THE BOOK--Playing The Percentages In Baseball

Thursday, January 03, 2013

Base scores

On Bill’s site, he was talking about converting scores in NFL to MLB, noting that 3 football points is like one MLB run.  I responded:

In MLB, it’s about 10 runs per win, while in NFL, it’s about 35 points per win. So, conversion is about 3.5 to 1. A 7-4 MLB game would therefore be about 24-14 in NFL (or really 27-17… it’s not just the multiple, but there’s a “base number” that each team gets). This is more obvious in NBA, where it’s about 30 points per win (similar to NFL), so 3:1 conversion to MLB. So, 7-4 MLB is like 109-100 in NBA. There’s a huge “base” number of points that each side gets, and then you do the multiplier. NHL is 6 to 7 goals per win, so 7-4 MLB is 5-3 in NHL. NHL is like MLB in that there’s no “base” scoring.

It also got me thinking how “true” a sport is in its scoring if there was no “base scoring”.  NBA gives you points basically for just possessions.  A huge amount of the scoring is simply based on having the ball in your hands.  Yes, you have to throw it in the basket.  But, what I’m trying to say is that the score differential in NBA is about the same as it is in NFL.  Basically, if you score an average of 5 more points per game in NBA, that means about the same as scoring 5 more points per game in NFL.  But, the total number of points per game is far different.

NFL could adopt a scoring system that gives you say a quarter point for every yard gained from the scrimmage line or something, and then we’d get a scoring system that might look more like NBA.  That is, you get points for possessions, but not for actually scoring.  I know, I know, in NBA, you get points only for the basket.  I got it.  When you make analogies, you are not making equivalencies.

It made me think of tennis, where the “points” you get, like yards in football, are not real points.  They only matter if you win the game.  And even the games don’t matter unless you win the set.

So, you can actually try to do the same thing with basketball.  For example, imagine you do tennis-style scoring in basketball.  You win a “game” if you get 4 or more unanswered points.  Once you have that, a new game resets.  So, the back-and-forth of getting two points is a wash.  Turnovers become a huge key.  If you make it 5 or more unanswered points instead, then you might see alot of 3-point attempts.  Imagine for example, you win a “game” if you need at least 5 unanswered points.  You score (that’s 2 points), the other teams come up court, but you steal, and score an easy basket (2 points, now at 4 points).  But if the other team scores, that wipes out your 4 points, rendering it meaningless.  Now your opponent is at 2 points.  Would be wild right?

Anyway, and this is just me, so I’m sure I’m in the minority, I don’t follow basketball because it just seems like an up-and-down game.  There’s no incentive to not be up-and-down.  There also doesn’t seem to be much randomness.  Well, I know there isn’t, because I’ve shown that to be true.  In a 48-minute game, the better team wins much more than the opponent.  I don’t know that that’s the best way to operate, especially in light of how MLB and NHL operate.  And even if that IS the best way to operate, I know that having an 82-game season is NOT the best way to operate.  And having 16-teams in the playoffs on top of that is not the best way to operate.  The NBA sucks as much of the randomness as possible to leave you with a very strong confidence that the team that wins the championship is indeed the most talented team in the league.  But, do we really want that?  Don’t we want to see some huge upset occasionally?  The other sports offer that because of their game structure or schedule.  NBA doesn’t.

Anyway, just a thought that popped into my head.

Wednesday, January 02, 2013

Random variation around a true mean

Phil tries to compare foul shooting to flipping a coin, and gets into “trying your best” and “not putting in full effort”.

In other words, you may have a true mean, but it’s contingent on your effort level.  So, you have a true mean at a particular effort level (or more likely in sports, a true mean at a particular health level).  But, once that effort of health level is established (to the extent that it can be), then any deviation from that true mean will be random variation.

If you have an 80% chance of a success at something, that is based on your particular health level at the time (not to mention externalities like your opponent, which in the case of foul shooting is non-existent).  But, once you make ONE attempt, you either are successful (100%) or not (0%).  You can’t get an 80% foul shot on ONE attempt.

Now, if you want to argue that if you had complete and perfect control, you are a 100% shooter…. well, ok, I guess.  But, that would simply mean that you have complete and perfect control 80% of the time, and 20% of the time, you mess up.  But, you only would know that AFTER THE FACT.  After the ball leaves your fingers, then you would know.  Which of course is hardly a prediction if only physics will dictate the outcome.  It’s predetermined fate at that point.

