For several normally steady playmakers, the leather sphere felt like a tennis ball on Sunday. Waking up from New Year's Eve, these fellows couldn't play either offense or defense.
Showing posts with label quant stuff. Show all posts
Showing posts with label quant stuff. Show all posts
Monday, January 2, 2012
New Year's Hangover
Friday, May 28, 2010
Antoine Walker: Not A Bust, Now Bust
Antoine Walker, a former Boston Celtic, Dallas Maverick, Atlanta Hawk, Miami Heater, and Memphis Grizzly, apparently filed for bankruptcy last week under Chapter 7 of the U.S. Bankruptcy Code. The linked article from the Wall Street Journal does a good job of outlining Walker's financial woes: $12 MM in personal debts but only $4 MM in assets. Yeah, this guy lived a bit too large. He generally lived up to his promise as the #6 pick in the 1996 NBA draft, scoring over 20 PPG for five years and helping the Miami Heat win the 2006 NBA title as their starting small forward. Although he took a lot of foolhardy three-pointers, his biggest disappointment was in his financial prudence.
Under 11 U.S.C. §523 and §727, a Chapter 7 case results, after liquidation of the debtor's estate, in discharge of all the debtor's debts that arose before the bankruptcy petition (with certain exceptions like tax obligations and domestic support obligations). Secured creditors get the value of their collateral, up to the amount of their secured claim, and unsecured creditors get whatever is left over from such collateral and the debtor's other assets. Walker is going to wind up with nothing going forward, other than his income-generating ability, whatever that may be.
What's more, it seems that Walker's biggest real estate liability is a $2.3 MM secured mortgage on a Chicago-area mansion. Illinois allows deficiency judgments (see 735 ILCS §15-1504(f)), which means that even if Walker's mortgage lender foreclosed on his house under ordinary non-bankruptcy procedure, they could still sue him for the difference if the market value of the mansion came in below $2.3 MM, which is likely given recent real estate trends. In Chapter 7, that potential deficiency claim by the bank will be discharged along with most of his other personal debts. This would not be the case in a Chapter 13 filing.
Under 11 U.S.C. §707(b), Walker's Chapter 7 filing might be deemed presumptively abusive and thus dismissed, or converted to Chapters 11/13, if his monthly net income (after deducting reasonable living expenses, mortgage payments, and domestic support obligations), multiplied by 60, exceeds $10,000. In other words, if his monthly net income exceeds $167, his case may be deemed abusive, unless he can show "special circumstances" such as military service obligation or a serious medical condition. It is hard to believe that Walker cannot bank a couple hundred bucks per month, but I suppose that is what you get when you live like Antoine Walker. In the WSJ article above, he claims to have zero income.
Thursday, November 19, 2009
I'm Looking Through You
The Hawks and Suns are receiving lots of good press for their hot 10-2 starts, each team atop its respective conference. My initial reaction is "It's early yet. They'll cool off soon enough." Yet if this were the NFL, the season would be 75% finished and the Hawks would be undeniable favorites for the championship! I'm not sure what this reveals more: that sample sizes in football are a bit too small (the Colts are hardly as unstoppable as their record indicates, and Buffalo need not have fired its coach for missing out on a 55% win percentage by just two games), or that the NBA season drags on too long. How much more information about team quality will we learn over 82 NBA games compared to the first 12? Sure, on the margin between lottery teams and mediocre playoff teams there may be some churning (will the Raptors make it? the plucky Rox?) but it's already pretty clear which teams are best. Viz., the same teams, generally, that pre-season predictions thought to be contenders. Other than (not insignificant) revenue considerations, why play five more months and cause more injuries just to determine playoff ordering?
When I have more time on my hands, I will construct a database showing the number of playoff wins for each playoff team over 2000-2009, and run some correlations against my earlier data set of regular season wins. (Or if anyone out there would like to be an unpaid JPO intern...)
Sunday, November 15, 2009
Fantasy vs. Reality
Fantasy hoops are a big deal, as Yahoo and ESPN can attest. And with each season, the fantasy leaguers get increasingly numerous and serious. There is a growing intelligentsia of fantasy aficionados -- some of whom get their own shows on NBA TV -- and a number of professional fantasy-focused websites. (See WinMyFantasyLeague.com). [Full disclosure: HOSS's brother is a contributor to WinMyFantasyLeague.]
This writer is not immune to the fantasy hoops bug (although my team, Turkoglicious, has been an early season disappointment). But one thing that consistently irks me about fantasy hoops is how poorly fantasy stats translate to real life, and vice versa. Exhibit A: Troy Murphy is considered a fantasy stud. Yahoo Fantasy ranked him 35th overall in its pre-season rankings, one spot behind Carmelo Anthony, and ahead of Rashard Lewis (36th), LaMarcus Aldridge (40th) and Carlos Boozer (44th) . In real life, would anyone take Troy Murphy before those three players? On the flip side, there are guys like Shane Battier and Luis Scola, who are very good players and great at the so-called intangibles (ball-on-ball defense, help defense, diving for loose balls) for which there are no statistics. As a result, Shane Battier is ranked a distant 135th.
There seems to be a few reasons for the fantasy/reality divide. First, unlike baseball, which is really an individual sport masquerading as a team sport, basketball is a quintessentially team game. But there is no stat for "making your teammates better", or if there is one, it is imperfect. An assist means you made a pass that led a teammate to score. But there are plenty of ball hogs who have high assist numbers simply by virtue of having the ball in their hands so much (see, e.g., Allen Iverson.)
Turns out there is a whole range of basketball skills that aren't accounted for in any traditional statistics, while some traditional statistics are completely misleading. Although steals and blocks are "defensive" statistics, they do not measure the quality of a defender's ball-on-ball defense. Steals are especially misleading. Again, take Allen Iverson, who loafs all game on defense and then and gambles on steals a few times a game: his steals stats were high but his defense lackluster throughout his career. Similarly, rebounds can be highly misleading. Of course, team rebounding is immensely important, but any post player will have 6 rebounds a game simply by virtue of standing near the hoop, and rebounds off a missed free throw are one of the easiest stats to accumulate in pro sports. As long as fantasy GMs and real GMs focus on traditional stats, fantastic defenders like Shane Battier will always be undervalued. Traditional hoops statistics give you a myopic view of the player's skill or value to the team.
