The Sports Economists Answer Your Questions


We recently solicited your questions for sports economists David Berri and Martin Schmidt, whose new book, Stumbling on Wins, explores the statistics of sports victory and the mistakes that teams make.

Your questions were particularly good for this Q&A, and Berri and Schmidt avidly took the bait, covering topics like draft strategy, inefficient scoring in the NBA, and salary caps. Thanks to all for your participation.


“Old-school” decision makers in sports are often reluctant to change, despite overwhelming evidence that their current strategy is flawed. Which often-repeated mistake is most frustrating to continue to observe?? – Mike


Not sure we would use the word “frustrating.”? One of the lessons of behavioral economics is that people are slow to adopt new information.? So one shouldn’t be surprised when decision-makers don’t quickly change strategies that the statistics say are sub-optimal.

As for oft-repeated mistakes, the overvaluation of scoring is one of our favorites.? This story was recently highlighted by Kim Hughes, the recently fired head coach of the L.A. Clippers.? Hughes made this observation in discussing the problems the Clippers had in the latter part of the 2009-10 season:

In late-season scenarios when you have as many free agents as we do, human nature takes effect sometimes. They look for points instead of the team first. That bothered me tonight. We had some guys looking for points too much. That should never occur, but it did occur. It’s not right, but it did happen. It’s not the way I like to play basketball, but when you have as many free agents as we do, I think it’s going to happen at times.

Hughes is arguing that players know their future salary is enhanced by the number of points they score (and we see this clearly in the empirical research).? But by looking for their shots, these players were diminishing the ability of their team to win.? Consequently – as Hughes observes – players in the NBA can actually be rewarded for taking actions that lead to fewer wins.

It’s important to note that revenues in the NBA are driven by winning, not scoring.? So players’ focus on scoring does not enhance a team’s revenue or profits.? In other words, hiring inefficient scorers raises a team’s costs (even inefficient scorers are expensive) and lowers a team’s revenues.

We suspect decision-makers are not fully aware of many of the issues we raise in our book.? But the problem with scoring was discussed by?Red Auerbach, the famed coach of the Boston Celtics in the 1950s and 1960s. So this issue was first raised long before we published our research. Yet it continues to persist.


In hockey and basketball, it seems that a couple of last-place seasons in a row to get top 5 draft picks really helps, because a couple of top stars make a huge difference. All the top teams have the top stars. This is obviously not the case in football and baseball. Do you think that a losing team would be doing the right thing in a five-year plan by tanking the last half of a season?? – DrS


It certainly is the case that a few “stars” in the NBA can make a huge difference.? The Pareto Principle argues that 80% of outcomes are a result of the efforts of 20% of people.? Although we are not sure how universally this applies, it does appear to work in the NBA.? About 80% of wins appear to be produced by 20% of the players.? So a team can improve dramatically when it can acquire one of the few players who produce most of the wins (i.e. Tim Duncan, LeBron James, Dwight Howard, etc…).

Given how wins are produced in the NBA, there is clearly an incentive to lose games on purpose at the end of the season to improve a team’s draft position (and thereby improve the team’s chances of acquiring a major producer of wins). Hence the need for the NBA to institute a draft lottery.? Published research certainly suggests that non-playoff teams have underperformed towards the end of the season. So there is evidence of “tanking.”

One issue a “tanking” team has to consider is the cost of losing games.? A study of gate revenue suggests that the first pick in the NBA draft produces about $4.4 million in revenue.? An additional loss, though, only costs about $200,000.? So a team would have to lose 22 additional games for the cost of losing to be equal to the expected benefits of the first pick.? That is not quite half a season, but is a substantial part of the regular season.? And we should add that the benefits of the first pick do extend beyond the first season.? So we are understating the potential benefits.

As for baseball and football, the expected return of players drafted in these sports doesn’t suggest that tanking is a good strategy. In baseball, very few drafted players even make it to the majors.? And in football, performance is simply not very predictable.? Cade Massey has argued that there is a 50% chance that a player taken with one of the first five choices will be a “flop.” Given these odds, tanking in the NFL doesn’t make much sense.? In fact, Massey and Richard Thaler argue that teams that get the first picks in the draft would be wise to trade out of these picks.


