Numbers Game: Part One

Many fans probably are unfamiliar with the term "tempo-free statistics" in discussing college basketball. Of the ones who have never heard of this concept, you may at least be familiar with the sister theology in baseball: sabermetrics. Like OPS, runs created and new stats have taken baseball by storm, basketball too is experiencing a shift. In the first of a two-part series, Kyle Lamb explains.

Scouring box scores among a crowded desk of old newspapers, baseball almanacs and crumpled up pieces of paper with chicken-scratch math, Bill James spent years trying to undo decades of learning.

While common voices of the national pastime, Harry Caray, Herb Score, Jack Buck, Vin Scully and Joe Nuxhall were still worshipping batting average, the holy grail of baseball statistics in the day, the 20-something James was about to revolutionize the way we viewed the boys of summer.

In an effort to disprove, what James may as well have considered propaganda, James began the first of many books in 1977 publishing the Bill James Baseball Abstract. The Abstract was a series of books providing statistical studies of previous seasons, citing new theories to gauge the success of baseball teams and their individual players.

These new statistics, called sabermetrics after the Society for American Baseball Research (SABR), berthed new terms such as runs created, win shares, range factor and the Pythagorean expected winning percentage.

Despite all of James' work over the course of two decades, it wasn't until Michael Lewis published Moneyball, a book released in 2003 that brought sabermetrics to the attention of the common baseball fan. Moneyball is an account of Oakland Athletics' General Manager Billy Beane, and his building of the A's by spurning high-priced free agents, and instead, concentrating on position players with exceptional on-base percentages and young pitchers with high strikeout rates and more importantly, inducing a lot of groundball outs.

In constantly overachieving with a budget among the lower half of Major League Baseball, Beane's Oakland teams consistently compete for divisional titles. The protégé of James, practicing many of his many teachings written over the past 30 years, suddenly woke America up to concepts taught to them since Little League.

Until recently, sports fans recognized the Pythagorean Theorem as simply a mathematical rule learned in high school geometry that a₂+b₂=c₂ with regard to area of a triangle. But James' efforts have introduced a whole new meaning.

James' version of the Pythagorean takes total number of a team's runs scored and squaring it, and dividing the number by the sum of runs scored squared and the team's runs allowed squared. The result is the expected winning percentage for the rest of the season, multiplying the number to get the expected number of victories. Remarkably, this method has been known to usually coincide within a few wins of the actual number, even earlier in the season.

Similarly, James created what's termed as the "Log5 method," which takes the winning percentages of two teams and gives an estimated percentage that one team would beat another if they play head-to-head.

Enter Dean Oliver, a 22-year old Caltech graduate after playing point guard from 1986-1988. Inspired by the work of James, and also by North Carolina legendary coaches Frank McGuire and successor Dean Smith, Oliver began pioneering his own work that was basketball-oriented.

While serving some time as an assistant coach for his alma mater, and also a scout, Oliver went to UNC as a graduate student, where he earned his Ph.D. in Statistics and Forecasting in 1994. Oliver had read Smith's 1981 book: Basketball, Multiple Offense and Defense, which referenced points per possession – a statistic designed to compare teams evenly regardless of how many possessions per game a team averages.

By all accounts, McGuire and Smith were the first known coaches to cite what's now called tempo-free statistics in basketball.

"Tempo-free stats capture the efficiency of the game by looking at how many points a team
generates per possession," Oliver said. "Possessions alternate from team to team in a game, so they end up being equal at the end of a game and, at the end of a season, a team and its cumulative opponents, have the same number of possessions.  So a team that runs a lot will score and allow a lot of points, but that doesn't mean that they are either a good offense or bad defense.  When they play a slower team in the playoffs, efficiency will win."

Oliver said he initially wrote a book in 1988, but was too young and naïve to get it published. In 2001, he consulted James on how to go about getting a basketball book published. James came back in 2002 and told him he had aspirations of writing his own basketball-related book.

So worried his inspiration would beat him to the punch, Oliver took a leave of absence from his job and in 2003, began work on Basketball on Paper. In 2004, his first book was released, taking the country by storm and even drawing the endorsement of James, who ultimately deferred to Oliver on the book.

