ancientHistory

First of all, Useful sites:

    Basketball-Reference, your first stop for anything.
    82 Games
    Pro Sports Transaction Archive
    Basketball value, adjusted plus-minus and play-by-play data downloads.

Not useful, but fun

    Trade Machine
    Draft Express - college stats and reports
    StatSheet - their NBA section isn't great, but the HS and college stats stuff is excellent

Basketball is the worst of the 4 major North American sports when it comes to stats being discussed in the media. Many of the ones most widely available are useless or extremely deficient (points per game, field goal percentage), and the most useful ones are not even tracked (possessions, field goals defended, passes). Thanks to the work of countless nerds we can improve on the available stats and estimate some of the missing ones.

Rate Stats
Things like points and rebounds are known as counting stats: they just count the events and present these numbers as if they mean something. They don't. You need a denominator to make useful comparisons. Knowing a team scores 101 points per game doesn't tell you how efficiently they scored. Get yourself a denominator and make a good stat: a rate stat.

In this case, we'll use possessions as the denominator, possessions being defined as the time during which one team had the ball until they had to give it up. (This means that an offensive rebound doesn't create a new possession. A new play is created by an OR. Some people use possessions to mean plays, but nerds don't.)

Because the NBA doesn't track team possessions we have to estimate it. We do this by starting out with the premise that a team can only end a possession by a) missed FG, b) turnover, c) trip to the FT line, or d) made field goal that doesn't involve an "and-1". There are lots of formulas to estimate possessions on the internet, I'll let you figure it out.

Once you have your possessions, you have the most important stat for team efficiency: points per possession. Actually, that stat is universally known as Offensive and Defensive Rating (ORTG and DRTG), and it's most often expressed as points per 100 possessions, because nerds hate decimal places. 107 is about the modern average. Good offenses score 112, good defenses typically allow 102.

Another thing you can do with possessions is get a pace metric. In 08-09, the average team had 92 possessions per game. GSW, the fastest team in the league, had 98; POR, the slowest, had 87.

Where can one find these wondrous stats? 1: Go to Basketball Reference dot com. 2 Hit the league summary link. Scroll down about half the page to "Miscellaneous Stats".




If you want to know where your team ranks in any of these stats, just click the column header and it will sort the stats for you.

Or you can just go to a team page and that stats and ranks for that team are laid out there for you nice and pretty.



Four Factors
Once you have overall offensive and defensive efficiency, you want more. Years ago Dean Oliver broke down the number of ways a team could improve their scoring efficiency into four: make shots from the field, get to the line, not turn the ball over, and rebound your misses to extend the possession. There are other ways to break down offensive stats, but you could do much worse than Oliver's Four Factors. Each factor has a stat:

1. Effective Field Goal Percentage. It is bullshit that a player who makes 2-4 on layup attempts has the same FG% as a player who hits 2-4 from behind the arc -- the latter player generated 6 points on his shots, the former only 4. Effective FG% takes care of this problem by adding .5 points for every 3Pt made, which means that a player hitting 3-6 inside the arc and one going 2-6 outside the arc have the same EFG%. This is the most important stat of them all, at the team and player level. League average is about 50%.

2. FT/FGA. Getting to the line is important, and this stat expresses that as a ratio of points generated from free throws to field goals attempted. This is the most ambiguous stat, and one which could be presented a number of different ways. B-Ref's version is good enough to credit teams that draw a lot of fouls. League average is about .24.

3. TO%. This one could be expressed as turnovers per possession, but B-Ref chose turnover per play. (A play, at the team level, is different than a possession in that a play ends when a shot is attempted whether it is offensively rebounded or not. Possessions end only when the opponents get the ball, thus an offensive rebound will not end a possession.) Not a big deal, and makes no real difference in the rankings of teams in this stat. League average is 14%.

4. Offensive Rebounding Percentage. First of all, rebounds, as a stat, are useless. There are offensive rebounds, and there are defensive rebounds. Two different things. Putting them together is like putting steals and turnovers into the same category, it's fucking bullshit. Next, rebounds per game, like all per game stats, are useless. We need a real denominator, not this "per game" bullshit denominator. Offensive rebounding is measured as the ratio of offensive rebounds to missed shots. The calculation is actually done slightly differently, but that's what it's getting at: for every potential offensive rebound, how many did you actually get?) League average is 27%.

