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LeBron James vs. AK-47 :: the SLC Dunk Stat Revolution Continues

I was inspired by Mac Diego and his spreadsheet comparisons. In case you missed them, here they are:

Favors vs. great PF's in their rookie and 2nd seasons.

Bismack vs. post players also entering the draft.

I think they could use some tweaking on presentation, and there's still a lot to discover about how much the data is telling us (I asked Mac Diego to also compare to some incredible stiffs—the idea being that if we can tell a difference between rookie Kevin Garnett and rookie Kwame Brown, then we should get really, really excited that rookie Favors compares so well with KG). But the info is great stuff, and indicative of a lot of great work.

Anyway, inspired by this stuff, I decided to do a different kind of stat analysis.

I'm not trying to duplicate Amar and his GO-rating charts. Those show us how much a defense ought to pay attention to a given player. And really, who can replace Amar.

Nor am I trying to duplicate Mac Diego's comparing.

Instead I'm trying to look at stats and determine three things: 

  1. How effectively is a guy filling his role on defense?
  2. How effectively is a guy filling his role on offense?
  3. How effectively is a guy filling his role as a rebounder?

See the preliminary results after the jump:

First, understand that this is still a work in progress. I expect to do a lot of tweaking as I go. But for right now, here's what a player's chart looks like:


So, what the hell does this stuff mean?

The top set of numbers (labeled Player Ratings) are the ratings for the named player. In this case, that is Andrei Kirilenko. Those ratings are all based on the three charts below. The goal of each of the stat charts is to create a ratio from which I then generate a numerical rating.

Obviously, there are three different stat charts.

Position Ratios

Each of these numbers compares the player's performance to other players in the league playing the same position. The league average numbers are derived from the top 60 players for each position, as found on So I'm basically getting data from each team's starter and primary backup guy for that position.

When comparing the player's performance with that of other players, I then create a ratio. In most cases the ratio is simply (player's performance) / (league average). However, in the case of opponents' PER, it is better if the player's performance is lower than the league average. That means he is holding his positional opponents to a lower PER than they usually achieve. So in this case, the ratio is inversed: (league average) / (player's performance).

I inverse the ratio so that everything is simple: ratios higher than 1 mean the player is above the league average, ratios lower than 1 mean the player is below league average.

On/off court ratios

These numbers compare how the team does at a given task when the player is on the court, vs. off the court. These stats all come from Most ratios are (on court) / (off court).

However, when looking at points allowed per 100 possessions, it's good if the number drops when the player is on the court. So, just like with the PER, the ratio is inversed. In this case it is (off court) / (on court).

Again, this ensures simplicity when looking at the ratios: above 1 means the team does better when the player is on the court, below 1 means the team does better when the player is off the court.

Defensive Gambling

This is a modification of Amar's Defensive Gambling stat (which happens to be my favorite of Amar's stats). The first modification is slight: I deducted offensive fouls since I'm using this stat to assess defensive skills, and offensive fouls aren't part of defense.

The second modification is significant. Here's why I did it:

As I was testing things out, I plugged in Al Jefferson's stats. His Gambling ratio was less than 1, which resulted in a negative rating (see the ratings at the bottom to understand why, just accept it right now). But as I looked at it, I realized that was stupid. Among centers, Al was seventh best in blocks per game. He was also right in the middle for his fouls and steals. So if two parts are average, and one part is significantly above average—then his rating should be positive to reflect that.

So I divided the personal fouls by 2. Why? Because it distributed the final ratings appropriately: good players had positive ratings and bad players had negative ratings. It just made the results align with the spread of all the other ratings.

My formula is: (steals + blocks) / ((total personal fouls - offensive fouls) / 2 ).

So, how do those stat charts relate to the ratings chart at the top?

Here we go, here's my reasoning, my methodology, my thought process, etc., etc., etc.

First, I am incorporating aspects of PER that I like, while getting rid of things I don't like. It's biggest strength is that it puts all of a player's box-score contributions into a single number. It simplifies comparing players. There are a couple of things I dislike.

First it's hard to see where a specific player's PER comes from. It's like my dislike for grades. It's great to know a student earned a C, but sometimes it's more useful to know why: Was it because he didn't turn in homework? Or because he didn't understand the work? Or because he understands the concepts, but has trouble transferring that understanding to test problems? Etc.

So, I break up a player's rating into three categories: offense, defense, rebounding. And then I break those categories into three or four subcategories. 