Is there any hope the Detroit Lions will go to a Super Bowl in the next 50 years? – KarenS


Dave is a fan of the Lions, so he definitely hopes so.? It is important to remember — as we often note — that American football (relative to basketball, baseball, and hockey) doesn’t appear very predictable.? This means that every year, fans can have hope (and Dave — after the Lions took Ndamukong Suh and Jahvid Best in the first round of the 2010 draft — does have hope for this next season).

Never-ending hope just doesn’t exist for those who follow the NBA.? Fans of the Pistons should have suspected the 2009-10 season was lost when the Pistons spent their free agent money on Charlie Villanueva and Ben Gordon.? Neither player had been very productive in the past. So when both were not productive this season – and the Pistons struggled – no one should have been surprised.


Why do you think the mainstream media frown on newly developed sports statistics?? – Patrick


The media has a significant problem when it comes to sports statistics.? This can be illustrated by comparing the NFL’s QB Rating to QB Score (the simple metric we explain in Stumbling on Wins and The Wages of Wins).? The NFL’s measure is literally calculated as follows:

First one takes a quarterback’s completion percentage, then subtracts 0.3 from this number and divides by 0.2. You then take yards per attempt, subtract 3 and divide by 4. After that, you divide touchdowns per attempt by .05. For interceptions per attempt, you start with .095, subtract from this number interceptions per attempt, and then divide this result by .04. To get the quarterback rating, you add the values created from your first four steps, multiply this sum by 100, and divide the result by 6. Oh, and by the way, the sum from each of your first four steps cannot exceed 2.375 or be less than zero.

In contrast, the calculation of QB Score is quite easy.

QB Score = All Yards – 3* All Plays – 30* All Turnovers

Given the simplicity of QB Score – and the fact that QB Score is more accurate and more complete than the NFL’s measure – why don’t NFL broadcasts report QB Score?

The problem is that the vast majority of the audience — much to our chagrin — has never heard of QB Score.? So every time the broadcaster reported QB Score, he/she would have to briefly explain how this works.? That would take up valuable air time (which could be spent on issues many might find more entertaining).

Yes, QB Rating is more complicated. But the audience doesn’t have to know how it is calculated (and we expect few would care).? Football fans do tend to know that a QB Rating around 100 is “good.” With this minimal information the fan can see whether a quarterback is having a “good” or “bad” game. And even if QB Rating isn’t quite right, most fans probably aren’t that concerned with the accuracy of the numbers cited during a broadcast.

A similar story can be told about batting averages.? People argued that batting average was a poor measure of a hitter’s performance in the early part of the 20th century.? But because most fans are familiar with this number, it is still reported in each and every baseball broadcast.? Yes, there are better measures of a hitter’s performance.? But broadcasters just can’t spend valuable air time explaining these to all the fans who are not really that interested.

The new statistics are really not created for broadcasters or other members of the media.? New statistics are created by researchers to help measure worker productivity.? They’re also created to help decision-makers make better choices.? Understanding what the numbers mean can help a team win more games, and therefore make fans happier.? Explaining these stats to most fans during a game, though, is not likely to increase the happiness of most viewers.


Regardless of the impact on revenues for pro sports teams, what do you think of the extended playoff structures that pro sports employs today? Baseball has included wild cards, and basketball and hockey playoffs seem to go on forever. Do these structures allow for more random outcomes for championship winners? I especially think this can be an issue in baseball. – Casey


Prior to 1969, the playoffs in Major League Baseball consisted of the World Series.? With only two teams in the playoffs, the team with the best record in baseball won the World Series about half the time.? From 1969 to 1993, the playoffs consisted of four teams.? Over the course of those 25 years, the team with the best record only won the World Series seven times (or 28% of the time).? We have now completed 15 years with eight teams in baseball’s post-season. Over these 15 seasons, the team with the best record has only won the World Series three times.? In fact, a team ranked 5th or lower in the regular season record has taken the title five times.? So with respect to baseball, the more teams in the post-season, the more random the outcomes.

Outcomes in basketball are less random.? Over the past 30 years, the team with the best record in the NBA has won the NBA title 16 times. The team with the second-best record took the title eight times.? Furthermore, over the past 30 years, only eight different teams have won an NBA title.? In contrast, nine different teams have won the World Series in the past fifteen seasons.

