So the NBA statistical revolution is underway: instead of Moneyball, we're moneyballin (see what I did there kek). New stats appear to be popping up everyday: PPP? WP? WS? What is a true rebound, and how does it differ from a normal rebound? How truthful is a True shooting percentage, and since when were regular shooting percentages lying to us?
Personally, I'm happy to see such a nerd mentality gaining prominence in both NBA circles and our beloved forum. It adds a lot more depth to discussions by providing new avenues of evidence that had previously been constrained by basic stats and evaluation-by-eye. Though we have yet to reach a comprehensive statistic that accurately represents either side of the ball, it feels like we're getting there, piece by piece, with each statistical uncovering representing another step closer to THE stat, or as Hadron-Collider-loving quantum physicists might describe it, the God Stat.
Still, if we're going to apply economic concepts to our love of the game, I think the time has come to go over some basic principles regarding the "dreary science", especially when the statistical tools we're using are far from perfect. In this post, I will analyze the Short Run Production Curve as taught in most upper-division Microeconomics courses and use it to forward a theory*, which works as follows:
- The Short Run Production Curve can and should be used as a measure of individual player production
- Efficiency should be regarded as a derivative of the curve and dependent on the input. In basketball terms, TS% is derived from a player's production curve when the independent variable is Usage.
- TS% is not only dependent on player ability but also on the Usage level
- Efficiency and Production are often at odds with one another relative to a player's talent level: increase one, the other decreases, and vice versa.
It sounds super complicated but it's not too bad. Let's go over it step by step. Jump!
First, let me explain the Short Run Production Curve.
Short Run Production Curve:
Above is the typical production curve. It represents how much you produce in accordance to one variable input. It's parts can be understood as follows:
- The Y axis is "Output", which can be all sorts of things depending on the situation: If you're a shoe company, it's shoes. If you're a video game company, it's video games. And so on and so forth.
- The X axis is the "Variable Input". Once again, this can represent anything you want respective to your point of interest. Do you want to see the effect of labor on production? The effect of computers? IT investment? Plot it on the X axis to make it the subject of your analysis.
- The point on the S-shaped line represents how much output results from each unit of input. So let's say we're talking about the output of a shoe company vs. the amount of workers hired. For each worker hired, there's a different effect on the output and the point on the line represents it. More workers = more output. Easy, right?
- This next part can be a teensy bit tricky: The slope of the line represents the efficiency level of the input. We all remember slope, right? Rise over run, etc. Now, our line is a curved line, not a straight line, which means that there's varying slopes respective to what part of the line you're looking at. On some parts, the slope is really steep. On other parts, the slope is really flat. This is all basic Calculus stuff, and really, even if you didn't take Calculus you'll soon realize that a lot of is easily intuited.
- If the slope represents the efficiency level of the input, then what does a steep slope mean? A flat slope? The answer is that a steep slope represents high efficiency, while a flat slope represents low efficiency.
Ok. So now we know what the parts of a production curve means. So what does it mean?
- When input is first introduced, it has little effect on output.
- After a certain amount of input is introduced, you start to see huge gains in output and efficiency.
- Though output still increases (as shown by the graph still reaching upwards), the slope of the curve begins to get less steep. This is where output still gains, but you are less efficient than you were before. So even though hiring workers at this point gets you more product, you're producing it at a lesser efficiency than before.
- After a while, the efficiency level becomes so low that the graph flatlines. You might get tiny bits of increased output, but it's not worth the cost of input. In really bad case scenarios, the efficiency level can even turn negative and you'll get decreased output even though you're inserting more input! If you're a production manager and you're in this position, you are fail.
Thx 4 boring me to sh*t, wtf is your point?
True Shooting Percentage vs. Points Per Game.
What if we applied the short-term production curve to a player's production? Of course, like I said before there is no "God stat" that can tell us the full value of a player. But let's limit it to the side of the basketball we understand most, offense, and even then let's limit it strictly to PPG. Why? Because by doing so, we can see that True Shooting Percentage represents the efficiency of PPG as it's related to the variable input.
Here is the Short Run Production Curve again, this time to represent PPG as the Total Product.
Same graph as before, but this time we replaced Variable input with Usage and Output with PPG.
Let's evaluate what this curve means respective to the new X and Y axis variables:
- The Variable Input has been replaced with the Usage statistic. Usage, as described in basketball-reference.com, attempts to approximate what percent of a team's offense involves a player. The higher the percentage, the more touches/shots/decisions a player gets to make.
- The Output has been replaced with PPG. Now, PPG is probably not directly correlated to Usage, since Usage allows for other many opportunities of offensive production. But out of the many offensive statistics we have, PPG is still the most valued and the most understood. Whether we're correct to do so is one thing, but that is the reality.
- Each point on the graph represents the effect of Usage on PPG. A player with a lot of Usage is more likely to get a higher PPG total than those with low usage. Makes sense right, if you're involved in 35 percent of your team's offensive sets, you're more likely to score a high PPG than someone who is not involved.