Efforts to expand basketball stats beyond the traditional have been choppy at best. The +/- stat, the holy grail for some hockey statisticians, turns out to be a highly dubious stat. How does Kevin Durant have one of the worst +/- stats in the league last year? Is he a detriment to his team or are his teammates so in awe of his ability that they just stand around doing nothing on offense? The likely answer is probably 'none of the above' -- but simply that +/- is not a useful stat for measuring NBA players' skill level or value to the team.
Some people have tried to devise new statistics that do a better job of capturing a player's value. ESPN analyst, John Hollinger, has devised a methodology for determining a player's actual value, called "Player Efficiency Rating" or "PER". The PER is built on traditional statistics, but adjusts for minutes played and for the team's pace of play. Although Hollinger stats are useful because they allow you to compare two players who average different amounts of minutes-per-game and play on teams with different styles, they still do not account for difficult-to-measure skills like ball-on-ball defense -- arguably one of the most important basketball skills.
There is a movement among some GMs to take basketball statistics to the next level. Some are lifting a page out of Billy Beane's playbook (of Money Ball fame) and attempting to do for basketball what a select group of young baseball GMs have done for baseball -- i.e., devise a modernized, analytical approach to determining a player's true value by using advanced statistical tools. Daryl Morey, GM of the Rockets, is an early adherent. Morey has not revealed his methodology, but if the success of the T-Mac-less-&-Yao-less Rockets is any indication, Morey is on to something.
This issue, however, remains an open debate. We, at JPO, would love to hear from our readers. What is the best way to measure a player's value to his team? Your answers can be general (e.g., Hollinger's PER) or position-specific (e.g., John Stockton once said that the way to measure a PG was to look at the FG% of his team). Post your responses in the "comments" section to this post.
This writer is not immune to the fantasy hoops bug (although my team, Turkoglicious, has been an early season disappointment). But one thing that consistently irks me about fantasy hoops is how poorly fantasy stats translate to real life, and vice versa. Exhibit A: Troy Murphy is considered a fantasy stud. Yahoo Fantasy ranked him 35th overall in its pre-season rankings, one spot behind Carmelo Anthony, and ahead of Rashard Lewis (36th), LaMarcus Aldridge (40th) and Carlos Boozer (44th) . In real life, would anyone take Troy Murphy before those three players? On the flip side, there are guys like Shane Battier and Luis Scola, who are very good players and great at the so-called intangibles (ball-on-ball defense, help defense, diving for loose balls) for which there are no statistics. As a result, Shane Battier is ranked a distant 135th.
There seems to be a few reasons for the fantasy/reality divide. First, unlike baseball, which is really an individual sport masquerading as a team sport, basketball is a quintessentially team game. But there is no stat for "making your teammates better", or if there is one, it is imperfect. An assist means you made a pass that led a teammate to score. But there are plenty of ball hogs who have high assist numbers simply by virtue of having the ball in their hands so much (see, e.g., Allen Iverson.)
Turns out there is a whole range of basketball skills that aren't accounted for in any traditional statistics, while some traditional statistics are completely misleading. Although steals and blocks are "defensive" statistics, they do not measure the quality of a defender's ball-on-ball defense. Steals are especially misleading. Again, take Allen Iverson, who loafs all game on defense and then and gambles on steals a few times a game: his steals stats were high but his defense lackluster throughout his career. Similarly, rebounds can be highly misleading. Of course, team rebounding is immensely important, but any post player will have 6 rebounds a game simply by virtue of standing near the hoop, and rebounds off a missed free throw are one of the easiest stats to accumulate in pro sports. As long as fantasy GMs and real GMs focus on traditional stats, fantastic defenders like Shane Battier will always be undervalued. Traditional hoops statistics give you a myopic view of the player's skill or value to the team.
Efforts to expand basketball stats beyond the traditional have been choppy at best. The +/- stat, the holy grail for some hockey statisticians, turns out to be a highly dubious stat. How does Kevin Durant have one of the worst +/- stats in the league last year? Is he a detriment to his team or are his teammates so in awe of his ability that they just stand around doing nothing on offense? The likely answer is probably 'none of the above' -- but simply that +/- is not a useful stat for measuring NBA players' skill level or value to the team.
Some people have tried to devise new statistics that do a better job of capturing a player's value. ESPN analyst, John Hollinger, has devised a methodology for determining a player's actual value, called "Player Efficiency Rating" or "PER". The PER is built on traditional statistics, but adjusts for minutes played and for the team's pace of play. Although Hollinger stats are useful because they allow you to compare two players who average different amounts of minutes-per-game and play on teams with different styles, they still do not account for difficult-to-measure skills like ball-on-ball defense -- arguably one of the most important basketball skills.
There is a movement among some GMs to take basketball statistics to the next level. Some are lifting a page out of Billy Beane's playbook (of Money Ball fame) and attempting to do for basketball what a select group of young baseball GMs have done for baseball -- i.e., devise a modernized, analytical approach to determining a player's true value by using advanced statistical tools. Daryl Morey, GM of the Rockets, is an early adherent. Morey has not revealed his methodology, but if the success of the T-Mac-less-&-Yao-less Rockets is any indication, Morey is on to something.
This issue, however, remains an open debate. We, at JPO, would love to hear from our readers. What is the best way to measure a player's value to his team? Your answers can be general (e.g., Hollinger's PER) or position-specific (e.g., John Stockton once said that the way to measure a PG was to look at the FG% of his team). Post your responses in the "comments" section to this post.
Thursday, October 29, 2009
Two Roads Diverged In A Yellow Wood
Inter alia, the 2008-09 NBA season saw two remarkable streaks: Cleveland won 39 of its first 40 home games (before dropping a meaningless finale by one point in overtime with bench players seeing the most court time) and Jose Calderon made an NBA-record 151 of 154 free throws. After two nights of this season, Cleveland is 0-2 (0-1 at home) and Calderon is shooting 60% on his free throws, having missed two of five.
Flipped coins don't have a memory of the prior flip, and so the probability of a given outcome (heads, say) is constant over time and independent of whatever happened earlier. Five heads in a row? Your chance of another head is still 50%. Yet athletic outcomes surely are not like that. Success breeds confidence and good habits, which breed more success; alternatively, an eternally wowing streak like 98 percent free-throw completion might weigh mentally and make a man more nervous. Clearly with Cleveland and Calderon, the positive-feedback side dominated last year. Yet in the season's first bounces, these guys collapsed on the metrics wherein they kicked butt in 08-09. That truly is surprising; their "memory" is now amnesiac. Much like children who have no books during summer vacation, basketball players apparently forget what made them great while they slumber in July and August.