So although basketball allows more teams into the playoffs, outcomes don’t appear as random as we observe in baseball.? The reason for this difference is what we call “the short supply of tall people.”? The NBA draws its talent from a very small population (really tall people).? As Stephen Jay Gould argued, the smaller the population a league draws upon, the wider the spread in the talents employed.? Applied to basketball, this means some teams get to employ players like Dwight Howard or LeBron James.? Other teams, though, have to employ lesser talents.? And when players who are substantially better get to play inferior talents, the outcomes end up being far more predictable.

As for hockey, outcomes are closer to what we observe in baseball.? Since 1985, only seven teams have finished the NHL season with the best record and won the Stanley Cup.?? The story in hockey may be related to the performance of goalies.? As we note in the book, the performance of goalies is not very predictable.? This is true across seasons, but also as we move from the regular season to the post-season.? So a team might have a great goalie in the regular season, only to see that same goalie falter in the post-season (and vice versa).? The inconsistency of goalies would likely contribute to the more random outcomes we observe.


In your opinion, should college basketball players be paid a real income greater than tuition?? How does the one-year rule affect those would-be high school NBA players’ lifetime earnings and competitive balance in college and the NBA? – B-ball fan


Published studies have shown that future NBA players generate far more revenue for their college team than they receive in tuition.? So in a free labor market, star college players would get more money.

We suspect there are two reasons to require one season of college basketball.? First, this is one more year of training the NBA does not have to pay for.? Second, it gives the players in the NBA draft some exposure to the public.? One issue with the drafting of players like Dwight Howard is that few people had ever heard of him before Orlando took him with the first pick in the draft.? By requiring these players to wait one year – a year most likely spent playing college basketball on national television – the NBA gets a player its fans already know.

For the top players, this one year is all they should play.? The research we report suggests a player loses five spots in the draft for each year he ages.? So there is a clear incentive to come out early.

We are not sure this rule has much impact on competitive balance (again, the NBA has never been that balanced).? Younger players do perform worse, so if you draft a player out of high school, you are probably not getting the same level of production as you would get from a player who is a year older (that is true until the mid-20s, when a player’s productivity slowly begins to decline).? So in that sense, giving bad teams a high -school player probably doesn’t help much initially.? The impact of age, though, isn’t that dramatic.


Would a salary cap in baseball work? – Jeff Nehajowich


We are not a big fan of caps.? Fundamentally, their effect is to transfer revenues from players to owners.? Salary floors help some, but not enough to make this, for us, a viable option.

We like two solutions better.? The first is to either expand (or allow teams from small markets to move) the number of teams in the large markets.? The reason the Yankees and Mets earn so much more than the Royals is that consumers in New York will pay a lot more than consumers in Kansas City for a baseball team. Expanding the number of teams in New York will reduce the revenues of the Yankees and Mets. This is essentially what is done in the English Premier League, where London currently hosts five different franchises.

The second solution is to have teams negotiate with each other to play games.? New York can only make money if Kansas City is willing to come play in New York City.? The negotiation would likely lead to a more equitable split of New York’s revenues – as it would include all revenues, not just gate revenues.

We should note that we don’t expect either solution to happen.? But both would result in a reduction in revenues earned by the Yankees.? To the extent this is a reasonable objective (and there is some question on this point as well), we prefer our solutions to a cap on salaries.


You did a study which showed that racism in the NFL means that white quarterbacks are paid more than black quarterbacks.? This made me wonder, is the N.B.A reverse-racist?? Specifically, are white players underpaid relative to black players who produce at similar rates?? – Daniel-san


The study of quarterbacks in the NFL suggests that race impacts pay.? And this effect is largest for the very best quarterbacks.? Simply put, the very best white quarterbacks are paid more than the very best black quarterbacks (even when performance is controlled for).

When we turn to the NBA, it has been suggested that white basketball players might be discounted (it has also been suggested that black players are discriminated against).? The data, though, doesn’t seem to show any pattern.? At least, the models for salary and the NBA draft we report do not show that there is a racial bias in the NBA.

There have been other studies that show a different story.? For example, Joe Price and Justin Wolfersin a fairly famous study – have presented evidence that referees in the NBA have a racial bias.?? This bias works both ways.? Specifically, white referees have been shown to be biased against black players, and black referees have been shown to be biased against white players.