- The slope of the graph, like before, represents efficiency. And though there are many statistics that try to represent efficiency, in terms of PPG the TS% is the one most commonly used, and therefore I will use it too.
- Therefore, just as how the steepness of the curve represented efficiency in the first graph, the slope represents the TS%. The steeper the slope, the higher the TS%. The flatter the slope, the lower the TS%.
With this knowledge we can derive the following assumptions:
- When a player first starts getting touches, the effect on TS% is minimal. It's hard to hit a reliable TS% if you're only average one or two shots a game. This is part A of the graph (to make it more accurate I could have put a lot of squigglies on this part)
- At a certain point, more Usage leads to huge gains in TS% (efficiency) and in PPG (production). Players get more time, get into a flow. They start scoring more points and do so well, staying within the limits of their game and hitting high percentage shots. (Part B)
- In Part C, we see that we're still getting good amounts of PPG gain, but our efficiency is starting to drop a bit. We're still at a respectable mark, we're just not hitting ridiculous efficiency points anymore. If we apply economic principles, part C is where production should be located because even though we're losing efficiency, Marginal Revenue is still greater than Marginal Cost... but let's not get into that.
- In Part D, we see that the effects on PPG is very small and the slope of the graph has near-flatlined. Think Larry Hughes on the Warriors right after the John Starks trade. The player is being asked to perform at a level beyond his capabilities, and though he does produce he does at too high of a cost. If you're a basketball player at this point of the curve, you are hurting your team more than you're helping.
Here is an example of the theory in action. The stats taken for this chart are off of basketball-reference.com, and the reason I chose Andre Iguodala's 2006-2007 season is because 1.) He plays a lot of minutes and a lot of games, 2.) Iverson is traded midway through, resulting in a significant difference in Usage.
Note the following:
- The correlation is not the strongest, since as aforementioned TS% is but one part of what Usage encompasses
- Still, there are some interesting points. Low Usage has higher efficiency ratings, High Usage has lower efficiency ratings.
- The big clump in the middle could represent part C of the Production curve.
- All data was calculated through Basketball-reference.com, using Game logs from the 06-07 season for both Andre Iguodala and the 76ers. The formula used for Usage was 100 x ((FGA + .44 x FTA + TOV) x (Tm MP/5))/(MP x (Tm FGA+.44 x Tm FTA + Tm TOV); the formula for TS% was Points/(2 x (FGA + .44 x FTA); graph was made on excel (which is why it sucks, my excel is in Korean and I can't read it)
I'm actually not the first person to do this, even on this forum. Philthiest did something very similar comparing Usage and Offensive Rating here: http://www.goldenstateofmind.com/2010/2/11/1305590/the-true-monta-ellis. And overall, I think offensive rating works better with Usage than PPG does, but using PPG does allow us to make some conclusions specifically relevant to this forum:
>>>ATT: BELOW IS THE POINT OF THE ARGUMENT<<<<
1. Efficiency is not production, it is a derivative of production.
2. Efficiency and production are often at odds with one another: to increase production, you often have to sacrifice efficiency. To be more efficient, you often have to sacrifice production. The goal is to reach the optimal levels of both so the player's worth is maximized, as philthiest so cogently describes here:
3. If you are comparing a player's TS% (efficiency) to another player's without comparing PPG or Usage, you are wrong. The valid comparison would be to compare players of either similar PPG/TS or Usage and see who's reaching a higher level of performance. Remember that efficiency is a derivative of the Total Product Curve, and every player is going to reach different levels of efficiency according to his usage. This point is especially relevant to those comparing Ellis's lesser efficiency with our higher efficiency players. Yes, they shot better... but they weren't used as much and weren't producing as much. If they were used more, could they have produced similar output? With similar efficiency? That is the comparison that needs to be made.
4. Just cuz a player is not as efficient as before doesn't mean he's on the wrong point of the production curve. This once again refers to Ellis. Was Ellis on part C of the curve or part D in 2010? Remember that in the last season, Ellis posted a 51 percent TS% while the league average was 54%. He also posted a 27% USG rating compared to the average of 19%. (Stats from hoopdata.com) So he definitely lost efficiency... but was it enough to be a detriment to the team?
The above was a theory. It's a theory based off a Microeconomic theory that I learned while studying Econ as a minor. I don't intend this to be some sort of final blow against bad thinking, but more of a starting point that can help change our mindset when comparing statistics. I hope it is successful in its intent since I just spent like 10 hours writing it and actually about 2 years thinking about it. I ran it by a few econ professors several years ago and they were like, yeah, it could work... just find data. For that, I'm thankful for all those enthusiasts who post up so many stats; I don't know where they find the time or how they do it but they are a godsend for nerdy basketball fans like me.
And in conclusion: GO WARRIORS
*I changed the word from hypothesis to theory because a hypothesis is something you test. I don't really try to do much testing here though.