Friday, October 9, 2009
Transitive Gaijin
Strange stuff over at NBA.com's annual survey of general managers.
58.6 percent of GMs believe that Tim Duncan is the best power forward in the league. 10.3% (about 3 respondents out of 29?) favor Dirk Nowitzki, and Pau Gasol earns honorable mention.
Meanwhile, 64.3 percent of GMs believe that Dirk Nowitzki is the best international player in the Association, with Gasol second at 10.7% (3 votes out of 28) and Duncan last with 7.1% (2 votes).
How can GMs rank Duncan > Nowitzki > Gasol in one setting, and Nowitzki > Gasol > Duncan in another? It is possible that ballots were completely open: rather than providing a list of candidates, the survey makers asked GMs to fill in their own answers. If so, it suggests that few people think of Tim Duncan as an "international" player. And rightly so, for this purpose: while there is certainly a centuries-old local culture in the U.S. Virgin Islands, the territories are sufficiently Americanized that b-ball development is not much different from its mainland form. Another possibility is that the ballot did provide explicit choices, but Duncan seems to stand out in respondents' minds as more quintessentially power-forward-ish, yet not so fundamentally foreign-ish. Thus, the reversal in the preference ordering may reflect how intensely the respondents associate Duncan with those respective properties.
What I'd like to know is: what's up with Dirk's new haircut?
Friday, June 19, 2009
Those Magic Changes
As the ’00s (the “oughts”, right?) near their end, I anticipate a host of popular journalism reviewing the best of the decade in a variety of fields: business, music, film, politics. Sadly, these were not ten great years for innovation or domination. The Big Three car companies in the U.S. California
Basketball is no more or less susceptible to whitewater rapids trips down the chasm of greatness. The ’80s gave us Bird, Johnson, McHale, Thomas, Worthy, Wilkins, Drexler,
(Compare this to the babies of the Oughts, full of probable all-timers: Gasol,
As a result of the dearth of quality talent among Nineties-vintage stars,this past decade was simply not an exciting time for pro basketball. Shaquille O’Neal and Tim Duncan won eight championships in the nine seasons after Michael Jordan left the Bulls, and their Finals foes were never very intimidating.
Instinctually, it seems that the team of the decade was the San Antonio Spurs, the only team to win 50 games in each of all ten seasons. Three of those ended with a title. The Spurs actually presaged their dominance in the abbreviated 1998-99 season, as Duncan and Robinson obliterated their competition on their way to a championship.
The Shaq-&-Kobe-powered Lakers reached 50 wins in each of the first five years of the decade, and then Bryant plus Gasol and Odom did it again in 2007-08 and 2008-09. They also made the playoffs in ’06 and ’07, as Bryant led a team of laggards including Kwame Brown and Smush Parker to the first round. The Lakers reached (and won) six conference finals, and won four of the six NBA Finals they played in. Had Shaquille O’Neal not left the team in 2004, the Lakers probably would have amassed five or six total championships.
Various Western teams threatened the dominance of
Actually, the second team that maintained greatness throughout the decade (besides the Spurs) was not LAL, but DAL. This past April,
In the East, there’s not much greatness to be found.
Two teams really stand out as attaining some level of sustained excellence in this decade: first, and most obviously,
Second, the Miami Heat had a desultory series of moments, reaching the playoffs with very different looks: first, the Mourning-Hardaway-Brown-Mashburn squad that achieved so much success in the late ‘90s; then a brand-new team of Bruce Bowen, Brian Grant, Eddie Jones, and Anthony Mason plugged in around Hardaway; then the jolly rogues of Dwyane Wade, Caron Butler, Lamar Odom, Udonis Haslem, Grant and Jones; then the golden aspirants of Wade, Haslem, Jones, Shaquille O’Neal, and Mourning; then the previous quintet minus Jones and with Gary Payton, Antoine Walker, Jason Williams, and James Posey; and finally, in 2009, a stripped-down bunch with Wade, Haslem, and a buttload of rookies. Ultimately,
Anyway, raw data showing the win totals for every NBA team in every season of this decade (1999-2000 through 2008-2009) can be viewed at this Google Docs spreadsheet. Any errors are mine; I constructed the spreadsheet by hand from data on basketball-reference.com.
What numerical conclusions can we draw? The teams with the greatest variance in performance were
The most consistent teams in terms of variance are the Spurs (consistently great), the Bobcats (consistently putrid), then
The most successful teams over the decade are the Spurs (57.6 wins on average), the Mavs (54.8 wins), the Lakers (53.0), the Pistons (49.7), and the Suns (49.1). No other team comes particularly close to the Suns’ mark. The worst teams are the Bobcats (natch) with 28.8 wins,
It is easy to predict the best teams of the coming decade.
Check jordanpushedoff.com in June of 2019 for an evaluation of these predictions!
Monday, June 8, 2009
Straight, No Chaser
Towards the end of overtime in last night's Game 2 of the NBA Finals, the Lakers took the ball with about 27 seconds left and a 3-point lead. ABC's Jeff Van Gundy (or was it Mark Jackson?) argued that Orlando should foul immediately. I thought this was bad advice. If you foul an 80% free-throw shooter, then there's a 64% chance that he'll make both shots and you'll be down by 5 points, and a 32% chance that he'll make only 1 shot and you'll be down by 4 points. There's only a 4% chance that he'll miss both shots and you'll have a chance to tie the game! My advice would be to try for a defensive stop and get the ball back. Granted, as Van Gundy observed, if the Lakers simply held the ball for 24 seconds, they would leave Orlando with only 3 seconds remaining to put a shot together. But they probably would not do that; rather, they would try for a score to augment their lead. This gives Orlando opportunity to either get a steal or a stop well before 24 seconds elapsed. It might not work, but the probability of success would probably be over 4 percent.
In the event, Orlando adopted perhaps a compromise strategy between my advice and Van Gundy's: they trapped the Lakers on the inbound pass (which was in the backcourt) and tried to effect either a steal or an 8-second violation. When this failed and the Lakers successfully advanced the ball across the half-court line, Orlando immediately fouled with 22 seconds left. They smartly chose to foul Lamar Odom, who is only a 62.3% free throw shooter (thus, a 14% chance that he would miss both, but an 86% chance that he would make at least one shot and make it a two-possession game). In the event, Odom made two free throws, Redick and Lewis missed three-pointers, and the ballgame ended as Jack Nicholson rose to congratulate the Magic's stars. A Coach Bhel would have handled things differently.