If you were running simple regressions (winning % versus some index for player salary, what sport has the lower R^2?)?? – Adam McCloskey


The National Football League appears to have the lowest correlation between pay and wins (comparing this value across different sports, though, is a bit unfair).? NFL teams play the least amount of games, and the outcomes of individual plays are an outgrowth of the interaction of 11 players on offense and 11 players on defense – one poor performance by one player likely leads to a poor result on the play.? Again, the game of football is the least predictable, and therefore it’s hard to tie team outcomes to football players’ salaries.


Do you agree with the contention (based on statistics) that football coaches are too timid on 4th down? If so, can you explain why they are too timid? Is it tradition, job security, or ignorance? – Erik Jensen


David Romer‘s argument is pretty convincing.? So yes, we do think coaches are too timid.? And we think all three reasons have some validity.? The first plays into the second – break with tradition and fail, and you have a good chance of getting fired.? Plus, it will also make it much harder for those raised in that coaching tradition to hire you again.? In terms of ignorance, or not understanding Romer’s piece, it is the case that the easiest place on the field to see his argument is around your opponent’s 35-yard line. This is the one place where coaches come the closest, but still fall short, of what Romer’s model would predict. So it is probably the case that coaches simply do not see how Romer’s results apply across the entire field of play.

We want to thank everyone for all the questions and comments received.? This was an impressive and interesting collection.? And we are going to answer a few more of these questions at The Wages of Wins Journal.


Maybe I'm missing something, but it sounds like adding extra teams to the baseball playoffs made the process _less_ random, not more.

When there are two teams, the one with the better season won about 50% of the time. Indistinguishable from pure randomness.

With 4 teams, the "best season" team wins 28% of the time, which is 3 percentage points above the expected random result.

With 8 teams, the "best season" team wins 20% of the time, which is 3.3 points better than the expected random result.

The sample sizes are too small to draw meaningful conclusions, but there's no data to support the conclusion that adding more teams makes the process more random.

Steve Nations

Regarding NBA teams tanking late in the year: Several years ago I looked at all the NBA champions going back to the late 70's. All of them had at least one player who was drafted in the top 3 overall. So clearly, basketball is not so much of a team sport, but a sport for one individual and four accompanists. So losing games in order to get a top draft pick seems not only like a good idea, but crucial. Of course, the lottery throws much of this out the window. So does the ability of a team like the Lakers to sign Kobe Bryant as a free agent.


RT Ian "With 4 teams, the "best season" team wins 28% of the time, which is 3 percentage points above the expected random result."

But the first place team should be better than the 4th place team. Therefore, they don't have equal expectations of winning.


The authors are misusing the word "random." Ian is correct, that the outcome is becoming less random. What the authors mean to say is that the outcome of the playoffs is becoming "less predictable" not "more random."


Lakers'2009 had Gasol and Odom, but both were drafted by other teams. Actually in last 25 years Lakers were drafting in top 10 only twice (both times - it was 10th pick)
Boston'2008 had no players drafted in Top4.
Detroit'2004 had Billups, but Pistons were his 5th franchise.

So clearly it is possibly to success in NBA without drafting high.


There were only a couple economics questions here. The rest were statistics.

Why wasn't the issue of public subsidies for sports addressed? That's a HUGELY relevant topic as we hear about the Tea Partiers, bailouts, taxes, government size, recession, public spending, etc. on the news every night.


still waitng for Levitt's superfecta...


"Never-ending hope just doesn't exist for those who follow the NBA. Fans of the Pistons should have suspected the 2009-10 season was lost when the Pistons spent their free agent money on Charlie Villanueva and Ben Gordon. Neither player had been very productive in the past. So when both were not productive this season - and the Pistons struggled - no one should have been surprised."

First what does "never-ending hope" even mean?

Secondly I'm pretty sure Ben Gordon was productive in Chicago, I mean I didn't follow them closely but I remember Gordon having clutch moments. And yeah, I know you guys will discount clutch with stats. Villanueva was just a bad signing, but Villanueva was just the kind of underappreciated player Billups or Hamilton was, the gamble just didn't work but that doesn't mean taking a chance on him was wrong.

