An article published in the New York Times last week began as follows:

For Free Throws, 50 Years of Practice Is No Help

by John Branch

CEDAR CITY, Utah -

Yes, an article from the New York Times was filed from Cedar City, Utah. 

Now Cedar City is home to a number of wonderful things.  There is

• Southern Utah University, a school that I think deserves far more attention than it receives (it’s really a very good school, and no, I am not just saying this).
• the Utah Shakespearean Festival, which won a Tony Award in 2000 (yes, it’s quite good).
• within a very short drive, a number of national parks including Bryce Canyon, Cedar Breaks, and Zion National Park.

Although all of this deserves more national attention, the New York Times ignored it all.  No, what John Branch wanted to focus upon was free throws.

Coming to Utah to Discuss Free Throws?

And why would Branch come to Cedar City to discuss free throws? It turns out that the Southern Utah Thunderbirds lead the NCAA in free throw percentage.

And that leads us to ask…. why would the New York Times send someone to Cedar City to cover the Thunderbirds ability to hit shots from the charity stripe?  Although the story involved a trip to Cedar City, the focus was on the following:

• Free throw percentage is remarkably consistent across time. An average college player hits 69% of his free throws. Players in the NBA and WNBA hit about 75%. With respect to the NBA and NCAA, these averages have persisted since at least the 1960s.
• It’s argued in the article that coaches can impact free throw percentage. At least, that is a reason offered for the superior free throw shooting observed at Southern Utah.
• Most coaches, though, do not focus on free throw shooting (hence performance does not change).  And coaches ignore free throw shooting (again, according to the article) because other aspects of the game are considered more important. After all, as the article note:

“There is little correlation between free-throw percentages and winning percentages. Only one of the 25 best shooting teams, No. 2 North Carolina, is also in the latest Associated Press top 25 rankings. Southern Utah has a losing record. That is why, despite accounting for more than 20 percent of scoring in men’s college basketball and just below 20 percent in the N.B.A., free throws receive a fraction of the attention from coaches, players and fans.”

The Importance of Free Throw Shooting

If we look at the NBA we can see evidence for why coaches should ignore free throw shooting.  From 1977-78 to 2007-08 the correlation between a team’s free throw percentage and team winning percentage is only 0.18.  In other words, free throw percentage explains only 3% of team wins [correlation is r, explanatory power is r²]. Given these numbers it’s clear that teams should just ignore free throw percentage.

Of course, there’s a problem with these numbers.  Our simple model of winning percentage supposes that wins are only explained by free throw percentage.  In other words, we didn’t include any other explanatory variable.  And since other factors definitely matter, our model is mis-specified.  In simpler terms, because we didn’t consider any other factor that impacts wins, our simple model really really won’t tell us the actual link between winning percentage and free throw percentage.

When we do specify the model for winning percentage properly we do see that free throw percentage does matter quite a bit.  And to see how much it matters, consider the productivity of players who struggle at the free throw line.

Shaq and Superman

Perhaps the most famous poor performer at the line is Shaquille O’Neal.  Shaq entered the league in 1992-93.  Across the next 16 seasons (ending with the 2007-08 campaign), O’Neal posted a 0.307 WP48.  Certainly this is an excellent mark (average is 0.100).  But relative to the following sample of all-time greats, Shaq comes up a bit short: Continue reading →

Today’s Guest Post is from Brian Burke.  Readers may know Brian from Advanced NFL Stats, a site that provides some of the very best statistical analysis of the NFL.  With football season over, Brian has turned his attention to college basketball. He already has a web site set up for college basketball [http://wp.advancednflstats.com/bball]. And this post introduces a very interesting approach to the analysis of this sport.  Before getting to the post I want to thank Brian for writing this for The Wages of Wins Journal.  Again, I think everyone will find this to be quite interesting.

Although I usually stick to football research, I’ve recently dipped my toe into studying basketball. I’ve built an in-game win probability (WP) model for NCAA basketball. Basically, it takes the score and time remaining from any moment of a game and estimates the chances that each team will win. Although others have developed WP models for basketball before, I’ve gone a step further and created a web site with a live feed that graphs the WP for every game in real-time [http://wp.advancednflstats.com/bball].