The second flaw with PER is that it doesn't address important parts of the game that don't show up in box scores. Things like setting hard screens, good cuts, rubbing guys off screens, hockey assists, solid team defense, etc. It doesn't include them because, of course, nobody keeps stats for things like "screen awesomeness." And if they did, boy would Kevin Durrant's PER drop (I can't believe how awful he and the rest of his team works with screens and cuts).

Of course, I'm left with the same dilemma as Hollinger was when he devised his PER formula: how can I assess those, if there are no stats kept on them? Well, I tried to think of some indirect ways to get at them.

A couple quick notes

A category's rating is simply the sum of its subcategories. I tried several things: averaging them, multiplying them, taking the natural logarithm and dividing by the cosine of ∆ (well, not that last one :). In the end, adding them seemed to give me the nicest looking results.

Also, there are going to be flaws with all the stats. That's just how it is. There are flaws with pretty much all stats. My choices were based on two things: 1-Can I get the information fairly easily (i.e. without spending hours upon hours finding, compiling, calculation, etc.) and 2) Of all the options, which data will best reflect what I want to bring out?


I wanted to break this into three parts: one-on-one defense, team defense, and disruptions (blocks and steals basically). They encompass the three basic parts of good defense: guard your man effectively, help your teammates and rotate effectively, and knock the ball around when you have the chance.

1-on-1 D

I looked at PER against. It is an imperfect way to do it, I know. Mostly because PER includes a bunch of stuff besides offense (AK's defense has nothing to do with whether the guy he's guarding gets more steals that game). But there some strengths to using PER: it's easy to look up, it incorporates shooting percentages, scoring, assists, etc. Plus, and this seems significant to me, it also includes useage. If an entry pass is denied, if a playmaker can't get a good angle for an assist and therefore just tosses the ball out to reset the play ... that is the result of good defense. The guy's useage will drop, and so will his PER. 

In the end, looking at PER against seemed a decent and simple way to assess 1-on-1 defense. And it becomes better when you compare vs. the average PER for a specific position. For example, the average PER for the top 60 Centers was 14.2. The average PER for the top 60 PF's was 17.1. This will be significant when we look at the defense of Millsap, Al Jefferson, and Favors. (this won't come today, but just be ready to be dazzled by Favors when I post all the Jazz player's stats).

Team defense

There's so much stuff involved in good team defense, and most of it isn't in a box score: rotating, help defense, etc. But in the end, it comes down to scoring. Can a team score easily or not? So I looked at how many points per 100 possessions a team gives up when the player is on the court vs. off the court. If a player is really contributing well to team defense, then the team should typically give up fewer points per possession when he's playing.


I'm looking at steals and blocks. I'd love to also look at deflections that push team to the end of the shot clock, but I couldn't come up with any way to get at that. 

And I'm also looking at bad outcomes when a player tries to get a steal or block but fails. Again, I couldn't find a way to get at some things I'd like to know: giving up a wide open layup because of a reckless passing lane gamble, giving up an uncontested weakside dunk because you tried to block a pump fake. But there is one major bad outcome I could get: fouls. 

So I went back to Amar's defensive gambling stat. It seemed the best way to get at what I wanted. 

And in homeage to Amar, I renamed Disruptions to Gambling.


I want to know four main things here: how effectively a guy can score, how well a team scores when he's in, how well he sets screens and gives out both assists and hockey assists, and how often does he make a mistake that screws things up.


I kept it simple: True Shooting Percentage. Faithful readers and commenters know I like this stat a lot. Maybe too much. But the beauty is it is an easy to find stat that incorporates everything I want to know about a player's ability to score: shooting percentage, three point percentage, free throw percentage, plus the number of shots for each. It's really a beautiful stat.

Because different positions tend to get different kind of shots, I thought the best comparison would be with the average TS% for each particular position.

Team Scoring

Like team defense, I'm looking at how much a team scores per 100 possessions when a player is in vs. when he's out.


Here I went very indirect. Because I wanted more than just assists. I wanted some way to look at screens, cuts. Finally I remembered something Clark posted a few days ago: if the Jazz run their offense perfectly 100% of their baskets will be assisted. Remembering that was like getting knocked in the head with inspiration. That was a way to see how well a player is doing the off-ball stuff that makes an offense hums. If he's doing it well the team will assist more of its scores when he's in than when he's out.

So yay for Clark.


The best way I could see at getting at mistakes was with turnovers. But simply counting turnovers wasn't good enough for me. Because a player's turnovers is directly related to how frequently the ball is in his hands and he's trying to make a great play happen. I went through all sorts of different ideas of how to look at turnovers. I pondered incorporating usage somehow, I thought of minutes played, etc.