Monday, May 4, 2009
Oompa Loompa, Doompadee Doo
ESPN’s television broadcast the morning of the final Bulls-Celtics game listed the results of a website poll whereby web readers could pick from among four predictions for the game: Bulls in regulation, Bulls in overtime, Celtics in regulation, Celtics in overtime. I don’t recall the precise numbers, and the poll does not seem to be available any longer online, but something like 30% of respondents predicted the Bulls to win in OT and 21% predicted the Celtics in OT. So more than half of poll-takers thought Game 7 would go to overtime! (In the event, Boston won 109-99, in regulation time.)
Now, the raw proportion of all NBA games across the land, across years that go to OT is probably no more than 5%. To the extent you know that two teams are evenly matched (and Chicago and Boston minus Garnett certainly are), you are probably on relatively safer ground to predict that the game will go to overtime. But I would think that for these even-steven Bulls and Celtics, the most prudently correct answer to the question “Will the next game go to overtime?” is surely “No”. So over half of poll-takers got it wrong, no?
At first glance, this looks to me like an example of the representativeness bias, whereby, e.g., if you ask a poll respondent, “Who would you more likely find in a library: (i) a woman, or (ii) a middle-aged woman environmentalist with glasses?” many respondents will choose the latter because it sounds more quintessentially library-esque. But, of course, back in the real world, maybe 55% of library patrons are women, while about 3% are middle-aged bespectacled tree-huggettes. People don’t handle probabilities well. An overtime game between the Bulls and Celtics feels more emblematic of that series, so people feel, however wrongly, that it will recur.
Perhaps my point is weakened because 4 of the first 6 Bulls-Celtics games actually did in fact go to OT, so out of that sample, it’s actually safe to predict extra minutes. But sometimes crazy shit goes down, just by fluke. It’s hard to believe that I should update my probabilistic expectation of overtime from 5% to 50%. What do the numbers say? Consider the following Bayesian probability formula:
Such an updating would require that the proportion of Bulls-Celtics games out of all the overtime games played in 2008-09 is roughly ten times the proportion of Bulls-Celtics games out of all the NBA games played this season. So let’s consider some data. (I obtained all these numbers from the wonderful basketball-reference.com.) In 2008-09, there were 1230 regular-season games and 45 first-round playoff games, for a total of 1275 games, of which 70 regular-season and 4 playoff, or 5.804%, were overtime games. Out of all those 1275 games, the Bulls and Celtics played 3 regular-season games and 7 playoff games, for a total of 10 games, which was 0.784% of the 1275 games. Out of the 74 overtime games, 4, or 5.405%, were Bulls-Celtics games. So, the answer to my equational riddle up above is 5.405% * 5.804% / 0.784%, which equals 40.0%. Hmmm, maybe I was too quick to criticize the masses. 40% is pretty close to 50%, so predicting an overtime game based on the available data is not such a stretch. What if we make the analysis more precise by truncating the data set just prior to May 2nd, the date of Bulls-Celts game 7? This would put us in the position of a Bayesian observer filling out that ESPN poll just after game 6. This only deletes two games from our data set — Bulls-Celts game 7 and Heat-Hawks game 7. Now the correct Bayesian probability of overtime is 44.4% ! Wow! My initial supercilious dismissal of the silly plebes was way off. It seems that ESPN web users internalized the available observations quite well. 44.4% is still not high enough to predict that Game 7 will go to OT, but it's dang close.
Meanwhile, the Atlanta-Miami series also seems to be indicative that the teams are evenly matched, but in a wildly different way. If Atlanta had won three games by huge margins and Miami had won three squeakers, then we might say that Atlanta is a better team and Miami has been touched by kind luck. But actually, the first six games were all settled by double-figure margins, and no game saw a lead change after the first quarter. We might say that the two teams are mediocre at best, and equally likely to suffer horrible mental holidays.
Now, the raw proportion of all NBA games across the land, across years that go to OT is probably no more than 5%. To the extent you know that two teams are evenly matched (and Chicago and Boston minus Garnett certainly are), you are probably on relatively safer ground to predict that the game will go to overtime. But I would think that for these even-steven Bulls and Celtics, the most prudently correct answer to the question “Will the next game go to overtime?” is surely “No”. So over half of poll-takers got it wrong, no?
At first glance, this looks to me like an example of the representativeness bias, whereby, e.g., if you ask a poll respondent, “Who would you more likely find in a library: (i) a woman, or (ii) a middle-aged woman environmentalist with glasses?” many respondents will choose the latter because it sounds more quintessentially library-esque. But, of course, back in the real world, maybe 55% of library patrons are women, while about 3% are middle-aged bespectacled tree-huggettes. People don’t handle probabilities well. An overtime game between the Bulls and Celtics feels more emblematic of that series, so people feel, however wrongly, that it will recur.
Perhaps my point is weakened because 4 of the first 6 Bulls-Celtics games actually did in fact go to OT, so out of that sample, it’s actually safe to predict extra minutes. But sometimes crazy shit goes down, just by fluke. It’s hard to believe that I should update my probabilistic expectation of overtime from 5% to 50%. What do the numbers say? Consider the following Bayesian probability formula:
Such an updating would require that the proportion of Bulls-Celtics games out of all the overtime games played in 2008-09 is roughly ten times the proportion of Bulls-Celtics games out of all the NBA games played this season. So let’s consider some data. (I obtained all these numbers from the wonderful basketball-reference.com.) In 2008-09, there were 1230 regular-season games and 45 first-round playoff games, for a total of 1275 games, of which 70 regular-season and 4 playoff, or 5.804%, were overtime games. Out of all those 1275 games, the Bulls and Celtics played 3 regular-season games and 7 playoff games, for a total of 10 games, which was 0.784% of the 1275 games. Out of the 74 overtime games, 4, or 5.405%, were Bulls-Celtics games. So, the answer to my equational riddle up above is 5.405% * 5.804% / 0.784%, which equals 40.0%. Hmmm, maybe I was too quick to criticize the masses. 40% is pretty close to 50%, so predicting an overtime game based on the available data is not such a stretch. What if we make the analysis more precise by truncating the data set just prior to May 2nd, the date of Bulls-Celts game 7? This would put us in the position of a Bayesian observer filling out that ESPN poll just after game 6. This only deletes two games from our data set — Bulls-Celts game 7 and Heat-Hawks game 7. Now the correct Bayesian probability of overtime is 44.4% ! Wow! My initial supercilious dismissal of the silly plebes was way off. It seems that ESPN web users internalized the available observations quite well. 44.4% is still not high enough to predict that Game 7 will go to OT, but it's dang close.Meanwhile, the Atlanta-Miami series also seems to be indicative that the teams are evenly matched, but in a wildly different way. If Atlanta had won three games by huge margins and Miami had won three squeakers, then we might say that Atlanta is a better team and Miami has been touched by kind luck. But actually, the first six games were all settled by double-figure margins, and no game saw a lead change after the first quarter. We might say that the two teams are mediocre at best, and equally likely to suffer horrible mental holidays.