In football WP estimates are very useful. Football is a game of strategy decisions such as ‘kick a field goal or go for the first down’, or ‘punt from your end zone or accept an intentional safety’. WP can tell you which decision is usually best and can identify when coaches are making big mistakes. It can also tell you which plays were truly important in any game. Sure, that incredible acrobatic 20-yard reception will make it on Sports Center, but the real ‘play of the game’ was that otherwise unremarkable 5-yard straight-ahead run on 3rd and 4 in the 4th quarter that let the winners burn another 3 minutes off the clock.

To be honest, once I started the WP project for NFL games, it just got to be plain fun. When the season ended I looked around for another sport to model and decided on college basketball.

The WP modeling technique I use is sometimes called an ‘empirical matrix.’ I took a set of play-by-play data from recent years of NCAA regular season games 1,782 games from the past 3 years—360 thousand in-game observations in all] and divided it up by home team lead and by time remaining. I simply observed the proportion of times that the home team went on to win the game. Table One presents these observations.

Table One: Home team winning with lead at different points in a college basketball game

With enough data, that’s almost all you have to do. But because of limited sample size in many of the cells (there may not be many combinations of 17 point leads with 19 minutes to play), the results will be somewhat noisy. To reduce the noise, I used logistic regression. For each minute of time remaining, I ran a regression using the current score difference to predict win probability for the home team. Graph One illustrates an example of the raw, unsmoothed data and the resulting regression estimate:

Graph One: Home Team Win Probability.

Here is what a typical game’s WP timeline looks like. This is the recent Villanova-Notre Dame game:

Graph Two: Villanova vs. Notre Dame

One thing I’ve already noticed that’s interesting about basketball is that the win probability equation is the same for nearly the entire game. In other words, a 6-point lead for the home team in the first 10 minutes of the game yields the same WP of 0.86 as a 6-point lead with 10 minutes to go in the 2nd half.

This surprised me. I would have expected any certain lead to be more decisive as the game went on, gradually becoming more and more insurmountable. In the graph I cited above, the “slope” of the curve would theoretically get steeper and steeper as the game goes on. When I went to make a graph of selected times in the game to show how the curve steepens, I could only see a single curve. I thought I had made some kind of error in Excel, but the curves were just superimposed. Not until the final couple minutes do the curves become very steep, when ultimately a 1-point lead with zero seconds remaining is as decisive as a 10-point lead.

Although basketball doesn’t have the same strategy elements as football, there are some interesting potential applications of WP in Dr. Naismith’s creation–when to start fouling, when to slow down the game, the value of simply possessing the ball, or how much the ref’s bogus call really swung the game.

I can’t answer all those questions just yet, and I should probably leave that stuff to the basketball experts. But I’ve already learned a lot, particularly from a comparative-sports perspective. Just as learning a foreign language helps one more thoroughly understand your own language, to truly understand a sport one should understand how it differs from the other sports. I’d like to improve the model in some ways, particularly with respect to non-continuous considerations in the crucial final minutes. For example, a 4-point lead is more than 33% better than a 3-point lead because the game is essentially out of reach of a single possession. I might also like to include factors such as penalty bonuses or time outs remaining.

I should also note that the model is generic. Even if my team, Navy, were playing at Duke, my model would yield the same WP estimate as for any two other teams. There are ways to factor in team strength, but a generic model is a good baseline for now. 

I thought I’d share this with hard core basketball stat-heads out there, and I figured this would be a good place. Thanks to Dave for allowing me to post here. And yes…I’ll probably have an NBA version up and running in time for the playoffs.

Brian Burke

The last time playoff basketball was seen in Charlotte, the following five players led Charlotte in Wins Produced: P.J. Brown (13.6 Wins Produced), Baron Davis (9.6 Wins Produced), Jamaal Magloire (6.8 Wins Produced), Elden Campbell (6.1 Wins Produced), and Stacey Augmon (3.2 Wins Produced).  And the team was called the Hornets.

After that team was eliminated by the New Jersey Nets in the second round of the 2001 playoffs, the franchise moved to New Orleans.  Two years later, the Bobcats began losing in Charlotte.  Four seasons of Bobcat basketball have now been played and the team has yet to win more than 33 games in a season.  This year – after 61 games – the Bobcats have only won 26 games.  Despite this record, John Hollinger thinks Charlotte has a chance to see playoff basketball. And Hollinger just might be right.

Charlotte’s New Rotation

If you look at what Charlotte’s players have done after 61 games, though, it might be difficult to see Hollinger’s point.

