.08 point per possession number, at least not too far outside the rather wide .80 to 1.31 number I put up there), it's worth launching even if your alternative is 1.14 points per possession.

You'll notice on each tab I put up two charts below the top one, one of them is intended to compare launching the shot with an 1.08 expected point per possession alternative. The other compares launchign with an 1.14 expected point per possession alternative. The numbers in each chart is basically the CPPP minus either 1.08 or 1.14, negative numbers in "()." So, a number in () means it's not worht it to shot. The more () you see on the chart, the harder you should think before launching the 34.5% 3 pointer.

Now, your "base line" number for not shooting may be much greater than 1.14 (i.e. 3 on 2 break, someone has a dunk) then of course launching a 34.5% 3 pointer, even in the optimal case for SCP and OReb%, may not be worth it. Aside from these situations (which probably are not the majority of situations in which Ariza had taken a 3 pt shot), it is generally a good ideal to shoot. Also, often the "base line" number is much lower than the 1.08 average because the shot clock is, say, down to 10 secs or the team is facing a top defensive squad. In those cases it's pretty much almost worth it to launch.

2. An Important Caveat

One thing I did not look at is the effect of shooting a particular 3 pointer on transition D. Not sure how it comes out, on one hand, higher % for missing and longer rebounds puts pressure on transition D. On the other hand, if you are shooting, at least you are not turning it over, which is even worse for transition D.

I suspect, however, that things don't come out that badly with the Rockets 3 point shooting since they are fairly good at getting back on D (Battier is particularly a great transition defender).

On a team that is horrible after long rebounds, then, the consideration is different. On such a team, one might be much more selective in launching.


3. More Generally

I went ahead and created the remainig tabs, which illustrate the same analysis with other types of more or less open Js. So, we got 3 pointers form 27% to 42%, and 2 pointers from 35% to 60%. Here are the results:

a. If you have a 27% shot at a 3, and your otherwise has a good or even average scoring chance on that possession (i.e. 1.08 to 1.14), you should pretty much not launch that 3. There are very few exceptiosn (i.e. your team awesome at tracking down your missed 3s, and awesome at putting it back to score), but you better think VERY hard before launching.

Now a 27% 3 pt shooter might have a better % at a given possession (e.g. WIDE OPEN CORNER 3), the calculation is differnet under those circumsances. However, these circumstances are probably no that common. So, when Antoine wlaker was hiting 27% of his 3s in a couple of those years, he's probably hurting his team with most of them.

b. a 30% shot a 3 (which sounds terrible) actually not hurt a team that much if we are talking a team like the Rockets, when the alternative for launching on most possessions is probably about 1.08. You come out even money or better when there is sufficient offensive rebounding.

c. As the % increse, the 3s becomes a better idea. Even a 36% 3 pointer a pretty decent idea even when your alternative is 1.14 points per possession. A 39 or 42% 3 pointer are "no brainers" unless you have a really really great shot.


d. 2 pt jumpers are a much worse idea than 3s. First, a 35, 40 or even a 45% two pointer are almost never worth launching early in a shot clock unless you really expect to perform much worse than average (i.e. 1.08) on that particular possession. This is not to say you don't need a mid-range game-- not at all. You need the midrange shots to set up other moves, you also need to hit a few when that's all you team can get and there's 5 sec on the shot clock. However, if you are, say, Juwan Howard standing 18 ft away from the hoop with 16 sec. on the clock and with the basketball, it's better to pass the ball than to take your 42% shot at the basket.

3. If you hit 50%, 55, or 60% on 2 pt jumpers, then they are more likely to be worth launching, even early in the clock when your alternative is run the offense and get the expected point per possession that your team gets.