-------------------
UPDATE JUNE 17TH: I just became aware of this June 10th blog post from Northwestern University professor of economics Jeff Ely. Check out the two Youtube animated graphs, showing the how the distribution of score differentials changes in the last 60 seconds of an NBA game, averaged over 12 years of data. Absolutely amazing stuff. The basic gist is that tie outcomes after 48 minutes are far, far more likely than 1-point victories or 2-point victories. You should also read the comments, which provide some speculative explanations for that data. I don't think this new information contradicts anything in my original post above.
Friday, March 27, 2009
I May Not Get There With You
During last night’s Suns-Blazers tilt, TNT announcer Doug Collins described Suns guard Jason Richardson as a “volume shooter” who needs to take a lot of shots to be “effective”. This is a common locution in pro basketball analysis, but I’ve never fully understood what it means. Is this is a backhanded way of saying that a player like Richardson plays no defense, grabs no boards, and is not much of a passer – so his only contribution to the team would be by scoring? But then the effect in toto of having him on the floor, considering all his negative contributions, would not be very good. Or is it a way of saying that J-Rich is an insecure and quirky guy who needs to develop a “rhythm”, or perhaps feel that he will be getting a lot of shot opportunities that day, in order for his shots to go in?
To try to further unpack some of these notions, we here at JPO did some simple statistical analysis and uploaded our data to public Google Docs spreadsheets. We considered J-Rich’s stats for the current season with Phoenix (though the data is a bit abbreviated, as he has only played about 50 games with the team after being traded from Charlotte) and his 2007-08 stats with Charlotte, during which he played in all 82 games.
In both seasons, we calculated some simple correlations between various offensive performance metrics. Some of the correlations are obvious: if a guy scores more points or makes more buckets, then his team probably tends to score more points, and is more likely to win, so we expect a positive correlation. In evaluating the question of whether J-Rich’s taking more shots helps his team win, we focused in particular on the simple correlation between his FG ATT and his team’s win or loss outcome.
To try to further unpack some of these notions, we here at JPO did some simple statistical analysis and uploaded our data to public Google Docs spreadsheets. We considered J-Rich’s stats for the current season with Phoenix (though the data is a bit abbreviated, as he has only played about 50 games with the team after being traded from Charlotte) and his 2007-08 stats with Charlotte, during which he played in all 82 games.
In both seasons, we calculated some simple correlations between various offensive performance metrics. Some of the correlations are obvious: if a guy scores more points or makes more buckets, then his team probably tends to score more points, and is more likely to win, so we expect a positive correlation. In evaluating the question of whether J-Rich’s taking more shots helps his team win, we focused in particular on the simple correlation between his FG ATT and his team’s win or loss outcome.
We found a weak 7% correlation in both seasons. Of course, causality is hard to interpret. This could mean that the team thrives when J-Rich shoulders relatively more of the scoring responsibility, freeing guys like Okafor or Steve Nash to do their thing. On the other hand (particularly with Phoenix) it could simply mean that the team thrives playing a faster pace, and more FG ATT by J-Rich is indicative of more FG ATT by all players on the team, and thus a higher chance of winning. These calculations would be easy, though we did not explore them due to lack of interest in gathering the data.
We also calculated the correlation between J-Rich’s field goal attempts and his field goal percentage in any given game. We found a 31% positive correlation with Charlotte, and a 17% positive correlation in his Phoenix tenure. So there is some evidence there that he is more accurate when he shoots more. On the other hand, this evidence could mean that his teammates are passing him the ball more because his initial shots on a given night were relatively accurate and they perceived he had a ‘hot hand’. Again, we could track this more precisely by gathering intra-game shot cart data and measuring accuracy over time within one game, but we really didn't feel like it.
We also computed J-Rich’s average FG attempts in wins and his average FG attempts in losses, and performed a two-tailed t-test based on a null hypothesis that the two averages are the same. Similarly, we computed J-Rich’s average points in wins and his average points in losses, and performed a two-tailed t-test for the null hypothesis that the two averages are equal. Basically, the difference was not significant at any reasonable level. Richardson’s points output shows a statistically significant difference (at a 10% level) in his teams’ wins vs. his teams’ losses, but we kind of expected that, as discussed above.
So in sum, I still have no idea what is meant by “he needs a lot of shots to be effective”. If he can’t do much other than score, why keep him on the roster? Someone more scrappy who can score less but do more other good stuff would be more valuable. J-Rich has by far the worst net plus-minus rating of any of Phoenix’s stars. Perhaps the secret of his “effectiveness” is more economic: fans come to see fireworks, not box-outs and extra passes.
Thursday, February 19, 2009
One For You, Nineteen For Me
Well, the trade deadline is gone, and there’s a lot of odd analysis going down in hoopsland these days. This Rocky Mountain News article frets that “The Nuggets already have eight players next season committed to make about $66 million. That gives them $4 million for five additional roster spots if they want to stay under the tax line.” Well, our journalist friend sure is begging the question there. Is it reasonable to say that an NBA team sees the aggregate salary threshold triggering luxury tax as a bad thing in itself, rather than simply a wrinkle that must be considered in the marginal cost of players? The typical analysis fails to consider how profit-maximizers (whether idealized or rough-and-ready) make decisions. Similarly, this article from February 16th suggests that the likeliest reason why the Detroit Pistons traded away backup PG Alex Acker, he of the $711,517 salary, was so they could get under the luxury tax line, rather than as a business decision like any other: is the cost of the investment justified?