Like all other stats, these are available at the B-Ref league summary page, under miscellaneous stats:



Hey, just noticed now that B-Ref added a "clubhouse" page for every team, and it has all the stats and ranks:



tl,dr Wrap-up
What have we learned?

    Per game stats are useless. Per possession is where its at.
    Offensive and defensive efficiency are defined as points scored and allowed per 100 possessions. These stats are known as ORTG and DRTG, and if you only know one thing about basketball stats this is what you need to know.
    Pace is defined as possessions per game.
    Four ways of scoring more efficiently:
    1) Shooting better (EFG%),
    2) Getting to the line (FT/FGA),
    3) taking care of the ball (TO%),
    and 4) rebounding misses (OR%).
    These stats are all available at Basketball-Reference.com. Learn to love that site.
    If you ever get lost in stats, learn to use the B-Ref glossary.

The previous post was a primer on advanced stats for teams. Here I'll talk about some player advanced stats for offense. (I may do defensive stats some other time.)

Let's start with the mega-stats, the ones that try to put everything important into one number. There are a zillion of these, everybody who first gets into the business tries to come up with a new one. I think there are only four that are popular enough to be worth talking about. In my experience they are of limited use from a tactical and strategic perspective, but they are useful for fans who want to compare player value.

Raw plus-minus
Take the score differential when a player is on the court, subtract it from when he is not on the court. That's essentially what plus-minus is, although there are a bunch of variations. The NBA actually started putting these in their box scores.



But I like to get my plus-minus the old fashioned way, from 82games.com



This player's team scored 4319 when he was on the court, 4655 when he wasn't. That doesn't tell us anything, because we don't know how many possessions he was on the court for. The grey cells are the important numbers, which tell us how many points were scored per possessions (actually 100 possessions, because nerds hate decimal places). When this player was on the court, his team scored 112.9 points per 100 possessions, when he wasn't on the court, they scored 116.2. His presence on the court didn't help all that much. He is a -3.3 on offense. On defense, different story: his team allowed 110.3 when he was on the court, 114.8 when he wasn't on the court -- he is a -4.5 defensively (that is, his team allowed 4.5 fewer points per 100 possessions when he was on the court). Mix the offensive and defensive plus-minus numbers and you get an overall plus-minus value: +1.2 points per 100 possessions better when he was on the court.

Adjusted plus-minus
Hold on, you're saying. That player plays against starters. Shouldn't he get a boost from playing against more talented opponents than some 12 man? This is the question adjusted plus-minus was meant to solve. Using a technique known as linear regression, we can account for the player's teammates and opposing players when he is on the court. I think there are a few places doing adjusted plus-minus, but Basketballvalue.com is the most comprehensive.

[Statistics people: Adjusted plus minus is a linear regression, the response variable being the the delta in points differential for a period of time during which the ten players on the court don't change, regressed on variables indicating the the identity of each of the ten players on the court. If you know anything about basketball you'll spot a big problem: the multicollinearity that arises since most of the high-minute players play with the same group of teammates for most of their minutes. Generally spearking, the standard errors for one season's worth of data render these estimates pretty unusable, and so most of the time multi-season estimates are used.]

Here is that same player's adjusted plus-minus numbers.

You can see that controlling for teammates and opponents moves his offensive plus-minus from -3.3 to -3.5, meaning it barely changed. His defensive plus-minus went from -4.5 to -4, which is a small change for the worse, although still a positive impact for the defense.

Offensive rating (there is a defensive rating, too, which I'll talk about some other time)

The father of advanced basketball statistics, Dean Oliver, came up with this one a long time ago. It is the only one, as far as I know, that isn't based on a regression-style framework (or what the baseball guys call "linear weights"). This is a good thing. I won't dwell on the nuts and bolts of ORTG, but I do want to point out what goes into it: all four factors (see below) are addressed explicitly, and also passing. So shooting, offensive rebounds, turnovers and assists, and foul drawing. Unlike plus-minus stats, which are essentially black boxes in that we have no idea how a +1.2 player ended up being +1.2, we can tell pretty well why a 117 ORTG player produced 117 points per 100 possessions. 117 is about 10 more than league average.



