After breaking down 2 point shooting and attempting to find a minimum threshold where you wont hurt your team we will go ahead and approach 3 point shots in more or less a totally different way. That makes sense right? Well, I will start
out things about the same but then I will take a totally different approach.
I'll start it off similarly to 2 pointers with a player who takes 100 3 point shots. If he makes all of them he will produce 300 points or 200 points over average. If he misses them all he will produce 30 points (30 offensive rebound chances = 30 points) or 70 points below average. This adds up to either, three pointers made * 3 + (three pointers missed * .3) - three pointers or three pointers made * 2 - three pointers missed * .7
If we use this to determine our minimum efficiency threshold (the point where a player begins to create positive points or credits for his team) we come up with 26 percent 3 point shooting. It's pretty low but it was low on 2 point shooting as well and it is consistent with the model. Well its not what I will use. Our 3 point value is 2.5 points instead of 3 and I will spend the next several paragraphs trying some how to explain how we get this number.
If we use the NBA league average of 36.2 % and credit 3 points per made 3, our team gets about 1.28 points per possession (.28 net).
If we take the NBA league average of 48.4 % and credit 2 points per made 2, our team gets about 1.12 points per possession (.12 net)
If we take the NBA league average of 36.1 % and credit 2.5 points per made 3 to the shooter as our system does, gets our team about 1.10 points per possession.(.10 net)
Well, if teams gain so many more points shooting threes at average rate instead of twos than why don't teams shoot all threes? It could be said that NBA teams would but defenses are schemed to stop this from happening and the way basketball works would make it beyond impossible. I think that it makes sense to look as these possession value disparities as normal. The difference can be explained by other factors rather than just say there is such a clear advantage to shooting threes and coaches in the NBA should just design offense to shoot as many threes as possible. This means that the values of threes and twos can be viewed as pretty much on par and average shooting teams gain no real advantage regardless of how many threes are made compared to twos. The 1.28 on threes and the 1.12 on twos should be near equal but because of what the numbers fail to represent in terms of distributing proper credit we get the significant .16 disparity between the 2. The equalizer here is assigning 2.5 for made threes. However I don't want to do that without attempting to theorize where that .5 point for made threes or alternatively the .16 between average 2 and average 3 went exactly.
I'll argue or at least attempt to make a point that the disparity comes from 2 sources. Free Throw Attempts and Assists.
For assists 87% of threes are assisted and only 52% of twos are assisted. Threes are not shots typically created solely by the shooter but are very much a factor of the other players creating offense and getting the ball to the three point shooter. Thus the higher assist rate makes sense as does the fact that we need to decrease some of the value of threes. Our assist factor is set at .8 per player assist and I will explain how we arrived at that factor in the assists section. Using these values we can add helper credits of .7 for threes and .42 for twos. Helper credits are not possession events but influence how much weight possession stats carry in terms of the value of possession. Thus if we use helper credits in NBA average shooting situations we would give threes .a value of 2.3 and twos a value of 1.58. The difference in average value of possession of threes versus two would then go from .16 to .09.
When looking at free throws I will group them with shot attempts. I'll consider shots that gained fouls as attempts to give us a real look at just how many free throws are lost when taking 3 pointers. These lost chances at free throws is what gives holes to the optimal efficiency of three point shots especially when compared to twos.
We will be using some extremes but I want it to illustrate the difference well. Players shooting two pointers get fouled about 16% of the time so if Average Player attempts 100 2 pointers he will get the shot off 84 times and get fouled 16 times. For every 100 2 point "attempts" Average Player will score about 118 points and for every 100 3 point attempts Average Player will score 128 points or a difference of .10 points per possession in favor of the 3 shooter as opposed to the original .16 from before adjustments. We could actually decrease the gap further if we logically (well my logic) say that shots that players were fouled on would have gone in at a better than average rate without the contact.
If we take the .07 deduction for assists and the .06 increase for free throws we end up with 1.21 point per shot for threes and 1.18 for twos. Close enough to make typical 3 point and 2 point shooting comparably efficient.
Putting it all together an average 3 point shooter and an average 2 point shooter produce a similar amount of points per possession if you adjust for the added importance of passing when shooting threes and the additional fouls created when attempting twos. We can do this because although assists don't change the value of possession they comprise a part of its ultimate result and because we consider shooting fouls as shot attempts that keep possession.
Thus by reducing a 3 points shot weighted value by half a point we get very similar point per shot value from 2 and 3 point shots. In the final formula we end up using 1 point for 2 point shots and 1.5 points for 3 point shots. The 1 and 1.5 I use reflect the net gain per possession. 2 and 2.5 can also be used but we then deduct possessions. Using 1 and 1.5 works well when we compare twos to threes because it makes some sense that a three would be worth 50% more than a two.
We'll also be seeing later how using 1.5 for threes fits well when determining a players true win value. A player who shoots our minimum efficiency percentages (using twos at 41.25% and threes at 31.8%) and that draw an average amount of fouls and commit an average amount of turnovers would create no wins.
Well if you want me clarify any of this mess please ask. This is a rough draft version that I posted up and I will continue to expand and evolve on these themes here at NBA Postup.
I'll take a look at free throw values for part III. Looking forward to feedback and questions.