It makes little sense to say that the Pistons dumped Alex Acker so they could get under (or close to) the luxury-tax line per se. Rather, one could say that given the Pistons’ aggregate salary position above the tax line, Joe Dumars noticed that, among other available roster shuffling options, by cashiering Acker they could save twice his annual salary of $711,517, or $1,423,034. Presumably if the Pistons were only $1 above the luxury tax line, they would have been less keen to jettison Acker to save $711,517 (his total salary, plus $1 in tax). And if, say, Acker’s annual salary were $20 and the Pistons were $5 above the luxury tax line, it is hard to imagine their dumping Acker just to save $25. There is some value to carrying a third point guard. And there is a nonzero probability that basketball value translates into economic value: if Acker is able to fill in during a couple games when Rodney Stuckey is injured, say, and he helps the team win a couple games and improve playoff position, his presence could be responsible for millions of dollars of extra revenue from playoff home games.
Perhaps we could say that owners are chary of paying luxury tax because they do not want to help competitor teams. But the orders of magnitude here are tiny: by dumping Acker, the Pistons avoided paying out $711,517 / 23 , or about $30,936, of luxury tax to each team (the dollar-for-dollar tax penalty is divided equally among all non-tax-paying teams). It is hard to imagine this making much of a difference to any individual owner’s P&L statement. Besides, a lump-sum cash transfer should not affect the recipient teams’ marginal decision-making regarding rosters: presumably, the acquisition or dumping of players should hinge on whether their contract value is justified by the attendant extra revenues, regardless of the team’s existing profit-or-loss level. Perhaps tax considerations (and here we mean real government tax, not NBA ‘tax’) might influence an owner’s decision-making if his distributions from the team corporate entity suddenly increase. Additionally, risk-averse owners might be slightly more willing to take on the gamble of a new player contract when they perceive they are pulling in more cash flow from the team. But again, thirty thousand dollars should hardly make much difference, so it is hard to see why Joe Dumars would think in such a way.
I have been assuming here that general managers act as pure profit-maximizers on behalf of their owners. But in some cases, owners place (the perceived chance of) winning above profits, such as when Knicks owner James Dolan signed off on Isiah Thomas’s rash acquisitions of Steve Francis, Jalen Rose, Jamal Crawford, and the like. Other rich or overzealous owners like Mark Cuban or Paul Allen may act similarly. If this is the case, then all bets are off: tax-paying teams would be less likely to worry about the tax, and also less likely to worry about transferring cash to other teams.
To be sure, irrational economic behavior is not rare: both corporate and individual decision-makers often fixate on avoiding thresholds that are better seen as arbitrary points on a continuum of financial positioning. For example, grandmothers from the Great Depression are likely to caution, “Don’t take on debt. Pay off your loans.” Well, if you can borrow at interest rates lower than the rates of return you are likely to earn from investing that money, then you certainly should keep your loans, or borrow more. Heck, Merrill Lynch carried a leverage ratio of 28:1 at the end of 2007. A leverage ratio of 1:1, or less, is one (extreme) point along a continuum of possible outcomes, but hardly the only logical one. Similarly, there’s little use in fixating on one rule, “Don’t go above the luxury tax line”, if that constrains you from making prudent investments. Other economic actors use crude heuristics, rather than careful analysis, to make decisions. It may be that, given how the luxury tax line has been constructed under the Collective Bargaining Agreement [i.e. the tax line is set at (i) 61% of average team revenues, minus (ii) average team benefits for players, including pension, 401(k), medical, and life insurance], breaching that line is a useful signal that a team is probably paying too much, given the typical magnitude of other team costs such as leases, administration, marketing, and other overhead.
So okay, it’s possible that team owners and management, crippled by bounded rationality, are anchoring on the luxury tax line as a fulcrum of decision-making. But still, most team owners have acquired their wealth through outsized success in other businesses, so they know how to run a business; it is unlikely that they would be distracted so. There is little evidence that they are in fact making decisions as NBA reporters suppose they are. (Sadly, team revenues and profits are not publicly reported, and so we cannot correlate profitability against player salary outlays.)
What about the scribes who write about the NBA: why do they so blithely accept the salary tax number as some kind of Demilitarized Zone, not to be breached? One writer said that “owners treat the luxury tax threshold the way Dracula treats sunrise” . Well, to put it nicely, most NBA reporters probably got started as college sports reporters and worked their way up; though constant learning is ostensibly part of their job, they are not necessarily policy wonks. It is they who are more likely the boundedly rational ones, stuck in a conceptual scheme that makes no sense.
It makes little sense to say that the Pistons dumped Alex Acker so they could get under (or close to) the luxury-tax line per se. Rather, one could say that given the Pistons’ aggregate salary position above the tax line, Joe Dumars noticed that, among other available roster shuffling options, by cashiering Acker they could save twice his annual salary of $711,517, or $1,423,034. Presumably if the Pistons were only $1 above the luxury tax line, they would have been less keen to jettison Acker to save $711,517 (his total salary, plus $1 in tax). And if, say, Acker’s annual salary were $20 and the Pistons were $5 above the luxury tax line, it is hard to imagine their dumping Acker just to save $25. There is some value to carrying a third point guard. And there is a nonzero probability that basketball value translates into economic value: if Acker is able to fill in during a couple games when Rodney Stuckey is injured, say, and he helps the team win a couple games and improve playoff position, his presence could be responsible for millions of dollars of extra revenue from playoff home games.
Perhaps we could say that owners are chary of paying luxury tax because they do not want to help competitor teams. But the orders of magnitude here are tiny: by dumping Acker, the Pistons avoided paying out $711,517 / 23 , or about $30,936, of luxury tax to each team (the dollar-for-dollar tax penalty is divided equally among all non-tax-paying teams). It is hard to imagine this making much of a difference to any individual owner’s P&L statement. Besides, a lump-sum cash transfer should not affect the recipient teams’ marginal decision-making regarding rosters: presumably, the acquisition or dumping of players should hinge on whether their contract value is justified by the attendant extra revenues, regardless of the team’s existing profit-or-loss level. Perhaps tax considerations (and here we mean real government tax, not NBA ‘tax’) might influence an owner’s decision-making if his distributions from the team corporate entity suddenly increase. Additionally, risk-averse owners might be slightly more willing to take on the gamble of a new player contract when they perceive they are pulling in more cash flow from the team. But again, thirty thousand dollars should hardly make much difference, so it is hard to see why Joe Dumars would think in such a way.