You can see where his value lies: shooting 54% is about 4% better than average. A player who takes a lot of shots and makes most of them is the single most valuable thing to be in the NBA.

I wish fans would take ORTG into their hearts. It is a good stat.

PER
Much hated in this forum, for reasons I've never been able to fully grasp. Out of all the "linear weights"-style metrics, PER has the most logical basis. I think what happens is that people don't really understand what it is saying, so that some results look funny. I'll explain a little bit what goes into PER:

First of all, PER is a pace-adjusted per minute production stat. Imagine a stat like Points/minute. Now subtract missed shots from it. Add offensive rebounds (the value of which is simply the team's points scored per play, because a OReb is giving the team an extra play). Subtract the value of turnovers (similar to ORebs, it is the expected points value of a team play). Calculate how many shots this player had that were assisted by a teammate, and subtract a percentage of that, giving the value of these assisted shots to his teammate. Add in the value of blocks, and steals, and defensive rebounds, and the rest. Now adjust all that for pace. You end up with PER.

There is nothing wrong with any of this. Hollinger's weights for the various statistical events are debatable, but don't seem wildly wrong to me. PER is just a per-minute estimate of what a player is producing on the court.

(The real problem, of course, is defense, for which PER relies heavily on rebounds and blocks and steals. Not a comprehensive look at defense. I'm not the first to suggest that PER would have been better as purely an offensive construct, where box score stats cover pretty much most of what we need to know.)

Now compare this to ORTG, which is a pure efficiency metric. What does that mean? That a player like Raja Bell who doesn't shoot much but shoots at a high accuracy will look good on ORTG, but look bad on PER. Or someone like Allen Iverson, who in his prime looked good on PER (because he did a lot while he was on the court), but looked terrible on ORTG. There's value to both of these approaches, but remembering what the numbers are saying is important. PER = production. ORTG = efficiency.


*****

The four factors framework I talked about for teams applies equally well to players. Remember that 4 factors means four ways of scoring more efficiently: Shooting better, Getting to the line, taking care of the ball, and rebounding misses. (4 Factors analysis ignores passing, which is a problem at the player level, but not at the team level. Let's ignore this for now.)

Each factor has a stat (actually there are any number of stats, but let's use the canonical ones):

    Shooting better - effective field goal percentage (EFG%)
    Getting to the line - Made free throws per field goal attempt (FT/FGA)
    taking care of the ball - turnover percentage (TO%)
    rebounding misses - offensive rebounding percentage (OR%)


What that means is that if a player has problems in one area, he can contribute in other ways.

Shooting is by far the most important skill. Effective field goal percentage measures his ability to hit shots accurately pretty well. But there is a tradeoff: if you were a player who had a one million dollar bonus in his contract if you hit more than 80% of your shots, what would happen? You'd only take wide-open shots that you were sure you could make, and pass every other time, even when you were partially open and there were rebounders under the basket and the clock was winding down.

That never happens, but I wanted to show another factor of shooting besides accuracy, which is usage. If you only take open shots, you aren't contributing all that much. This is why Eddie House (bless his heart) is not as valuable as Tracy McGrady, even though House is much more accurate from the field.

So there's a tradeoff between accuracy and usage. We're not really sure the precise nature of this tradeoff, but everyone understands that it exists.

Players who shoot poorly from the field can also generate offense by getting to the line. There are some players who have a real skill in this area, all out of proportion to their general basketball skill: I'm thinking of Kyle Lowry and Louis Williams, who get a huge number of points at the line despite not doing much from the field.

Turnovers at the player level is a minefield. Quick: who led the league in each of the last two years in turnovers per minute? Steve Nash. How bout in TO% (turnovers per play)? Nash comes in #2 this year, #9 last year. Clearly, turnovers don't tell us much about player value. But just as obviously, turning the ball over is a bad thing. So what gives?

Unfortunately, I don't have an answer here. I can tell you that assist:turnover ratio is a dumb stat -- it really doesn't make sense to combine these stats in this way. The turnover stat includes all kinds of acts that are not related to passing (three second violations, offensive fouls, traveling, etc). 82games breaks down the turnovers into various types:

That's a place to start. Maybe combining turnovers with assist percentage (as seen on Basketball-reference.com) is the way to go. Or maybe assists:bad pass turnovers is more along the right track (82games has this).

