Why prevent NBA teams from only playing four players?


Chris Kaman seeing his psychiatrist.

Realistic rating: 9.5

Last night, Lakers center Robert Sacre invoked a little-known NBA rule when he fouled out of the Lakers-Cavs game. With the Lakers not having any players available on their bench at the time of Sacre’s sixth foul, they would have been down to only four players had Sacre been forced to leave the game, thus triggering Rule No. 3, Section I, which states:

“No team may be reduced to less than five players. If a player in the game receives his sixth personal foul and all substitutes have already been disqualified, said player shall remain in the game and shall be charged with a personal and team foul. A technical foul also shall be assessed against his team. All subsequent personal fouls, including offensive fouls, shall be treated similarly. All players who have six or more personal fouls and remain in the game shall be treated similarly.”

First off, let me say that as a huge proponent of instituting “power play”-type situations in many sports other than hockey (I’ll save that for a later post), I’m vehemently against this rule. Wacky things in sports like a shortstop having to pitch, a goalie having to take a shootout shot, or a quarterback having to punt are ALWAYS insanely entertaining—highlights fans talk about for years. Playing a basketball game with four players more than qualifies for that category. Why go out of your way to prevent such fun from occurring?

Possible exploitations

The other issue I have is that I don’t understand how referees can arbitrate when a team qualifies for this rule. The reason the Lakers triggered it was because they only dressed eight players that night, and that number shrank down to five due to a Nick Young knee injury, a Chris Kaman foul out, and a Jordan Farmar leg cramp all occurring prior to Sacre’s sixth foul. But how could the refs know if Farmar’s cramp was really a “cramp”?*

The reason I bring this up is because teams could theoretically lie about the health of their players if it would keep a star player with six fouls in the game. A prominent example of a situation in which a team could benefit from exploiting this rule would be Game 4 of the 2012 Eastern Conference Finals between the Miami Heat and Boston Celtics. When LeBron James fouled out with 1:51 left in the first overtime, the Heat fell apart without the league MVP, eventually losing in a second overtime to notch the series at 2-2. Since LeBron was such a valuable asset to have on the floor, it’s almost certainly  worth the tradeoff of having any potential fouls he commits be technicals, so the Heat would surely prefer to have him on the court, even with that corollary in place.

The issue, though, is that according to the wording of the rule, it seems that since the Heat had available players on their bench, LeBron could not remain on the floor. This is wherein my question lies: What would have prevented Heat bench players like Norris Cole and Mike Miller from suddenly “””””“cramping up”””””” (add like seven more quotation marks) and reducing the number of available Heat players to just five, thus forcing LeBron to stay in the game? (Even if the Heat couldn’t sub out for the rest of the game, retaining a player of LeBron’s caliber would still likely make such a ploy more than worthwhile.)

*It should also be noted that the Lakers were on the verge of putting Steve Nash—who was resting that night—in the game, but decided against it. Wouldn’t that technically have made him “available,” thus negating the Sacre situation?

Miscellaneous issues

1. Another issue about this rule is that it—admittedly, very marginally—changes the strategy of the game before a player fouls out. Whenever a player has five fouls, it gives a strategic edge to his opponents, because the player theoretically doesn’t want to foul out, so he may be a bit more tentative on defense, allowing teams to deliberately go at him when they have the ball. Without that fear, a five-foul player may continue to play at his normal defensive standard.

2. If the six-foul player accrues a tech every time he fouls, what happens if he draws two of these? Does he simply not have a technical foul limit anymore?

3. Can other players who had previously fouled out now come back in the game with the technical corollary in effect? So many questions.

4. What if Sacre suffered a truly debilitating injury. Would his writhing body have to lay in the corner of the court while his teammates played? Or would the Lakers have had to forfeit, even though they had a double-digit lead?

It’s worth noting that the Golden State Warriors encountered a similar situation in 2010, but when Devean George fouled out, the referees forced Don Nelson to play a clearly hobbled Chris Hunter.** This seems like a clear double standard compared to the one the referees employed for the Lakers last night.