I have been assuming here that general managers act as pure profit-maximizers on behalf of their owners. But in some cases, owners place (the perceived chance of) winning above profits, such as when Knicks owner James Dolan signed off on Isiah Thomas’s rash acquisitions of Steve Francis, Jalen Rose, Jamal Crawford, and the like. Other rich or overzealous owners like Mark Cuban or Paul Allen may act similarly. If this is the case, then all bets are off: tax-paying teams would be less likely to worry about the tax, and also less likely to worry about transferring cash to other teams.
To be sure, irrational economic behavior is not rare: both corporate and individual decision-makers often fixate on avoiding thresholds that are better seen as arbitrary points on a continuum of financial positioning. For example, grandmothers from the Great Depression are likely to caution, “Don’t take on debt. Pay off your loans.” Well, if you can borrow at interest rates lower than the rates of return you are likely to earn from investing that money, then you certainly should keep your loans, or borrow more. Heck, Merrill Lynch carried a leverage ratio of 28:1 at the end of 2007. A leverage ratio of 1:1, or less, is one (extreme) point along a continuum of possible outcomes, but hardly the only logical one. Similarly, there’s little use in fixating on one rule, “Don’t go above the luxury tax line”, if that constrains you from making prudent investments. Other economic actors use crude heuristics, rather than careful analysis, to make decisions. It may be that, given how the luxury tax line has been constructed under the Collective Bargaining Agreement [i.e. the tax line is set at (i) 61% of average team revenues, minus (ii) average team benefits for players, including pension, 401(k), medical, and life insurance], breaching that line is a useful signal that a team is probably paying too much, given the typical magnitude of other team costs such as leases, administration, marketing, and other overhead.
So okay, it’s possible that team owners and management, crippled by bounded rationality, are anchoring on the luxury tax line as a fulcrum of decision-making. But still, most team owners have acquired their wealth through outsized success in other businesses, so they know how to run a business; it is unlikely that they would be distracted so. There is little evidence that they are in fact making decisions as NBA reporters suppose they are. (Sadly, team revenues and profits are not publicly reported, and so we cannot correlate profitability against player salary outlays.)
What about the scribes who write about the NBA: why do they so blithely accept the salary tax number as some kind of Demilitarized Zone, not to be breached? One writer said that “owners treat the luxury tax threshold the way Dracula treats sunrise” . Well, to put it nicely, most NBA reporters probably got started as college sports reporters and worked their way up; though constant learning is ostensibly part of their job, they are not necessarily policy wonks. It is they who are more likely the boundedly rational ones, stuck in a conceptual scheme that makes no sense.
Monday, January 26, 2009
Kodachrome Maybelline
With too much time on our hands, we at JPO decided to aggregate the 2009 all-star picks made by a variety of pundits:
David Friedman
TNT's Inside the NBA crew (as summarized by David Friedman)
Marc Stein of ESPN
John Hollinger of ESPN
Peter Vecsey
The SI / SI.com crew
Our raw data can be found here (it's a Google Docs spreadsheet). Basically, if a given analyst chose a given player to the All-Star team, we coded that cell as "1". Otherwise, we coded a 0. We then calculated an average score for each player across the 12 analysts. The average score is found in the extreme right-most column of the spreadsheet. We then sorted the players according to their average scores.
The data has a bit of a problem in that some of the analysts (Hollinger, Stein, Vecsey, Friedman, and the TNT guys: Webber, Payton, Smith) took the fans’ choices of starters as a given, and chose only reserves. As a result, those analysts are assuming that Allen Iverson and Amare Stoudemire should be part of the team, and as a result, I coded Iverson and Stoudemire as "1" for those analysts. The SI analysts, who chose starters and reserves, all did not pick Iverson to be a member of the East team, and it is highly likely that none of the other analysts would independently choose Iverson to be a starter; his average score of 0.583 would have probably been zero if the fans had not chosen him. Four of the five SI analysts, though, picked Stoudemire to be on the West team, which suggests that most of the Hollinger Stein/Vecsey/Friedman/TNT group would have picked Stoudemire as a reserve even if he were not a starter chosen by the fans. Thus, Stoudemire's average score of 0.91 is likely only slightly inflated above what it would be if he were not "locked in" by the fans’ vote.
What stands out from this analysis? Surprisingly, 8 of 12 analysts chose Shaquille O’Neal to the West team, equal to the number (8) who chose Pau Gasol, playing for a much better team. Steve Nash, the former six-time all-star starter and two-time MVP, received only two votes, fewer than Paul Millsap, who got three. It seems likely that next year Billups and Shaq will fall out of this discussion, while guys like Durant and Millsap, who received only a couple votes from this sample, will be much more serious contenders. I also would expect Greg Oden and Andrew Bynum to put up all-star caliber performance next year, particularly given the likely strength of their teams.
In the East, I was surprised that 11 of 12 analysts chose Paul Pierce, who is averaging only 19 and 6 while shooting 44% from the field. Also, every analyst picked Joe Johnson, which is mildly surprising: he got more votes than Devin Harris (who has surely wowed more than JJ has) and Jameer Nelson or Mo Williams (who have quarterbacked their teams to a much better record than Johnson has). Also, three of the analysts decided to omit Chris Bosh from their squad. Chris Bosh — he of the 23 points, 10 rebounds, and 50% field goal percentage! — actually lost out to Zydrunas Ilgauskas for backup center on the ballot of two selectors.
My ballot, if anyone asked me, would most closely resemble that of Steve Aschburner or John Hollinger for the East all-stars, and Paul Forrester for the West all-stars.
David Friedman
TNT's Inside the NBA crew (as summarized by David Friedman)
Marc Stein of ESPN
John Hollinger of ESPN
Peter Vecsey
The SI / SI.com crew
Our raw data can be found here (it's a Google Docs spreadsheet). Basically, if a given analyst chose a given player to the All-Star team, we coded that cell as "1". Otherwise, we coded a 0. We then calculated an average score for each player across the 12 analysts. The average score is found in the extreme right-most column of the spreadsheet. We then sorted the players according to their average scores.