The true mean is about the PROPERTY of an element.  So, 80% success rate at foul shooting is a property of the player.  The outcome is random variation around that true mean.

Thursday, December 27, 2012

Integrity of a season

Tyler asks about the Bettman’s claim of the “integrity” of an NHL season.

In my view, the “integrity” issue is a non-issue.  We have no problem with the Canada Cup and World Cup in hockey or World Cup in soccer. 

Tyler however makes the point that in the old days with fewer teams, everyone played everyone else a large number of games, so a 44-game season had plenty of coverage in terms of head-to-head matchups.  And Bettman is implying as much with a 48-game season (meaning 2 to 4 games against each intra-conference game and zero inter-conference).  But, Tyler asks why not just 2 games against intra-conference opponents, so that even at 28 games, the season has “integrity” (as Bettman could define it).

Then we have the example of the NFL, which of course only plays 16 games, in a 32-team league.

It goes back to how much spread in talent there is.  And a long time ago, I showed the equivalency of a regular season length for the 4 sports.

If we treat the NFL’s 16-game season as the minimum number of games to have a season with “integrity”, the equivalency in the other sports is:
19 games NBA
48 games NHL
92 games MLB

So, Bettman is right, using the NFL standard (1 NFL game = 3 NHL games, in terms of what we learn about each team’s talent).  But I imagine a 14-game NFL season would also be acceptable, and so that brings us down to 42 games for an NHL season.  Furthermore, the NHL not only allows more teams in the playoffs, but they play more games in the playoffs.  Whereas an NFL team needs to play 3, maybe 4, games in the playoffs, an NHL team will play 16 to 28 games in a 4-round series. 

In NFL, the eventual winner will have played some 17 games in a regular 14-game season.  The equivalent in NHL would be 51 games including playoffs.  Strip out an average of 23 games for the Cup champion (or whatever it actually is), and it only needs 28 games of regular season play.

And in a 15-team conference, playing home-and-home against each team gives us 28 games.  That I think is the integrity point, if 14-game NFL regular season is your standard.

Friday, December 21, 2012

Bettors and sports

About twenty years ago, Loto Quebec (the provincial government agency that regulates lotteries and gambling) introduced Mise-O-Jeu (Faceoff) that allowed betting on the NHL.  They basically gave odds for wins, and you multiplied all three odds to determine your payoff.  The NHL of course fought them, but, naturally, they lost.

It seems that this is the standard protocol, that the leagues keep fighting the government, they keep using the same arguments, the courts keep siding against the leagues not buying into their arguments.  Now, it’s MLB’s turn.  Here are some relevant articles, one with Selig’s deposition, and legal experts wondering why testimony is being redacted of the plaintiffs themselves.

Wednesday, December 19, 2012

How much should the NHL give to the players?

I was struck by the following information:

Indeed, according to the The U.S. Professional Sports Market & Franchise Value Report 2011, average franchise values in the first decade of this millennium increased 141% for the NFL (from $423 million to $1 billion), 101% for MLB ($233M to $491M), 78% for the NBA ($207M to $369M) and 54% for the NHL ($148M to $228M). This over a decade that witnessed a once-in-four-generations recession.

I have no idea what the company is (not Forbes), but you gotta figure whatever biases exist won’t be systematic toward or against one sport.  They also provide year-by-year valuations.  If we focus from 2006-2010, the total increase in valuations are as follows:

2006	2010	change	League
180	228	27%	NHL
353	369	5%	NBA
376	491	31%	MLB
898	1022	14%	NFL

Valuations increase in NBA has been almost nothing, but NHL has jumped since the last CBA to MLB-level increases.

I’ve said in the past that MLB GM’s are getting smarter, giving out less money per revenue to players.  The less players get, the more the franchise is worth.  NHL righted their model by dropping the share of revenue from 74% to 54%-57%.  That was a huge drop in share, and so, teams became more profitable, and so, they were worth more.

Did it swing too much?  Let’s look at multiple of valuation per dollar revenue:

Revenue	Worth	Multiple	League
98	228	 2.33 	NHL
127	369	 2.91 	NBA
210	491	 2.34 	MLB
265	1022	 3.86 	NFL

Interestingly, MLB and NHL are in about the same boat, they’ve gained in valuation in similar rate, and their multiple of worth per revenue is the same.  And yet, in pales in comparsion to the NBA, which barely has more revenue than NHL (really?!  I’m very surprised), anyway, 30% more in revenue, and yet each team is worth 60% more.