Today, Oliver is the Director of Quantitative Analysis for the Denver Nuggets after serving Seattle for six seasons as a statistical consultant. To drive home the point about efficiency, and the importance of tempo-free statistics, Oliver uses the Phoenix Suns as an example.

According to Oliver, Phoenix, before the acquisition of Shaquille O'Neal, averaged 104 points per game. By comparison, the 1987 Suns' team featuring Walter Davis and Larry Nance averaged 108 points per game. On paper, the 1987 team was considered a better offensive team, despite winning just 36 games. But as Oliver shows: this year's team was generating 112 points per 100 possessions, whereas that team was averaging 108 per 100 possessions.

Basketball on Paper introduces basketball fans to alien concepts. Among them: the basketball court is split into nine zones, six inside the 3-point line and three outside, for purposes of scouting and charting shots. Further, Oliver explains a complicated formula for Offensive and Defensive player ratings that attempt to quantify a player's value to his team.

"I look at points produced by a player and the possessions they use to do that -- that's the offensive part," he explained. "Then I estimate how many points a player can be said to be responsible for giving up defensively per possession.

"The message of the methods is that individuals do things to contribute to their team offense and defense.  We measure some of these - shooting, getting to the line, defensive rebounding, etc. - but we don't measure others - denying a good player the ball, allowing a poor offensive player to take a bad shot, etc.  My methods try to account for these, but they are estimates.  Numbers help, but use your brain."

But perhaps chief among all the information introduced is the idea of the four factors. The four factors state that winning basketball games come down to four very simple concepts: shooting, rebounding, free throws and maximizing possessions (i.e. not turning the ball over).

Remember though, the objective is to derive at these statistics not through quantity, but rather quality.

Instead of field goal percentage, something called "effective field goal percentage" is used, which calculates field goals made plus 50 percent of the 3-pointers made divided by the total number of field goal attempts. This essentially accounts for the fact 3-point attempts are worth an extra point.

To further break this down, 3-point field goal rate is measured, which is how many 3-pointers in 100 possessions a team averages of all their field goals.

Offensive rebounding percentage is simply the percentage of rebounds gained on the offensive end. Free throw rate accounts for the number of free throws made divided by the total number of field goals attempted. And lastly, instead of blindly counting number of turnovers per game, turnover rate accounts for the percentage of a team's offensive possessions that end in a turnover.

Likewise, these numbers are reversed and counted for a team's opponents against the defense.

"These factors explain who wins," Oliver explains. "They break down the score, which also explains who wins, one level to say a little about the ‘Why'.  A team cannot lose all four of these things and win a game.  A team rarely loses three and wins a game.  The ‘Why' gets exposed a little bit through the four factors."

Oliver's book has inspired many others to take advantage of the internet explosion, and further disseminate this new wave of statistical research. Though Oliver and others have done a majority of their research geared toward professional basketball, these metrics are applicable to the collegiate game.

John Gasaway was affectionately known as a blogging hero. His nickname, "Big Ten Wonk" sounded more like a circus clown than a basketball analyst. But still, Gasaway studied Oliver's writing as well as the information provided online by Ken Pomeroy, whose site grew notorious for tempo-free statistics.

This past fall, Gasaway threw away his anonymity, shrouded in secrecy by his popular blog, and instead joined Pomeroy at Basketball Prospectus is modeled after its' baseball counterpart by the same name, which analyzes professional baseball players according to sabermetrics.

For three years, Gasaway was the Big Ten Wonk, posting his observations about Big Ten basketball and analyzing games by points per possession, efficiency rating (which is the number of points scored and given up in 100 possessions), turnover rate, effective field goal percentage and points per weighted shot (points divided by field goals attempted plus 47.5 percent of free throws attempted), among many others.

Gasaway, an Illinois native and graduate, moved to Minneapolis in November 2004 from California. It was at that time he started blogging as the Wonk.

"I was very afraid of my first winter in the Twin Cities and I was looking for an indoor activity for my first winter," he joked. "Illinois looked like they were going to be pretty good, but I decided not to do a team-based blog and instead do a blog on the entire conference. I wasn't sure how the whole blog thing worked, which seems pretty dumb now, but actually in 2004 there was a lot more mystery and curiosity about blogs than there is now."