The data has a bit of a problem in that some of the analysts (Hollinger, Stein, Vecsey, Friedman, and the TNT guys: Webber, Payton, Smith) took the fans’ choices of starters as a given, and chose only reserves. As a result, those analysts are assuming that Allen Iverson and Amare Stoudemire should be part of the team, and as a result, I coded Iverson and Stoudemire as "1" for those analysts. The SI analysts, who chose starters and reserves, all did not pick Iverson to be a member of the East team, and it is highly likely that none of the other analysts would independently choose Iverson to be a starter; his average score of 0.583 would have probably been zero if the fans had not chosen him. Four of the five SI analysts, though, picked Stoudemire to be on the West team, which suggests that most of the Hollinger Stein/Vecsey/Friedman/TNT group would have picked Stoudemire as a reserve even if he were not a starter chosen by the fans. Thus, Stoudemire's average score of 0.91 is likely only slightly inflated above what it would be if he were not "locked in" by the fans’ vote.
What stands out from this analysis? Surprisingly, 8 of 12 analysts chose Shaquille O’Neal to the West team, equal to the number (8) who chose Pau Gasol, playing for a much better team. Steve Nash, the former six-time all-star starter and two-time MVP, received only two votes, fewer than Paul Millsap, who got three. It seems likely that next year Billups and Shaq will fall out of this discussion, while guys like Durant and Millsap, who received only a couple votes from this sample, will be much more serious contenders. I also would expect Greg Oden and Andrew Bynum to put up all-star caliber performance next year, particularly given the likely strength of their teams.
In the East, I was surprised that 11 of 12 analysts chose Paul Pierce, who is averaging only 19 and 6 while shooting 44% from the field. Also, every analyst picked Joe Johnson, which is mildly surprising: he got more votes than Devin Harris (who has surely wowed more than JJ has) and Jameer Nelson or Mo Williams (who have quarterbacked their teams to a much better record than Johnson has). Also, three of the analysts decided to omit Chris Bosh from their squad. Chris Bosh — he of the 23 points, 10 rebounds, and 50% field goal percentage! — actually lost out to Zydrunas Ilgauskas for backup center on the ballot of two selectors.
My ballot, if anyone asked me, would most closely resemble that of Steve Aschburner or John Hollinger for the East all-stars, and Paul Forrester for the West all-stars.
Tuesday, November 25, 2008
El Canadiense
Normally at this blog we try to stick to careful analysis and rise above base emotion, but wow, Phoenix was trailing by 12 points with 9 minutes left and they came back to win by 1, thanks to 12 subsequent points and 4 assists from Steve Nash!
Granted, it was only Oklahoma, but that was a hell of a game to follow from one's computer. I would not have wanted to write a sequel to my “Epic Fail” post from last week, also involving Phoenix.
It's also interesting that the online availability of real-time scores, even with play-by-play updates, has allowed fans to invest emotionally in games no matter if they're stuck at the office, or if they're overseas. Just as, 50 years ago, the onset of television allowed fans outside the arena to get themselves hyped about the ongoing status of a sports match, the internet allows anyone with a computer to pray for their side and bite into some drama. Back in 2004 when Sacramento (a favorite team of mine at the time) went against Minnesota in the second round of the West playoffs, I was living in Europe, and I stayed up until about 4 in the morning, looking at little circles moving across my computer screen on ESPN's play-by-play tracker, hoping that Webber could pull the boys through. It didn't happen, but the risk and thrill of that experience was way better than just going to sleep and waking up the next morning to check the score.
Granted, it was only Oklahoma, but that was a hell of a game to follow from one's computer. I would not have wanted to write a sequel to my “Epic Fail” post from last week, also involving Phoenix.
It's also interesting that the online availability of real-time scores, even with play-by-play updates, has allowed fans to invest emotionally in games no matter if they're stuck at the office, or if they're overseas. Just as, 50 years ago, the onset of television allowed fans outside the arena to get themselves hyped about the ongoing status of a sports match, the internet allows anyone with a computer to pray for their side and bite into some drama. Back in 2004 when Sacramento (a favorite team of mine at the time) went against Minnesota in the second round of the West playoffs, I was living in Europe, and I stayed up until about 4 in the morning, looking at little circles moving across my computer screen on ESPN's play-by-play tracker, hoping that Webber could pull the boys through. It didn't happen, but the risk and thrill of that experience was way better than just going to sleep and waking up the next morning to check the score.
Friday, October 24, 2008
First-Game Premium
It is about that time to get organized and figure out what NBA games I’m planning to go to over the course of the season. In my case, it is a bit complicated – my main basketball friend has a Mon-Thurs constraint: he can only watch games four days of the week. Unfortunately, he spends the rest of his week in NYC and they don’t seem to have any NBA teams there anymore.
Checking out some of the online ticket sites, I notice an interesting pattern: the first-game premium. How much would you be willing to pay to watch the first home game vs. the second home game of the season?
Let’s take the Celtics. If we try for mid-level seats at the Garden, one ticket is about $200. Compare that with the second home game, a mere 3 days later. A comparable ticket is about $70. Would you be willing to pay an extra $130 to watch the first home game?
Now of course you may think that these two games are not the same. The opponents are different, the day of the week is different, and so on. In the Celtics case, the first game is with the Cavs, while the second game is with the Bulls. So it is fair to assume that most people would pay more to watch the Cavs. But the first home game is on a Tuesday, and the second game is on a Friday. So this goes the other way – probably more people want to watch on Friday. Perhaps the different team can account for the $130 spread, but I doubt it.
The Celtics may be a special case as winners of the NBA Finals. Maybe a lot of fans want to relive the NBA championship. But then again, I remember that Game 6 was in Boston and it was after all the biggest margin of victory in any finals clincher.
So let’s take a look at some other teams.
Lakers: Mid Levels running about $140 for Game 1 (Portland) vs. about $75 for home Game 2 (Clippers).
Pistons: Lower Level Baseline running about $55 for home Game 1 (Indiana) vs. about $35 for home Game 2 (Washington)
Bulls: Lower Level Baseline running about $100 for home Game 1 (Bucks) vs. about $80 for home Game 2 (Grizzlies)
Raptors: Endzone seats about $85 for home Game 1 (Warriors) vs. about $150 for home Game 2 (Pistons)
This last case shows something interesting – at some point, the team has to matter. In any case, I’ve decided to skip on LeBron and check out Bosh/O’Neal when they play the Celtics on 11/10.
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