And the three non-NFL leagues combined are worth about the same as just the NFL, even though they have 64% more revenues.  Obviously, NFL is the model they aspire to.

Wednesday, December 05, 2012

Exhiliration Gap

Poz gives us his list of the sports better viewed live than on TV, with NHL on the top and NFL on the bottom.  I especially agree with Poz here:

The volume over how much someone does not like hockey corresponds precisely to how few times that person has seen a live hockey game.

I should also add that it matters where you sit, how big the crowd is, how important the event.  If I had to pick one event to watch live, and it didn’t matter at all where I sat, I’d probably go with the final game for the men’s World Cup (soccer).  But generally speaking, a random NHL game would beat a random high-level soccer game for me.

Baseball loses it live with respect to the pitcher/batter, which is the most fascinating part of the game, that “game within the game”.  Watching it live, I have no idea what the count is, whether the pitcher threw over the plate or outside, etc.  Naturally, I prefer the live portion when it comes to baserunning and fielding, but since most of the “action” in a game is focused on batter/pitcher, I gotta go with TV on that one.

I don’t know if there’s any aspect of football I prefer live than on TV.  Maybe the kick/punt return for the touchdown?  Maybe the long bomb?  I guess anything where you need to see half the field.  Best part of live football is the pre-game tailgating frankly.

I’ve seen high-level tennis live (at Jarry Park… that guy that renounced his Canadian citizenship in favor of British against a Quebec player… forget their names now).  I think I’m about even there, live or TV.

What say you?

Thursday, November 29, 2012

Are the Forbes numbers worse than useless?

Michael Lewis noted that Bill James preferred the honest mess than the tidy lie.  I love that, and I live that.

Tyler notes that Forbes may simply be providing the tidy lie, as he tries to check into some of their numbers.  And I agree, that the tidy lie is worse than useless.  At least insofar as the revenue numbers are concerned.

One would think their valuation numbers might make more sense, since we see teams trade hands all the time in all the sports, so it provides a checkpoint.  However, I’m just guessing, and hopefully, someone else can verify how far off their numbers are.  (And I seem to remember us having a thread on this already.)  Basically, the Forbes valuations are “forecasts”.  And any team that is sold can then be measured against the forecast (arena/stadium combination deals notwithstanding).

Saturday, November 24, 2012

Decertification

A great article that talks all about decertification in the NHL, NFL, and NBA.

Funny how the league that has labor peace is the one that does NOT have a revenue-splitting system.  And yet MLB players’ share of MLB revenues is on par with the rest of the leagues.

Solution?  Get the owners from the other three leagues to get smarter GMs.  That’s what Moneyball gave MLB.

Friday, November 23, 2012

Proskauer Rose’s Bob Batterman

He seems to be considered the architect of negotiations with NBA and NHL.  And so, the catalyst for decertification as part of negotiations for the other side.

Whether it makes sense for professional athletes to have a union at all is also now a point for debate after the mess negotiations have become in the NFL, NBA and NHL in the past 18 months.

“A lot of academic commentators would tell you it’s the leagues that really want the unions,� Grow said. “Because under U.S. law … they can violate federal antitrust laws in ways that they couldn’t if the players weren’t unionized. Normally, under antitrust laws principles, a salary cap would be illegal.�

Wednesday, November 14, 2012

What happen if you attempt a shot on your own basket?

Interesting rule interpretation if true, by one of the commenters to this video:

The referee f-cked this up on two different counts. First, shooting at the opponents basket does not count as an actual shot attempt. So, from the time he takes possession at :06, his team takes until the :18 second mark to get the ball over half court. You should have a :10 second violation.

The second count, which should have been called before that even, is that by definition throwing the ball off your opponents backboard is the same as a dribble. So, after the first shot hits the backboard and he catches it, his dribble has ended. When the ball hits the backboard a second time, the whistle should have blown for double dribble.

Monday, November 12, 2012

This week in inertial reasoning

MLB hands out two MVP awards, two Cy Young, two of everything, but the other leagues (NFL, NBA, NHL) have only one.  The NFL did look like they used to hand out two awards for a while, but then they stopped the inertia.

