Not so much fun, but long and technical.

I didn't have anything to do at my job today, so I decided to revisit a statistic I created about a year and a half ago, but updated somewhat.  I thought about this today because I wondered how good Andre Miller is compared to the other point guards of the league.  I'm a huge fan of Miller's and I would be open to the Sixers resigning him after the year ended.  So without further ado: What I wrote some time ago, with updated statistics and analysis:

Clearly, the hardest position on the basketball floor to evaluate is point guard. This is so for two reasons. First, the point guard is expected to demonstrate intangible qualities, like leadership and playmaking. But also, it is because the goals for a point guard seem to contradict each other. To explain what I mean by this, first I'll talk about two power forwards with exactly the same skill set, except Forward A is a much better rebounder than Forward B. While we would expect the two forwards to have similar scoring averages, Forward A's would probably be a little better than Forward B's. That is because A would collect offensive rebounds and instantly have a shot attempt available, while B would not be able to receive the ball. Also, on a more indirect note, Forward A would collect more defensive rebounds, leading to more possessions all around for his team. But through this example, we see that rebounds work in concert with scoring average. But, point guards do not rebound. Instead, their primary evaluative statistic, aside from scoring, is assists. Assists work against the individual's scoring average. If a player has an opportunity to pass the ball or shoot the ball, the team may score either way, but the player's scoring average will only improve if he shoots. A basket, though, is a basket, regardless of who makes it. Thus, when evaluating point guards, assists and scoring have to be treated equally.
Points per game is the most basic way to measure a player's productivity, but as previously stated, point guards need to have their passing evaluated as well. Thus, to calculate how many points per game the point guard directly creates, the guard's points-per game must be added to a weighted assist total.
So, how do we determine the weighted assist coefficient? It's tempting to say that each basket is worth two points, so each assist that leads up to the basket must be worth two points as well. However, this does not take into account three point baskets. When taking three pointers into account, the average basket in the 2005/06 NBA season was worth 2.175 points. By that, we can conclude that each assist should be worth 2.175 points as well. The equation is as follows: Points created by player= Points per game + 2.175(Assists per game). Are we done? Not yet.
We forgot about turnovers. Peewee coaches have been stressing ball control for years, but these showboating NBA players just care about razzle-dazzle. Hence, we need to take turnovers into the equation. Conceptually, it should seem obvious that an assist is worth more than a turnover, regardless of what coaches say. That is because an assist always leads to a made basket (natch), while turnovers do not always prevent a made basket. But, we have to assign some value to a turnover, so how do we do it?
Magic. Nah, what we need to do is look at the total possessions a team has in a game. Then we see how many points the team scores, and finally how many turnovers it has committed. These are the only three numbers we need. First, we subtract out turnovers from possessions. These possessions are 'wasted'; the team could not have scored from these. What we are left with are the amount of possessions the team could have scored with. We must divide points scored by eligible possessions. Thus, what we have is points scored per eligible possession. This, theoretically, is the amount of points the team scores per eligible possession, and the amount it would score on all possessions if no turnovers occurred. To get total possessions, add turnovers and field goal attempts and subtract offensive rebounds.  This is because a possession can end in either a shot attempt or a turnover (or free throw attempts, but we'll get to that a little later) and offensive rebounds increase shot attempts and turnovers, but they don't add possessions.  They just prolong possessions.  This part is not some agreed upon fact, just a judgement call I made.  For the 2007/08 season, a team scored 1.42 points per eligible possession. (The average team scored 99.9 points per game, had 84.41 possessions per game, and averaged 14.11 turnovers per game). To conclude, a turnover is worth 1.42 points a piece.
Now, we have all we need to calculate a point guard's ability to directly influence scoring. The equation is as follows: Points per game + 2.175(Assists per game) - 1.42(Turnovers per game) = Scoring directly influenced by point guards (or any player really, just that this metric works best with the floor generals). But we can do more with this.  Since some players play more minutes than others, we can equalize the minutes.  Say hypothetically, what would each player's contribution be if he played 40 min. a game at the same level he played his current minutes at.  Or, since some teams play at a faster pace, artifically increasing his numbers, how would he do playing at a standard pace.  Now, I'm not saying players will perform at the same level for increased minutes or a decreased pace, but it aids in comparison.  And remember I said I'd get to free throws?  Well, here I am.  Free throws are difficult to add in because of the different ways free throws occur.  They can occur without interrupting possession (think "And One" Calls), after the defense is over the limit, and so on.  I haven't found a place or site that differentiates how free throws occur.  Thus, I excluded them altogether.  If you think about it, most free throws result because of a foul during a shot.  If that is so, it is listed as a shot attempt, whether it goes in or not, and so those free throw occurrences are included in possessions per game.  The free throws which aren't included in possessions are the ones where the defense commits a foul after reaching the limit.  In those situations, the point guard hasn't really done anything anyway (except maybe draw the foul, in which case he shoots free throws), and so those 'fouled' possessions are excluded from the formula altogether.  This is not a perfect solution, I understand.  But it is the 'fairest' one I could come up with.