@Steve Nations. Any knowledgeable basketball fan will tell you supporting players like Ginobili, Fisher, Horry, Haslem and Posey are just as critical to winning a title as the top drafted superstars.




You remember Gordon's highlights: scoring and late game scoring, so you think he's good. Unfortunately, he doesn't do non-scoring tasks well, and isn't even that good at scoring per shot attempt. You're following the same sub-optimal conventional wisdom that Detroit followed. The point being made was that people who base their opinions of players on their overall ability, not just their total points, would have accurately predicted this year's results.

As for your comment to Steve Nations, there are 2 issues. First, your so called supporting players range from average players (Posey) to one of the best players in the league (Ginobili). I see no reason to lump them together like they are similar. Second, just because "knowledgeable" basketball fans think these players are important, doesn't mean they actually are. 1 awesome player of the Lebron James, Dwight Howard, Chris Paul school along with a roster of average players would be a 55 win team and an annual title contender. I don't think any of those average players (plentiful in the league) are anywhere near as critical as the superstar player (a handful in the league).



It would be interesting to see a study on how the amount of points scored, or how often scoring actions take place, affects the "predictability" of games. By that I mean, do the best basketball teams win because basketball victories require a significant amount of baskets (scoring actions), meaning the best players can pile up points, making it harder to overcome their impact.

A similar case could be made for tennis matches and golf. It takes a LOT of points to win a 3 or 5 set tennis match, and the top players tend to dominate over and over. In golf, you play 18 holes, but you score 60 to 70 strokes, in four different rounds. The best golfers tend to fill the leaderboard week after week, even if they don't "win" each tournament because of the size of the field. In team sports, I think its pretty tough for an inferior volleyball team to be a superior one, because volleyball matches are a couple of games to 21.

Then you could move down the line. While football teams score the next most points, those scores are actually inflated by making a touchdown worth 7 points and a field goal worth 3 points. In reality, a football team can generally win by scoring a combination of five or six touchdowns/field goals. This allows an "inferior team" to beat a "superior" team if they can produce a handful of scoring actions while limiting the other teams. But a superior basketball team can't be easily stopped from scoring, because they have 50 plus chances to score per game.

I'd put the number of scoring actions in baseball right around those of football in an average game. The scoring average for sports like hockey and soccer would be way down. A good hockey team now scores maybe 3 or 4 goals per game on average. Meaning an "inferior" team only has to prevent a very small number of scoring actions, while coming up with a small number of their own to win.

In soccer, the scoring averages are even lower, maybe two goals per game and you win. Yes, superior soccer teams win a lot of games, but I'm tempted to believe soccer is among the least predictable game from contest to contest.

Again, we assume the superior team will win more often than not. But does the number of scoring actions per game impact how often "upsets" happen.

I don't have the numbers, averages or statistics to answer this question. Just bringing it up based on this Q&A. It seems to me on the surface that the more scoring actions necessary, the more predictable the outcomes become.



h65465: "First what does "never-ending hope" even mean?"

I'm not sure I can define it, but anyone who's ever been a Detroit Lions fan would understand. It's a sort of hopeless hope you have when your team is ridiculously pathetic, but occasionally shows signs of greatness. Or even goodness. Or (in the Matt Millen years) signs of mediocrity.



The authors are not misusing the word random. Randomness does not imply uniform probability.



By "scoring actions" I'm curious if you mean actually putting the ball in the basket/goal or shooting at it? I assume you mean actually putting it in scoring. If that's the case, I'd be really interested in this too, as well as an analysis of whether (as I believe) the teams that allow the fewest "scoring actions" also allow the fewest "scoring attempts." IMO, it would be interesting to see if, say, basketball teams that win more games are more succcesful at not allowing teams to shoot, or at actually keeping the shots from going in (blocks, atlered shots).

I can almost guarantee that that's what's happening in soccer. A team like Manchester United wins a lot of games, and score a lot of goals (the goals per game average is actually a little over 3, last time I checked, but your point is no less valid because of it), but they also don't allow many "scoring attempts." Less attempts = less "scoring actions" in their case. However, I would be curious if a superior goalkeeper in soccer or hockey, or a great shot blocker in basketball has more of an impact than team defense/turnovers.



