Big Ten Wonk
Tuesday, November 01, 2005
This is TFS: tempo-free stats.
Tempo-free stats aren't new. The legendary Frank McGuire, who coached North Carolina to a national championship in 1957, used the term "points per possession" as far back as 1959 in his book on defense in basketball. And his successor at Carolina, Dean Smith, also charted games on a possession-by-possession basis. (Last season during the Illinois-Michigan State game, Dick Vitale marveled at the scoring prowess being displayed by the Illini and wondered aloud how it would look if it were being charted on paper by Coach Smith, who had measured offensive efficiency by tracking possessions.)

Nor are tempo-free stats some peculiarly exotic artifact available only from blogs. Something as familiar and mundane as a free throw percentage is, after all, a tempo-free stat. So are three-point FG percentages and assist-turnover ratios. These numbers aren't inflated or deflated according to the pace of the game. (Last year in the wake of Illinois' success, many writers began calculating a number for assists per field goal--another example of a tempo-free stat.) And since I'm certainly not of that ilk who has to grow my own wheat for my bread, I gladly take 3FG pct. numbers on faith from the Big Ten's stat page.

(Strictly speaking, of course, an overall FG percentage is also a tempo-free stat. It's just not a particularly useful one--and hasn't been since the introduction of the three-point shot. Read more here.)

But if you're interested in other things in addition to free throw and three-point percentages and A-T ratios, as most people reading this post no doubt are, then you need to ignore every other stat on the Big Ten (or any conference's) stat page. And I don't mean that to sound harsh. But I do mean it literally. "Scoring offense," "rebounding margin," turnovers, assists, individual points per game--they're all magnified or shrunk according to pace.

(Individual points per game does admittedly tell me one thing I find interesting. It tells me which player on his team the coach thinks should be doing the bulk of the scoring.)

Different teams play at different speeds. In a college game, with its two 20-minute halves and 35-second shot clock, 80 possessions (for each team) qualifies as a fast game and 60 indicates a slow one. In 2005 in games played within the seven alleged "power" conferences (ACC, Big East, Big Ten, Big 12, C-USA, Pac-10, and SEC), teams averaged about 68 possessions per game. (Non-conference games, played mostly in November and December, tend to be faster.) But that average took in everything last year from a North Carolina-Maryland track meet in January with 93 possessions (neither team feared running with the other) to an Illinois-Michigan still-life in February with just 52 possessions (one team definitely feared running with the other). If we can factor out the distortion caused by even these wildly different paces, we can compare any player to any other player or any team to any other team.

And that's where hoops analyst Dean Oliver comes in. Counting a team's possessions during the game may not be new but what is relatively new (newer than 1959, anyway) is the ability to arrive at a very good estimate of the number of possessions in a game after-the-fact simply by reading the box score. As a precocious 19-year-old (!) in 1988, Oliver published a piece in Basketball Digest where he set forth his method. Building on Oliver's work, we today estimate the number of possessions in a college game with the following equation:

Possessions = FGAs - orebs + TOs + (0.475 x FTAs)

Why does this work?
To count the number of possessions in a game we need to find those "events" in the box score that mark the end of a given possession. Turns out there are essentially three ways for a possession to end:

1. On a field goal attempt that does not result in an offensive rebound. If the shot goes in, then, of course, the possession's over. (Unless you're fouled, in which case an FTA will be recorded--see below). If the shot's a miss and the opponent records a defensive rebound, the possession's over. For our present purposes, we treat any FGA that does not result in an offensive rebound as marking the end of the possession.

Thus the first element in the equation is: (FGA - oreb).

2. On a turnover. A TO, properly named, results in a change of possession every time. This includes not only steals and errant passes landing in the front row but also offensive fouls and shot-clock violations.

3. On a free throw. Here's the only tricky part (and it's actually not that tricky). Just like field goal attempts, some free throws result in a change of possession and some don't. But, unlike FGAs, we can't simply deduct offensive rebounds from FTAs and arrive at something close to the correct figure. (Side note: offensive rebounds on free throws are exceedingly rare.) For example, in any instance where a player is awarded two free throws, that first FTA will never, of course, result in a change of possession. So how do we figure out how many FTAs mark a change in possession?

Through a highly advanced and oh-so-technical method known as, um, watching the games and counting. Immediately following the 2005 season, blogger extraordinaire Ken Pomeroy, bless his soul, went over the play-by-plays of 30 games and arrived at 0.475. In other words, on average 47.5 percent of FTAs will result in a change in possession.

(This number, known as a free throw multiplier, will change according to the particular FT rules of the league or level you're looking at. Thus the NBA number is different than the college number.)

So, to recap, the sum of these three elements--FGAs absent an offensive rebound; turnovers; and about 47.5 percent of the FTAs--gives us our estimate for number of possessions:

FGAs - orebs + TOs + (0.475 x FTAs)

(Disclaimer: there are hoops realities that can be missed or at least not captured perfectly by this equation. For example, in the scenario used above where the FGA goes in and the shooter is fouled, the equation views the "and-one" free throw as something akin to half (0.475) a possession. We view it, of course, as a continuation of the previous possession. Which is why I recommend the following course of action....)

How to use this method
The easiest way to apply this equation, of course, is simply to take a team's season totals for FGAs, orebs, TOs and FTAs and plug and chug. I'm certainly not here to tut-tut and rap knuckles over the proper usage of a method I had no hand in creating. And goodness knows even the plug-and-chug method should yield results that shed some interesting light on the more standard tempo-skewed statistical fare. But for my own purposes, I prefer a slightly different approach....