So here's how the point guards compared for the 07/08 season.  The age and team are for last year. "DP" is Direct Points, what I created.  "DP/40" is Direct Points per 40 min and "DP/40Pace" is Direct Points per 40 minutes divided by the pace factor for the player's team and then multiplied by 100 so it's not a crazy fraction.

Rank  Player      Age     Team       DP            DP/40        DP/40Pace

    1       Paul          22         NO       42.78         45.51            50.07

    2       Nash        33        PHO      35.93         41.90            45.55

    3        James      23       CLE       40.83         40.43            45.22

    4        D.Wllms   23        UTA       36.81         39.47           44.91

    5        Ford           24       TOR      22.53         38.34             43.23

...........................................................................................

   19      A.Miller      31        PHI        28.46           30.93             33.26

I'm sorry, I thought about listing all 48 players I ran the analysis for here, but that seriously would have taken all day, cuz I would have to have manually formatted the entire list.  I wish I could import a spreadsheet onto SBN.  If anyone knows how, please tell me (assuming you've read this far).  Anyway, Miller falls into the middle of "2nd-tier PGs", with Raymond Felton, Ramon Sessions, and Earl Watson surprisingly ahead of him.  The fading Jason Kidd is also ahead of him in this second tier group.  Miller is ahead of Mo Williams, Jameer Nelson, Mike Bibby, Gilbert Arenas (though Arenas only played like 19 games), and Kirk Hinrich.  Rebounding is not taken into account, which helps explain Kidd's diminshed value.  Sessions' place ahead of Miller and some others is explained away by a small sample size.  He only played 26.5 minutes a game in 17 games. 

Anyway, Miller did not do as well as I thought he would have.  While I don't think I would put him in the 'elite' category, which is a somewhat arbitrary class, I would have listed him as the best of the 2nd tier.  On the surface, his stats would agree with me.  17 points, 6.9 assists, and 2.5 TOs.  What gives?  Well first, the assist seems to be making a comeback.  I remember years when only Jason Kidd would log over 10 of them a game.  Now, 4 players (Nash, Kidd, D. Williams, and Paul) topped 10.  And Miller's 6.9 only tied him for 13th in the league (and two more players had 6.8 assists).   Second, while Miller's PPG look impressive, of the guards I looked at, Miller was 11th in the league in minutes played, so while he put up good numbers, it took him a relatively long time to do it.  While that's not too bad, when compared to numbers in an equal amount of time, Miller's performance looks less than stellar. 

Conclusions: Miller is not as 'unexpendable' as I originally thought.  While I still think it behooves the team to resign him, this has a lot to do with the fact that the team doesn't have good replacements waiting in line.  He's not elite, but average, and given his age, I would not expect him to be a quality PG much longer.  A two or three year deal seems like a worthwhile gamble for the team, assuming it makes a reasonable effort, either throught the draft or some other means, to secure a 'point guard of the future' type.  While I'm not saying the metric I've shown you today is by any means the end all of point guard evaluative measures, it represents my best effort to create a metric that takes into account both the scoring and passing function of a point guard.  Thank you for reading this far (if indeed you have)