Is playing 11% inter-conference games too few to consider the two conferences as conferences, and instead should be leagues?  But the 20-25% that the other leagues play IS enough to consider them conferences?

Wednesday, November 07, 2012

Is MLB playoff format a necessary evil?

Here’s an interesting comparison between NBA and MLB from David.

Because of the setup of a basketball game and a basketball series, you are FAR more likely to get the two best teams into the NBA Final than you would get the two best teams into the World Series.  In order to improve that for MLB, you’d have to have less playoff rounds (and maybe even more regular season games).  Is this necessarily a desirable outcome?

What is it that people want?  Drama?  Or drama that involves two good-maybe-great teams?  Or drama that involves two great teams?  Realizing of course that the more high drama points you want, the less number of drama episodes you will actually get.

To put this in non-sports terms: would you rather have only the Batman/Nolan trilogy, or would you rather have the five X-Men movies plus two Fantastic Four movies plus Green Lantern plus all five of the Superman movies plus the two Hulk movies plus Thor plus all the non-Nolan Batman movies (i.e., every Superhero movie outside of Avengers, Iron Man, and Spiderman)?

That is: quality v quantity?

Wednesday, October 24, 2012

When “positions” are really roles, and not positions

The NBA announced that their all-star ballots are not going to separate centers from the forwards, and will simply have “front court” players.

The NHL used to separate by LW, C, RW on their all-star ballots, then they merged the two winger positions, and then finally at some point, they did like the NBA does, and just have forwards (and defensemen and goalies). 

I don’t follow the NFL, but I presume they don’t distinguish between left and right, guards and tackles?

MLB has the “outfielder” position for as long as I can remember.

But, when it comes time for awards, the separation comes back.

Let’s focus on baseball.  We have to accept that the fielding awards that are being given out have an offensive component to them. It makes sense for example that you have a fielding award for 1B, because you need a certain level of hitting talent to be able to play 1B.  There is no doubt that Gold Glove OF Darin Erstad would have earned a Gold Glove as soon as he started playing 1B, and as long as he was deemed a good enough hitter to play 1B, then he is there to earn the title for best-fielding 1B.

But take a look at LF/RF.  We find both better hitters AND better fielders in RF these days.  Alex Gordon for example if likely a shoo-in for the Gold Glove in LF.  But put him in RF, where he has more competition both as a hitter and as a fielder, and suddently, he’s just a top candidate.

Not to mention that LF is a “poor man’s” RF.  The skillset required to play LF is a subset of the skills to play RF.  Any RF would find it simple enough to play LF.

This is unlike the other positions, where for example, 2B has some skillset that the SS doesn’t have, and 3B has some skillset that the SS doesn’t have.  Even 1B (scoops) has some skillset that the 3B doesn’t have.

But for LF and RF?  The only way to accept that LF and RF should be split is if MLB puts in a ton of great hitters in LF, similar to the way that 1B is somewhat overloaded.  But we don’t find that.  Now, perhaps that will change in the future, and perhaps the skillset of the 1980s (speed) will come back in the future.  And maybe taking a slow approach to changes is advisable.

However, I’m not bound to these ideas.  I’m ok with making changes as the situations dictate, and in my view we should have two corner OF awards, rather than one for LF and one for RF.  Indeed, Ichiro’s transition from RF to LF, even though he’d never played LF, is as good a case as any to show that we don’t need to make the distinction.  And a stronger case is that the amount of time that players have played at LF+RF dwarfs any other pairing.

I know you may think this is a “slippery slope” to eventually have three outfield awards (meaning, all three awards claimed by CF).  But, I don’t buy that.  If logic suggests we get there, then we’ll get there.  But, I don’t think that the illogic of a slippery slope demands that we go there.

***

When I say “Gold Glove” I just mean “best fielder”.  I’m usurping Rawling’s name for its ubiquity, just as much as Kleenex and Frisbee are synonymous with their products.

NCAA v Noll

Good to see Roger Noll back in the news.  He offers a method to split revenues.

I would prefer a more American-centric solution (free market), rather than what NCAA is doing.  But as long as NCAA’s monarchy is what we have to compare against, then whatever Noll is proposing would seem to be better.

Getting kids to sign away their life in perpetuity is unconscionable.  If Gary Bettman wants to protect genius billionaire owners from signing obviously talented world-class players to no more than five years, and since David Stern has imposed something similar as well, then at the very least, NCAA should have considered that there should have been a term limit to whatever the kids signed.  The NCAA has simply gone so far over the line that all we can see is a dot.