Because running the numbers through this equation yields an estimate of the number of possessions, I'm most comfortable checking that estimate against another number. And there is no better number to check against than the estimated number of possessions for the opposing team.

Take Michigan State's Sweet 16 win over Duke last March. Here are the relevant totals for the Spartans:

65 FGAs - 16 orebs + 16 TOs + (0.475 x 23 FTAs) = 75.9 possessions

Duke's numbers looked like this:

51 FGAs - 9 orebs + 22 TOs + (0.475 x 24 FTAs) = 75.4 possessions

Averaging these two results gives me the number that I use for the game: 75.7 possessions. If you do this for every game Michigan State played last year--that is, find the average between MSU's estimated number of possessions and their opponent's in each game--and total the averages from all 33 games, you arrive at the following number: State had about 2,285 possessions last year.

That number again: 2,285. (The plug-and-chug method, by the way, yields a result of 2,261.)

What can be done with this number?
First, a quick note on what not to do with this number. Do not divide it by 33 (the number of games played last year by the Spartans) and say, "Michigan State averaged 69.2 possessions per game." Because that statement, while literally accurate, is nevertheless misleading: Michigan State played three overtime periods last season (one against Indiana and two in the classic Elite Eight game against Kentucky).

What I think most people mean, though, when they say "average number of possessions per game" is something more like: "assuming a 40-minute game, how many possessions will there be?" So we need to adjust the 69.2 down slightly. When you hear me say "Michigan State averaged 68.5 possessions per game last year," then, keep in mind the ultra-accurate phrasing would actually be: "Michigan State averaged 68.5 possessions per 40 minutes last year." Bottom line: count OTs and adjust accordingly.

Now on to the good stuff....

With 2,285 in our back pocket, we can look at an array of familiar stats for Tom Izzo's team--but now on a tempo-free basis. That is, we can now actually make use of many of those numbers on the Big Ten stat page, simply by dividing each of them by 2,285:

Michigan State recorded 1.13 points per possession last season (2,590/2,285), 0.247 assists per possession, and 0.197 turnovers per possession.

These are numbers based on the Spartans' entire 33-game season, including games against opponents like Nicholls State, Delaware State, and Oakland. No offense against any of the above, but I prefer to look at tempo-free stats from the 16-game conference season whenever possible.

For instance: Michigan State scored 1,183 points on 1,048 possessions in their 16 conference games, yielding a points-per-possession (PPP) figure of 1.13. You will often see this PPP number referred to as offensive efficiency. In the Spartans' Big Ten games their defense gave up 996 points on those same 1,048 possessions, which translates into an opponent points-per-possession (Opp. PPP) figure of 0.95. This is customarily labeled as defensive efficiency.

Lastly, subtracting the defensive efficiency number from the offensive efficiency figure gives you a result often called the efficiency margin. In State's case this number was a very good +0.18. (How revealing is this number? One particularly outstanding fellow blogger has pointed out that of 17 "power"-conference teams in 2005 who posted efficiency margins within their own conferences of +0.10 or better, 10 made the Sweet 16.)

The four factors
Once again, we estimate the number of possessions with this handy little item:

Possessions = FGAs - orebs + TOs + (0.475 x FTAs)

The four factors on the right side of this equation give us the basic elements of both offensive and defensive efficiency for teams: FGAs (how well you shoot); orebs (how well you rebound your misses); TOs (how well you hold on to the ball); and FTAs (how often you get to the line).

Here are the most commonly used tempo-free measures for each of these four factors on offense:

1. Shooting. Effective FG pct. (eFG pct.) = (FGM + (0.5 x 3PM))/FGA. (Read more here.)
2. Offensive Rebounding. Oreb pct. = team orebs/(team orebs + opponent drebs). (Read more here.)
3. Turnovers. TO pct. = TOs/possessions.
4. Free Throws. Free throw proficiency = FTM/FGA.

The efficiency measures for defense are, for the most part, simply flipped around:

1. Shooting. Opponent eFG pct. = (Opp. FGM + (0.5 x Opp. 3PM)/Opp. FGA.
2. Defensive rebounding. Dreb pct. = team drebs/(team drebs + opponent orebs).
3. Turnovers. Opp. TO pct. = Opp. TOs/possessions.
4. Free Throws. Opp. FT opportunities = Opp. FTA/Opp. FGA.

(Note that a team's offensive free throw efficiency is measured not only according to how often they get to the line but also according to how well they shoot once they get there. How well your opponent shoots free throws, conversely, is held for better or worse to be largely a matter of luck. Thus your opponent's free throw opportunities are measured as a ratio between attempts: FTAs and FGAs.)

That, in a (rather large) nutshell, is an intro to tempo-free stats for teams.

What about tempo-free stats for individual players?
Now that we have the basic principles covered (and rather than harangue you for another 2,000 words), I think a series of links should suffice on this front....

On the offensive side of the ball, I like the simplicity and intuitive cogency of points per weighted shot (PPWS), a stat developed by John Hollinger and renamed brazenly by yours truly. Read more about PPWS here.

For a given player, we can also determine an estimate for their own individual possessions, a number that is very handy when assessing a player's turnovers and assists. (More on calculating individual possessions here. In effect, individual possessions is the result of multiplying the percentage of minutes played times team possessions. That percentage of minutes played, by the way, is also the jumping-off point for calculating individual rebound percentages--more on that here.)

And, for his part, Dean Oliver has developed (much) more sophisticated measures of individual offensive performance--read more here. (Oliver is even working with the WNBA on a project to record individual tempo-free defensive stats.)

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