Finally, offensive rebounding percentage, which you can get from basketball-reference and 82games. Good bigs average between 10-15%, good smalls 5-10%. Think about it: teams average 25-30%, so if your center is getting 15% of your team's missed shots, he's accounting for half of your total offensive rebounds by himself.

*****
Where to get these numbers

First of all, you need basketball-reference in your life. Here is a mini-primer on how to use this site.

First of all, season summaries by team or by player. Let's take my favorite player of all time, Oliver Miller. Say I want to look him up on basketball-reference.



Halfway down the page are his advanced stats.


Mouseover the column headers to get a description of the stats. I've talked about some of them already -- the important ones I haven't discussed are

    TS%, which combines FGM and FTM into a kind of points-per-scoring-attempt stat.
    OWS, DWS, WS - offensive, defensive and total Win Shares. I'm not going to talk about these, they're based on ORTG and DRTG.
    AST% - assist percentage, the percentage of teammates' made field goals assisted by the player while he was on the court. Big Ollie had a career 14.2%, which means that he assisted 14% of his teammates FGM while he was on the court, which is pretty good for a center I think.
    Usage% I've mention already, it's important. Remember 20% is average. Big Ollie didn't use a lot of touches.


Remember that PER is scaled so that the average in every season is 15. Look at Miller's PER, which consistently varies around 15 for his career. This means that per minute, Miller's production was about average.

Now look at his ORTG: 103. During the 90s when Miller played, the league average was something like 105, so Miller produced at slightly below average efficiency. Where did he suffer, where did he excel? I've given you the tools to solve this.

Point: Miller shot 54% EFG over his career. League average is about 50%. So Miller was good from the field.

Point: Miller got to the line 2.7 times per 36 minutes. Teams as a whole get about 25 FTA per game, meaning the average player gets 5 per 48 minutes (you follow? 25 per game divided by 5 players = 5 per game, or 5 per 48 minutes), or about 4 per 36 minutes. So Miller was not good at getting his ass to the line

Point: Miller's turnover percentage is terrible: 22% is the worst turnover percentage among centers in the 90s. His assist rate is pretty good, as I said, so he was probably used a lot in a playmaking capacity, generating both turnovers and assists. Brad Miller may be a good comparison here.

Point: He was a decent offensive rebounder: 9.5% is probably slightly above average.

Point: Look at his usage: 16% is below average, but not wildly so. Basically, it's Kendrick Perkins's level usage.

So you get a picture of a player who shot reasonably well from the field, didn't take a huge amount of shots but wasn't shy either, passed a lot, turned it over a lot, and pulled his weight on the glass (har) -- overall, an average offensive player. That's what PER says, that's what ORTG says.


***

I walked you through that because I wanted to show that if you're going to use an all-in-one megastat, it's important to know why it's telling you what it's telling you.

That took a lot longer to write than I thought. I was going to use that as an intro to a tutorial on Basketball-Reference's Play Index feature, which is where I get most of the data I post here. Those of you who think I have access to some kind of mega brain database -- now you know my secret. I'll write that tutorial some other time.

I was also going to include a short primer on statistical concepts relevant to the stuff I talk about, primarily uncertainty and linear regression. That too will have to wait.

USEFUL LINKS YOU SHOULD KNOW

    Basketball-Reference should be the first place you go for anything. The only things they don't have are play-by-play and shot chart stuff.
    82Games has plus-minus stuff, along with some shot location numbers (like "jumpers" and "inside").
    Hoopdata has more detailed shot location data, including boxscore stuff. Very neat.
    BasketballValue has all the adjusted plus-minus numbers you need. (I talked about these a little bit above, and I talked a little bit about the problems with the statistic before. Some other time I'll go into detail). They also have raw data downloads for anyone looking to get in on this hot nerdy action.


Semi useful, and very cool:

    Do you like charts like this?

    You'll like http://nbagraphs.tumblr.com/



    How about x & os stuff?

    Go here: http://nbaplaybook.com/


    Player transaction flowcharts - not updated for this season, but fascinating nonetheless.