Total Offensive Efficiency (Overview)
One of the statistical rankings I did on the old site was something I called Total Offensive Efficiency. Its origin was the plus-minus system used by about 95% of high school basketball coaches, but tweaked to take into account modern research on the relative value of various contributions/stats. One of my goals was to show how players with modest stats could be valuable contributors to winning teams, while some players with gaudy stats were not always all they were cracked up to be. Reminder that this was before sites like KenPom were publishing these types of numbers, so I am pretty happy with how the basketball world has embraced similar concepts. In hindsight, I see some problems but I think the core concepts are sound. You can find the links to specific years, but here is the overview of the system.
What are a basketball player's contributions on offense and how do they really relate to scoring points? How important are turnovers? Missed shots? Free throws?
Well, I came up with a very simple stat called TOTAL OFFENSIVE EFFICIENCY (TOE). It is intended to be a simple measue of how much a player contributes to his team's offense.
Here is how it works:
OK, next, I added up each player contributions to give a raw score (TOP or "total offensive production").Now, how to compare the values from team to team or player to player? Obviously, one wouldn't want to compute a per game average, as some players play more minutes than others and some teams play at different tempos, resulting in more or fewer possessions per game. So, what I did is I took each player's TOP and divided it by the number of possessions each player is on the floor (on average), giving a TOP per possession stat (or TOE).
The bottom line is we have the offensive contributions PER possession for each player. So, a player with a rating of 0.25 would contribute a point every 4 times down the floor (which is VERY good by the way).
Realize that I am not saying that guys on the top are hands down better players offensively (as there are other variables that are tough to control for), but rather that these players are the most productive/efficient (whichever term you might prefer).
Generally speaking, TOE will supply you with a general ratio of a player's contributions on offense as compared to how their negatives hurt the team. It is NOT an overall measure of one's ability to score, but rather, how a player's contributions help his team to score. As the Mike Kelley critics will point out, there IS a place for some of the guys toward the bottom of the ratings in a good offense. You just can't have too many of them and still have a good offense.
Let's take an example of an efficient player (at the time of TOE's inception), Carson Cunningham of Purdue. So, why was Cunningham an efficient player? Well, he was shooting almost 50% from the floor, with some 3's thrown in. He was above 80% from the line. He averaged about 14 PPG. And his assist to turnover ratio was an exceptional 45-11. That my friends is the definition of efficient and is exactly what this stat is supposed to measure.
Well, I came up with a very simple stat called TOTAL OFFENSIVE EFFICIENCY (TOE). It is intended to be a simple measue of how much a player contributes to his team's offense.
Here is how it works:
- A made basket is worth 2 points and a three-pointer 3 for obvious reasons.
- A missed shot is worth -1.33 points. Why? Because that puts the break even point at 40% for shooting. I wanted to keep the break even point low enough so as to reward guys who DO take shots for their team, costing them some on their shooting percentage. For example, I didn't want Mike Kelley rewarded for NOT taking shots when some other guy might be penalized for shooting say 43%, but taking a lot of shots and putting points on the board. Still, we DO need a cutoff at which shooting the ball is costing your team and I believe that 40% is a nice point for this. Team shooting percentages are in the low 40's as well, so it corresponds there as well.
- ADDENDUM: After some trial and error, someone realized that while the players were correctly rewarded for 3 point field goals made, the penalty was too great for misses (since the break even point is different for three pointers). So, to put the break even point at 33% and NOT 40%, I lowered the penalty for a missed three to a simple -1 (from -1.33).
- FT are worth 1 point. A miss is worth -2. This puts the cutoff at 67%, meaning you have to hit at least 67% to be of positive value to your team. In the future, I might tweak here to get the cutoff lower, say 60%, but let's leave it where it is for now for simplicity sake.
- ADDENDUM: I did lower the FT threshold to 60%. Mathematically speaking, it should be at 50%, but I wanted to keep it at 60% to account for the missed front ends of 1 and 1's.
- An offensive rebound is worth 1 point since research shows that each possession is worth about 1 point.
- The opposite goes for turnovers which are worth -1 point.
- Assists are worth 2 points. I realize that at times an assist might come on a three, but the percentage is pretty small so again, for simplicity, let's leave it at 2.
- ADDENDUM: I later lessened the value of an assist. Some felt that an assist should not be of the same value as the individual who scored the basket. While I feel that assists are NOT as easy to accumulate as some made it appear, I still relented and lowered the value for assists to 1.5.
- ADDENDUM #2: For a while now, I have known that a fundamental error in this formula has been the fact that for a field goal scored with an assist, the total value has been greater than 2 (or 3), which puts the whole system slightly out of whack. Rather, the combined value of a FG/AST should never be greater than 2.0. Some buckets are entirely due to the shooter (FG's without an assist), and those plays still result in the shooter receiving "full" credit. However, there are other shots in which the passer might play the most important role, say on a dish following penetration in which the shooter is left with an uncontested layup. On a play such as that one, the passer might deserve say 1.8 of the 2.0 points, while the shooter only deserves 0.2 of the 2.0 points.
The problem then lies in how to figure this into the formula given that obviously I haven't seen each scoring play to assess it. Well, as luck would have it, there actually is a group of fellas that has figured the average distribution of these two points. I don't have the link handy, but if anyone wants it they can drop me a line and I will dig around and find it. Anyway, the average value of a FG is 1.3 points, while the average value of an assist is 0.7, putting the value of a bucket twice that of an assist (again, on the AVERAGE). So, this adjustment has been made in the formula.
What results is a lower TOE for each player. Whereas a top score used to be around .200 and an average score around .130 or so, a good score is now around .100 while a so-so score is now around 0.050.
OK, next, I added up each player contributions to give a raw score (TOP or "total offensive production").Now, how to compare the values from team to team or player to player? Obviously, one wouldn't want to compute a per game average, as some players play more minutes than others and some teams play at different tempos, resulting in more or fewer possessions per game. So, what I did is I took each player's TOP and divided it by the number of possessions each player is on the floor (on average), giving a TOP per possession stat (or TOE).
The bottom line is we have the offensive contributions PER possession for each player. So, a player with a rating of 0.25 would contribute a point every 4 times down the floor (which is VERY good by the way).
Realize that I am not saying that guys on the top are hands down better players offensively (as there are other variables that are tough to control for), but rather that these players are the most productive/efficient (whichever term you might prefer).
Generally speaking, TOE will supply you with a general ratio of a player's contributions on offense as compared to how their negatives hurt the team. It is NOT an overall measure of one's ability to score, but rather, how a player's contributions help his team to score. As the Mike Kelley critics will point out, there IS a place for some of the guys toward the bottom of the ratings in a good offense. You just can't have too many of them and still have a good offense.
Let's take an example of an efficient player (at the time of TOE's inception), Carson Cunningham of Purdue. So, why was Cunningham an efficient player? Well, he was shooting almost 50% from the floor, with some 3's thrown in. He was above 80% from the line. He averaged about 14 PPG. And his assist to turnover ratio was an exceptional 45-11. That my friends is the definition of efficient and is exactly what this stat is supposed to measure.