“There are three kinds of lies: Lies, damned lies, and statistics.”
-Mark Twain popularized it, but attributed it to British Prime Minister Benjamin Disraeli. Either way, consider credit given.
With that for an opening, you probably wonder what I have in store. I am not presenting anything sinister or anti-statistics, but I wanted to make the point that you should (and I do) take what I am about to present with a grain of salt. So, caveat emptor.
The ball got rolling in my mind when I tried to quantify the potential impact of Allen Iverson in Charlotte for Iverson in CLT? Yes, please. I presented a crude calculation of potential offensive efficiency for the Bobcats based on swapping out the numbers per shot of Raymond Felton and Raja Bell and replacing those attempts with attempts at Iverson's points per shot number. There are a lot of faults with that and I noted that it was far from perfect (if even remotely useful). But the thought was in my head, “How can I use known numbers for a player to predict his addition (or subtraction) on (from) a team?”
When ESPN released their predictions for the coming season, I was disappointed. Surprised, no – but I was disappointed – I want the Bobcats to be good but expectations are low. Should they be though? When I ran the numbers for Emeka Okafor and Tyson Chandler following the trade, Tyson came out looking strong defensively. There were no surprises with his offense – he is limited, has been, will continue to be barring an unexpected late blooming. But…those defensive numbers were very strong and easily surpassed Emeka's. And that got me thinking – could Tyson's defensive presence make up for the offensive loss of Emeka? Even if the Bobcats struggle to score 90 points, you can still win games if you force your opponents into 89.
My initial off the cuff approximation would not do – but how to handle it. Well, for one thing, offense (and defense) is more than just field goal attempts. Possessions are also used up by free throw attempts and turnovers, while they are extended by offensive rebounds. In equation form, you could estimate a player's possession usage as such:
The next thing to consider is the points a player produces – we stick with team possessions as the baseline for comparison, so points per 100 team possessions. The last thing we want is a combination of those two: How efficiently does a player get his points – so we will be using points per possession used.
With that said and out of the way, here are Emeka and Tyson's respective numbers, at both ends of the court:
What do you notice? Well, I am drawn to one thing in particular – the low number of possessions Tyson uses. Yes, Emeka is a better post scorer, but Tyson leaves more possessions for his teammates to use, with fewer turnovers and a slightly higher offensive rebounding rate. The downside: Big men tend to be the most efficient scorers for a team (and Emeka with the Bobcats was no exception), so he is leaving more possessions for less efficient players. And now my attempt to combine all these elements:
What it attempts to do is calculate the expected efficiency of a player B, taking over for player A. The first three terms of the equation are simple enough, the offensive (or defensive) efficiency of A's team minus his points scored per 100 possessions (or allowed) plus player B's points. The chunk of the equation attempts to account for the fact that some players tend to use more (or less) possessions than their counterparts (also a concern with Iverson, who has a very high usage rate). The next term figures out how many possessions we need to account for and the final chunk attempts to guess what efficiency those will be scored/allowed at. A couple of notes:
-Note 1: The possession calculation can be negative, allowing removal of some points from the efficiency when a high usage player comes along. This way we would not just add LeBron James 30+ points per 100 possessions without accounting for the possessions he would be taking from teammates.
-Note 2: The first term on the top of the fraction of the bottom line estimates the efficiency of A's teammates, just in case it is not clear. By removing his points and possessions, we can see what they would do without his contributions.
So, what happens when we look at the Bobcats and their addition of Tyson Chandler using this tool? Well, we first have to decide on what efficiency to start with. Considering the Bobcats will enter this season looking largely like the team that followed the trade for Boris Diaw and Raja Bell, I will use the Bobcats' team efficiencies from December 12th on. You can find fault with just about any subset of the season I choose, so for at least this first calculation we go with this.
From 12/12 on, the Bobcats had an offensive efficiency of 105.02 and a defensive efficiency of 105.07 – basically, they were average. When you take the numbers and the equation above, we get expected efficiencies of 104.90 offensive, 104.61 defensive. Pythagorean Wins for those efficiencies? 42.
Am I saying the Bobcats will win 42 games next year? No. Am I saying that I expect them to improve dramatically defensively, while seeing only a slight decline in offense? Well, I am not saying that – but the numbers I just gave you are. The question is, do you believe them?
I am not heading to Vegas to wager on the Bobcats win total, as I do not have near that level of faith in this – but they did a reasonable job of approximating the change between D.J. Augustin and Raymond Felton when applied to the Bobcats. The equation also came within a point of predicting the decline in Orlando's offense with Rafer Alston as opposed to Jameer Nelson. Maybe there is some use to it – or maybe it just one of the three types of lies. As NBA fans, we are still learning how to quantify the game we follow the way baseball has and at the very least, I had some fun going down this rabbit hole.