Pomeroy's site,, tracks many of these statistics, especially efficiency rating on both offense and defense, tempo, which is the average number of possessions per 40 minutes and Pythagorean expected winning percentage, which calculates the expected winning percentage playing against an average basketball team.

Through years of analysis, Oliver determined that with a high accuracy, you can estimate the number of possessions in a given game by subtracting offensive rebounds from field goal attempts, adding turnovers and then adding 47.5 percent of free throw attempts. By doing this calculation for both teams and producing an average will produce a reasonably accurate estimate of possessions.

After finding the number of possessions, dividing a team's points by the number of possessions will give you the points per possession that team scored. Multiplying that by 100 gives you the offensive efficiency (points per 100 possessions) of that same team.

To determine what Pomeroy calls "adjusted offensive efficiency", he multiplies the offensive efficiency by the national average, and divides that by the opponent's adjusted defensive efficiency. This essentially provides an adjusted number for points per 100 possessions, taking into account the strength of the opponent. Every game is totaled and then averaged by the number of games played, giving a season efficiency average.

Accordingly, the same can be done for defensive efficiency and comparing to the opponent's offensive efficiency.

Pomeroy has more than just fans interested in these statistics.

"Somebody had told me about Ken's information, and what he was doing," said Longwood head coach Mike Gillian whose program is still in its five-year Division I probationary period, "and it's not that we use it solely, but if we look through it, I think it's worth it for an hour if you're sitting there late at night look at all this stuff, it's worth your time looking for something that backs up what you're doing."

Oliver estimates nearly 50 percent of the NBA organizations use tempo-free statistics in some capacity. Gasaway and Gillian estimate that a majority of all Division I programs are using them to a degree, though Gasaway cautions there are still several head coaches that do not pay attention to them.

Among some of the head coaches known to use them are: Roy Williams, Mark Few and Wisconsin head coach Bo Ryan, who Gasaway says is very big on them.

"Bo Ryan for example is a big advocate and has always used them," Gasaway said. "He speaks to his team in terms of ‘we want to score more than a point per trip and hold the other guys to less than a point per trip.' His use of the tempo-free stats long predates mine and predates the internet's use."

Another Big Ten head coach, Ohio State's Thad Matta is known to chart everything that occurs during his team's games and practices.

Matta is known for keeping track of every shot, every plus/minus score for every combination of players on the floor at the same time and very intricate details that gives he and his coaching staff the most information possible.

He's also big on tempo-free statistics.

"Yeah absolutely," he said when asked about whether he kept tabs on them. "We do fouls, steals, offensive rebounds, defensive rebounds, assists, turnovers, charges, shooting percentages, offensive scoring rates per possession, defensive scoring per possession – all those things we look at.

Pressed for what he put a higher emphasis on, Matta named two of Oliver's four factors.

"Two of them: taking care of the ball and making shots," he said. "Those are the big things that I think this team have to do to be successful."

ESPN Basketball Analyst Jay Bilas says like all stats, these are a good way to measure teams' deficiencies both offensively and defensively. However, he cautions to always look at the big picture.

"If you look at tempo-free stats, and you say alright, Princeton in adjusted stats is better defensively than North Carolina, and (Princeton forward) Noah Savage scores more points per game in efficiency than (UNC forward) Tyler Hansbrough does," Bilas explains, "when you put them both on the same floor, that's not going to be how it turns out.

"You can do that stuff all you want to, but there are other variables that go into it as well," Bilas added.

It's a point even Oliver agrees with.

Because basketball is more of a team-oriented game than say baseball, statistics, especially individually, don't always as easily tell the story.

"Basketball is a dynamic game where the player interactions are big," he said. "How players fit together matters, so player value changes with context, unlike baseball (context does matter there, but less).  So
Latrell Sprewell had different values depending on whose method you used."

However, Oliver's simplification is this: knowing what wins basketball games, you can derive which players best provide the intangibles statistically to help their teams win.

In part two of a Numbers Game, learn more about the Pythagorean and how it's used to predict which team might win a game. Hear more from Oliver, Gasaway and Bilas about these stats and whether they might be part of cited mainstream statistics in the near future.



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