Certainly you can make the case of educational value, of spreading the risk across all students, and so on.  That the “Picasso value” of playing for Duke is something that has been cultivated, and therefore, doesn’t need to necessarily flow through to the ball players.  You can make a whole bunch of such cases.  It’s not like players end up getting twice as much playing for the Yankees simply because they are the Yankees.

But, in the absence of anything fair and decent, then we have to impose something non-complex.  No one likes this one-size-fits-all solutions, but one must dislike the NCAA’s approach even more.

Glove-slap: Millsy.

Monday, October 15, 2012

Biggest rule changes in each sport in the last twenty-ish years?

I’ve been following sports since around 1976 or so.  And I’ll try to think about the biggest rule changes in each sport that I’ve followed to any extent.  This is just me off the top of my head, so I may miss several of the big ones.  So in the comments, start with the sport, and then put your nomination.  And it has to be an actual rule change, not a defacto rule change.

Baseball - lowering top of strike zone?  balk rule? HR video review?

Hockey - goalie crease/protection?  five-minute majors on serious infractions?  second referee? removal of center line for offsides? video review on all goal calls?  suspension for coach and player(s) for a bench clearing brawl?

Football - QB protection? starting point for kickoff? video review on challenge?

Basketball - zone defense?  3pt line?

Soccer - ?!?

Tennis - video review?

Golf - rules are perfect, except for the rules that were changed, in which case, THOSE rules are now perfect?

Boxing - fewer rounds?

Other sport?

***

Again, don’t comment on my list as if it’s not good enough.  I’m telling you it’s not good enough!  Just tell me what YOUR list is, and then we’ll come up with a more definitive list.

Friday, October 12, 2012

Competitive Analytics Consulting for NBA

This blogger seems to be well-taken with this basketball consulting company.

And another blogger chimes in as well.

I don’t know any of the people or companies I just linked to, so if there are some Straight Arrow readers that want to offer their opinion, please feel free.

Wednesday, October 03, 2012

Donald Fehr speaks!

I just love the brutal honesty here:

And the only point in the negotiation is how far/how fast are players going to make concessions.

Just in this century, you have basketball, hockey and football (owners) all come in and say, ‘We want what we want because we want what we want. And you have to give us what we want, because we want what we want.’

And that appears to be the basic approach. And it’s true whether they claim severe financial distress like hockey did the last time, or whether there’s no conceivable distress that anybody with two synapses can see, which is what you see to some degree with the NFL and basketball, and with hockey this time. I’ll tell you what I mean by that in a second, but that’s just the way they do it.

And it’s just like what happened with the NFL referees. They had no reason in the world for them to lock out the referees, for goodness sake – except that they can. And that’s what they do.

Monday, September 10, 2012

How much risk do we want to assume in sports?

We can make our cars safer, if we were willing to spend as much on a car as we do on a house.  We can make our roads safer if we were willing to have a special tax that can deploy a special police unit that has massive enforcement on moving violations.  While we may say “one death is too many”, we don’t actually act in that manner.  We accept that we can never reduce the probability to exactly zero.  Hence, while a death is tragic, we continue to behave that it is part of the everyday living of life.  We assume a certain amount of risk in what we do.  And there’s a certain amount we are willing to pay to reduce that risk, but beyond a certain point, we figure we don’t want to spend that extra dollar to reduce the risk of death by that extra percentage.

So, while fans have been killed in the stands, there’s only so much that we are willing to spend to further reduce the chance of death.  We’ll put netting to extend beyond the glass by the goalie net, but we don’t put the net throughout the arena (in NHL anyway, but we do in lower-level arenas). 

We don’t ask the fans to come to the game with helmets on, even if doing so would reduce the chance of death.  There’s a certain point at which we prefer to take our chances while living, rather than be preoccupied with the chance of death.  Bicycles with helmets were frowned upon when I was a kid, but are mandatory now.  Seat belts are mandatory in cars, but drivers don’t wear helmets.  Pro hockey players would play without helmets as late as the 1970s, early 1980s, until it became mandatory (except for those grandfathered in).  Hockey goalies would not even wear a face mask until the late 1950s, early 1960s, and still some didn’t wear in the early 1970s.  The idea of not wearing a hockey mask today seems completely foreign.  A few basketball players wore a protective face mask. Dave Parker tried different masks, including a football-style helmet.  Ellis Valentine had a special attachment to his helmet. John Olerud would wear a helmet all the time on the field, because of his head condition. 