In the end, the simplest way seemed to be looking at simple assists to turnovers and comparing that to the average for that position. And it also seemed valid—since although it's not perfect, number of assists does reflect the frequency a player is involved with plays.

So that's what I looked at.

Boards Rating

I wanted rebounding to be its own category. Part of this was watching 6 years of the Booze. He rebounded well. But because rebounding was lumped with defense so often, that made people think his defense was better than it was—it statistically disguised his putrid D. I didn't want that to happen.

So I decided to look at it as its own category. And I did so simply: offensive and defensive rebounding rates of both the team and the player. Each player's individual rates are compared with the average rates of the position. The team rates is compared when the player is in vs. when the player is out.

From the ratios to the ratings

Now that I picked the stats I'd use to measure everything, I needed to decide how to weight them. The basic idea is that I want equally important subcategories to get the same kind of rating. So if 1-on-1 defense and team defense are pretty much equally important—if a 5 means awesome 1-on-1 D, then a 5 should mean equally awesome team D. I've had to fanangle with the stats to try to achieve this. I expect this is where I'm going to continue fanangling a lot as I test out more players, get a bigger sample size, and refine the stats so they really do work as they ought.

The basic fanangling

My starting point was this: take the ratios and subtract 1. All good ratings would be positive and bad ratings would be negative. For example, AK's TS% turns into 0.05 (because he was above the average) and his points allowed per 100 possessions turns into -0.01 (because the team allowed slightly fewer points when he was off the court). Then I decided to multiply by 100. That would give me, I expected, a lot of happy ratings. AK's TS% turns into 5. His Team D turns into -1.

But sometimes things got messy. The main issue was regarding smaller stats. Take offensive rebound rate. AK's was 6%. The league average for SF was 4.3%. AK's ratio turns out to be 1.49, which would churn out a whopping 49 rating — all over one more offensive rebound per game. That didn't make sense to me.

So I've adjusted how each ratio is multiplied in an attempt to make the ratings fairly consistent with one another. I expect I'll do a lot more adjusting as I go on.

Judging the importance

I also decided that some things are less important. Those subcategories are those marked yellow. For both Gambling and Mistakes, the reason is simple infrequency. Let's say the Jazz get 100 possessions in a game, and they cough up 12 turnovers. Those 12 turnovers aren't insignificant, but they have a smaller impact than how effectively the team runs its other 88 possessions. Particularly since the other team is also going to give up 12 turnovers.

The same principle applies to steals and blocks. They have an effect, but 4 blocks and 6 steals doesn't have as much effect as the other 90 possessions. 

So they are deliberately ranked less than the other subcategories.

The rebounding

Whether this is brilliant or not, I don't know. But I adjusted the rebounding stats. The idea is this: if a player is doing his job on defensive rebounding then he is boxing out effectively. If he boxes out effectively, then his team is more likely to get the rebound whether or not that player actually ends up getting credit for the rebound. In that way, team rebounding seems, to me, a bit more indicative of effective defensive rebounding than individual rebounding. 

On the other hand, offensive rebounding strikes me as opposite. Partly because the shot selection of the team has such a huge effect, and partly because of how players are positioned—for every pair of players, a defender and the offensive player, the defender is usually closer to the hoop. That means offensive rebounding isn't so much boxing out as it is working through the box out. If the player fights through, but the rebound takes a different bounce it isn't as likely to end up in a teammate's hands. So I ranked individual offensive rebounding as more important than team offensive rebounding.

The end

Anyway, that is what I've done and what I'll be working on over the summer. Below I'm posting the Ratings for LeBron James (he and AK were the two guys I focused on while building this preliminary system).


So, what does it mean that LeBron has a D Rating of 17.83? Right now I don't know. I have plug in a whole lot more players to create a context that can create meaning for these numbers. 

One thing I like already: LeBron's Playmaking is negative, but AK's was positive. That's because if you put AK in, suddenly the team's assists go up. But put LeBron in and the team's assists go down. LeBron may have great court vision, but that doesn't mean he and his team do great off-ball stuff to generate great shots. Particularly not when he's in.

And incidentally, that Playmaking rating was the one that started all the tweaking. When I first created what I thought were reasonable formulae, AK's Playmaking was in the 40's and LeBron's was about -8. Fascinating stuff.

From here I'm going to put through all the Jazz players into the ratings and see how they end up. And then it will be the big stuff—putting in enough current and former players to perfect the formulae, create a context, and see what, if anything, the ratings actually mean.