Table One: The Charlotte Bobcats after 61 games in 2008-09

So far the Bobcats have employed 23 players in 2008-09.  If you look at the productivity of all these players – as reported in Table One – it’s clear that most of these players have not very helpful.  Only four players – Emeka Okafor, Gerald Wallace, Raymond Felton, and Raja Bell – have posted a WP48 [Wins Produced per 48 minutes] that’s above average.  For fourteen Bobcats, WP48 is in the negative range.  With such a collection of talent, we are not surprised to see a team with a winning percentage below the 0.500 mark.

Looking at all the players Charlotte has employed this season, though, is misleading.  Many of these players (like Adam Morrison, Jared Dudley, Matt Carroll, etc…) are no longer on the roster. 

And many of those that are on the current roster are not playing much.  As Hollinger notes, Larry Brown – the much traveled coach of the Bobcats – has settled on the following eight man rotation:

Starters: Raymond Felton, Raja Bell, Gerald Wallace, Boris Diaw, Emeka Okafor

Reserves: D.J. Augustin (backing up the guards), Vladimir Radmanovic (backing up the forwards), DeSagana Diop (backing up Okafor)

If we focus just on these eight players, this is actually a very good team.  Given these player’s WP48 marks thus far – and guessing at how many minutes each will play the remainder of the season – here is a crude projection for each player in Charlotte’s rotation across the last 21 games: Continue reading →

The hot topic in basketball these days is the measurement of a basketball player’s productivity.  For years we have had the traditional box score which can be viewed through the lens of NBA Efficiency, TENDEX, Points Created, PERs, Game Score, Wins Shares, Win Score, and Wins Produced.  And then we have the non-box score approaches of plus-minus and adjusted plus-minus.  With all these measures out there, it seems unlikely that we need to call attention to anything else.  Nevertheless, I thought I would devote a post to a measure that’s in my morning paper each day.

The Miller Metric

Each morning the Salt Lake Tribune is delivered to my house in Cedar City.  Not surprisingly, the Utah Jazz gets quite a bit of coverage from this paper.  And part of this coverage is a measure of performance that I don’t think is seen much outside of Utah.   Larry Miller – the long-time owner of the Jazz who recently passed away – devised a measure called the Miller Metric.  The measure is calculated as follows:

Miller Metric = Points + Rebounds + Steals + Blocked Shots + Assists – Turnovers – Shot Attempts – Personal Fouls

Each time the Jazz play the Miller Metric is reported and it’s also part of the season statistics reported for the team.

Looking at the Miller Metric I am reminded of Win Score, or the simple measure of performance we introduced in the Wages of Wins. 

Win Score = PTS + REB + STL + ½*BLK + ½*AST

- FGA – ½*FTA – TO – ½*PF

These two measures are not exactly the same.  The obvious differences included the weighting of blocked shots, assists, and personal fouls, as well as the inclusion of free attempts in Win Score.  But the measures are similar in how shooting efficiency is treated.  Unlike NBA Efficiency, TENDEX, Points Created, PERS, and Game Score; Win Score and the Miller Metric require players to shoot efficiently from the field.  Specifically, instead of subtracting missed shots (the approach taken by NBA Efficiency), bothe the Miller Metric and Win Score subtract field goal attempts.  Consequently, despite the differences cited, the Miller Metric (per 48 minute) and Win Score (per 48 minute) have a 0.92 correlation (from 1977-78 to 2007-08).

Evaluating the Jazz

To see the similarities, Table One presents evaluations of the Utah Jazz – after 60 games – by both metrics.

Table One: Evaluating the Utah Jazz in 2008-09 with PAMM and PAWS

Table One presents position adjusted figures for both measures.  For the Miller Metric the position adjusted measure – what I call PAMM [Position Adjusted Miller Metric] – is not as necessary.  This is because free throw attempts are ignored by the Miller Metric (at least, I get the numbers the Tribune gets when I ignore free throw attempts).  As a consequence, although shooting efficiency from the field is required by the Miller Metric, from the line efficiency is not required (i.e. the more you shoot from the line the better you will look regardless of free throw percentage). 

If you add free throw attempts to the Miller Metric – by subtracting ½*FTA from this measure – the correlation with per 48 minute Win Score rises to 0.94.  And then a position adjustment will clearly be required.  In other words, as you move from a measure that focuses more on scoring totals to one that focuses more on scoring efficiency, you have to consider where a player is playing on the court.