We come therefore to Brandon McCarthy. 

The first question is if we want to make these protective head gears mandatory or not.  Throughout history, it has always been the same response: no!  But, then years would go by, and the idea of assumed risk starts to be better understood.  At some point, the governing bodies decide that the health risk is too much for them to bear, that it is in THEIR best interests to enforce mandatory head gear on those they are charged to govern over.  While individually, we each have our own level of assumed risk, we still have to accept that if something goes wrong, someone ELSE is going to bear a cost to it.  That’s why seat belts are mandatory.  That’s why bike helmets are mandatory.  Professional leagues or their insurance carriers have huge investments in players, paid on guaranteed contracts.  They want to protect their assets and don’t want to bear the healthcare costs.

Pitchers would rebel at the idea of additional protective headgear.  It’s uncomfortable, it’s extra weight, it’ll make the sweat more.  It’s the same kind of reasons that hockey players use as they shun protective eye gear (face masks) when they graduate to the pros.  If you don’t make it mandatory, each player assumes his own risk.  And the NHL and NHLPA seems fine with that decision, that they’ll mandate a certain kind of helmet, but not go all out to the full face gear.

What’s going to happen is that McCarthy may have his own headgear, like Olerud, Parker, and Valentine, like Jacques Plante.  The other pitchers will look around and calculate the risk is too low based on such few examples of horrific episodes.  Other goalies looked at Jacques Plante and figured their risk was too high, and they all eventually adopted the face mask.

Basically, the free market will set the path, and once you get to a tipping point of the number of participants that have adopted a certain kind of protective headgear, then it will become mandatory.  Until then, it would have to remain voluntary.  You can’t go 0 to 100 in the mindset of the participants.  It has to be a gradual change.  Maybe it will be an accelerated path like hockey goalies and their face masks, and maybe it will be a slow burn of acceptance like hockey players and their helmets.  And maybe, it’ll never reach the point that it will get mandatory, as hockey players and their face masks haven’t been accepted yet (even though they are mandatory as youth).

Saturday, September 08, 2012

Why are NFL referees paid so little?

In the NHL, NBA, and MLB, the top field official makes in the neighborhood of 300,000$.  The top players in the NHL makes over 10MM$, and the top players in the other two leagues make over 20MM$.

The top players in the NFL makes over 15MM$, putting them comfortably with the other three leagues.  But the top NFL field official makes under 100,000$.

Now, you are going to say “but they only play 16 games!” (plus pre-season and playoffs).  This is true, but this doesn’t affect player salaries.  The NFL takes in more money than MLB even though they play ONE-TENTH as many games.  So, do we want to pay for NFL officials on a per-game basis, or relative to revenue?

Perhaps it’s the number of field officials?  The NHL has about 75 officials, the MLB has close to 100.  The NBA is probably close to 60.  The NFL has about 120 officials.  So, if they have to spread out more, then maybe instead of topping out at 300,000$, they top out at 200,000$? 

Then again, the four NHL officials are watching 12 guys on the ice.  The four MLB officials are watching 10-13 guys on the field.  The three NBA officials are watching 10 guys on the court.  The seven NFL officials are watching 22 players on the field.  It’s a 3:1 ratio of players to officials. 

And even though you have twice the roster size in NFL than NHL and MLB, their top players are paid in the middle of those two leagues.

It seems to me that the top NFL officials should make as much as the other leagues, even though they officiate far fewer games.

As for the answer to my question: because the owners can.

Friday, September 07, 2012

Savviest basketball owners the NBA never had

Wow, what a story!

But if the Spirits couldn’t join the N.B.A., the Silna brothers wanted to share in what the A.B.A. didn’t have: national TV revenue. They settled with one-seventh of the television money generated annually by each of the four surviving A.B.A. teams — the Nets, the San Antonio Spurs, the Indiana Pacers and the Denver Nuggets.

The arrangement began to get public attention as the size of the league’s network TV deals swelled. The four surviving teams have tried to extricate themselves from the arrangement, but have not found a way.

In perpetuity!

Do the sale prices of these four teams reflect a lower enterprise valuation than other similar teams in the NBA?  Clearly it should have some effect.