"The NBA clearly needs to institute a draft lottery?" The NBA has a draft lottery. Did I miss something?


Regarding the response to this question: "In your opinion, should college basketball players be paid a real income greater than tuition? How does the one-year rule affect those would-be high school NBA players' lifetime earnings and competitive balance in college and the NBA? - B-ball fan"

The authors ignored the part of the question referring to the competitive balance in college. I think this rule has had a terrible effect on competition and college b-ball given the sorting of these one-year players to particular coaches (see Calipari, John). Why should college b-ball be a one-year farm system to the pros? I would rather see players such as John Wall go straight to the pros. I would favor college basketball adopting the college baseball early entry rule: a baseball player can go pro straight out of high school. However, if he elects to go to college, then he has to wait 3 years before entering the MLB draft. Given that the current rule favors both the NBA and the NBA players, I won't hold my breath waiting for a change...



A somewhat different question, more in the realm of mathematics than economics:

If what we really cared about was maximizing the odds of the best team winning the tournament, how would we organize the tournament? (Or some other similar criterion.) Assume we have some 'budget' for the number of games we can afford to put on.

To start with, I'm pretty sure knock-out tournaments are terrible. One single bad result eliminates a competitor. Round-robin probably does OK, but after a while you're wasting games on poor competitors who clearly have no chance of being best.

In the real world, we care more about TV ratings and excitement than picking the best competitor, which is why knock-outs are so popular - every game is make-or-break for both sides, so excitement is maximized.


@ Daniel-san: Can we please stop the tedious use of the term reverse-racist?

If something is racist, it's racist. It doesn't matter which race is being favored.


"This is essentially what is done in the English Premier League, where London currently hosts five different franchises."

Not really, though. The American model of the league dictating where "franchises" come from isn't accepted over here. The makeup of the league is determined not by the league but by a system of promotion from (and relegation to) lower leagues which go all the way down to your local 11 fat men pub team. There are minimum requirements (particularly as to the stadium in which the team plays games) but they are set down in the rules and provided they can be met it's performance on the field that determines league eligibility.

The point about London is not right, either, regardless of technical quibbles. London is three times the size of Manchester (which has two clubs in the Premier League, including the richest in the world), over seven times the size of Birmingham (also two clubs), easily nine times the size of Liverpool (two clubs) and so on. So London's an underachiever, compared to many cities in England.

The point about London is not the relative success of the teams in the city but the sheer number of teams that it can support. As well as five in the Premier League London has two teams in the league below, four in the league below that and two more in the league below that. And that's just in the leagues where all the teams are professional - there are plenty more in the tiers underneath the full-time professional leagues. On that metric London is streets ahead of the rest of the country in footballing terms.

The governing bodies do have some say if teams want to relocate, incidentally, (see Wimbledon, now MK Dons, in 2003) but professional teams relocating (areas, not stadia) is an incredible rarity in England.



"So although basketball allows more teams into the playoffs, outcomes don't appear as random as we observe in baseball. The reason for this difference is what we call "the short supply of tall people."...As for hockey, outcomes are closer to what we observe in baseball. "

Shooting percentage is 10% in hockey, 40% in basketball. Roughly speaking, one quarter of basketball is as random as one game of hockey. It has nothing to do with the supply of tall people.



There is ample evidence that one elite basketball player is not enough to win a title. Name a single NBA team carried by one elite guy and four also-rans? Maybe LeBron will get it done this year, but otherwise, all recent title-winners have supported multiple top-caliber players. Maybe they weren't all tier 1 super stars, but they were all better than average. Now, is there some hindsight bias here, where we are remembering or evaluating certain guys as better than they actually were because of their involvement in a championship team? Certainly. But even in their time, without this sort of backwards looking, who would argue that Magic, Bird, Isiah, Jordan, Duncan, Shaq, Wade, Pierce, or Kobe didn't have at least one top-notch teammate at the time of their victory? Now, obviously, not all of these teammates need to be top draft picks, as Duncan won the bulk of his titles with lower picked guys, but they still turned out to be stellar players. There is simply no evidence of a 'one-man-show' team winning the title in the NBA. Many have competed, in the sense that they had very successful regular seasons and somewhat successful post-seasons, but even Lebron's best shot resulted in a sweep.