Regardless of the free throw attempt issue, there are clear similarities between both PAMM and PAWS (Position Adjusted Win Score).  The top six players on the Jazz – Carlos Boozer, Deron Williams, Andrei Kirilenko, Paul Millsap, Ronnie Brewer, and Mehmet Okur — are the same by both measures. And both measures regard these six as the only above average players on the team.  In sum, both PAMM and PAWS are telling similar stories. Continue reading →

Traditionally sports teams visit the White House after winning a championship.  This past week, though, we were able to witness a change that Chicago Bulls fans can believe in.  The Bulls were invited to the White House by Barack Obama, the team’s most powerful fan. 

Clearly such an invite trampled on historical precedence.  And in general, historical precedence is not easily ignored (see baseball’s anti-trust exemption).  So let’s imaging Congress passes a law restricting the power of President Obama to visit with his favorite team in the White House.  If the Bulls can only visit when they win another title, how soon can the Bulls expect another visit?

The Bulls Today

For an answer, let’s look at the Bulls today.  The Bulls have won 27 of their first 60 contests in 2008-09; with an efficiency differential (offensive efficiency minus defensive efficiency) of -1.5.  This differential mark is an improvement over last year (-3.2) but is still below average.  When we look at the individual players, reported in Table One, we can see why this team is below par.

 Table One: The Chicago Bulls after 60 games in 2008-09

So far eleven players have logged at least 500 minutes with Chicago in 2008-09.  Of these, only three – Joakim Noah, Luol Deng, and Thabo Sefolosha — have posted WP48 [Wins Produced per 48 minutes] marks that are above average.  And of these three, Sefolosha has left the team and Deng may have suffered a season ending injury.  So the Bulls have problems in 2008-09.  It’s still possible Chicago will make the playoffs in 2009, but a return trip to the White House as NBA champions is going to have to wait.

The Very Good

So let’s look at next season.  Here are the players under contract for next season: Noah, Deng, Brad Miller, Derrick Rose, Kirk Hinrich, Tyrus Thomas, John Salmons, Tim Thomas, and Jerome James. 

Based on past performance, three players are likely to be productive in 2009-10.  But Brad Miller – with a career WP48 entering this season of 0.197 – plays the same position as Joakim Noah.  If the Bulls can move one of these very good players to power forward, then their starting frontcourt looks solid.  If not, substantial production is going to be stuck on the bench next season.

The Good

After these two big men, the next most productive player is Deng.  As noted, Deng is hurt.  And although his production is still above average, he’s not what he once was.  Two years ago Deng posted a 0.234 WP48.  This season his mark is only 0.116. 

When we look at the individual numbers – listed in Table Two – we can see where Deng has slipped.

Table Two: Evaluating Luol Deng

From Table Two we see that Deng’s Net Possession (Rebounds + Steals – Turnovers) are unchanged from 2006-07.  His shooting efficiency, though, has fallen quite a bit.  And this decline is part of a trend.  Last year Deng increased his shot attempts from 2006-07 and his efficiency dropped.  This year his shot attempts were reduced and his efficiency fell even further.   If Deng is going to return to what he was two years ago, someone is going to need to figure out why his shots are not dropping.   If that problem can be solved, the Bulls have a small forward that can produce for years to come.  If not, the Bulls can turn to….

Well, the Bulls did just trade for John Salmons.  Although Salmons has been above average the first five games he played in Chicago, his career WP48 entering this season was 0.064.  And in Sacramento this season he was also below average. So it seems likely that Salmons is not the answer.

The Average

Fans of the Bulls probably don’t think Salmons is the answer.  For fans of this team, the future is Derrick Rose.  Rose was the number one pick in 2008 NBA draft and it’s expected that he will be a star.  After 60 games, though, his numbers are a bit disappointing.  Yes he is averaging 16.6 points and 6.3 assists per game.  But when we look at the per-48 minute numbers – and compare Rose to an average point guard and t0 what other “star point guards” did their rookie season – Rose often comes up short.

Table Three: Evaluating Derrick Rose

Just looking at Rose and the average point guard, we see a player that’s about average with respect to shooting efficiency, rebounds, turnovers, blocked shots, and free throw shooting.  And he’s below average with respect to steals and assists.  In sum, at this point Rose does nothing particularly well.  Continue reading →