**Nellie had to swap in three injured players, instructing each of them to throw a quick intentional foul, so that he could eventually put George back in the game. Here’s a video of some of that genius strategy:


Well, the obvious solution to me, as referenced above, is to simply remove this rule and force teams to play with four players.

If the league *must* have some form of this rule, then I’d simply suggest a steeper penalty than just a technical foul whenever the six-foul player draws a whistle to prevent any of the aforementioned chicanery. Perhaps something like a flagrant foul—where the team gets two free throws and the ball—would do the trick.

Bottom line: Teams playing four players would almost never come into play, so changing this rule really isn’t that intrusive. (According to SportsCenter, it’s only happened twice in the last 10 years.) If a team screws up this badly, let the opposing team (and fans) reap the benefits.


Who to really blame for sports stadium subsidies


Your tax dollars at work.

Realistic rating: 5.5

Last week, I wrote a piece for the Federalist about how the media covers government subsidies for professional sports stadiums. (Like my last post on tennis ranking methods, this is a post about media coverage—not a proposal about a formal rule or protocol from a new team, but it still gets a “realistic rating” simply for the likelihood of it occurring.)

First off, if you aren’t familiar with this issue, I’d direct you to a piece in The Atlantic about how government subsidies for stadiums are a horrible deal for taxpayers. (In my article, though, you’ll see why you should skip the headline on that story and just go straight to the text.)

Unlike the tennis rankings post, this idea of placing more blame on the politicians who hand out these sweetheart deals rather than the owners who ask for them has a much higher likelihood of being more widely adopted by the media. (For obvious reasons, mainly that this isn’t some entirely new-fangled statistics idea being thrown out by some guy on the Internet but simply a shifting in what appears to be a 2-3 option decision.) And as the terrible effects of crony stadium subsidy deals become more well-known, more smart people will investigate the true causes and see where to point the finger.

Anyways, take a look at the whole piece here.

A better way to rank tennis players all-time


Realistic rating: 1.5

Over at Deadspin last week, I wrote about a better way to rank tennis players than the current format of simply ranking the most grand slams won.

Most sports media members learned long ago how incredibly mindless the “who has the most rings” argument is—well, except Shannon Sharpe, and Dave Dameshek, and ok, well a lot of not-so-smart talking heads and writers. Still, most people are at least smart enough to understand that Robert Horry isn’t better than Michael Jordan. But for some reason, we still apply this methodology when ranking tennis players.

(Before you read any further here, you should probably go read the original post.)

There aren’t formal rules for leagues to adopt being proposed with this idea, but it still gets a “realistic rating” for the likelihood this methodology is actually adopted by analysts and the general public. The big issue to consider is simply that the bigger numbers get, the harder they are for analysts to easily spit out on TV or fans to bring up in bar debates. Smaller numbers like the number of rings (or in the case of tennis, really fancy cookie jars) are ones anyone can easily remember, and thus, they’re the ones we universally associate with certain athletes.

This isn’t to say we should just give up on ratings systems that produce metrics that have than two significant figures, but it’s simply an acknowledgement that for statisticians to push their ideas into the mainstream, they should take hurdles like this into consideration.

Is 1st-and-11 really an effective way to curtail offenses?


Drew Magary had an interesting idea on Deadspin yesterday about how to curtail record-setting NFL offenses: Make 1st downs 11 yards rather than 10.

This got me thinking about our society’s enslavement to base-10 principles (and how if we really wanted to keep with that enslavement, we should just go full metric and switch to 1st-and-10 meters, since 11 yards is roughly 10 meters.)

But is an increased frequency of first downs really the reason offenses are becoming so unstoppable? The data suggests otherwise. Via SportingCharts.com, here’s the data since 1992 on the percentage of drives that go three-and-out plotted against the average drives per season per team. (Admittedly, the three-and-out rate probably isn’t the best statistic to measure this, but it’s the best I could dig up and should pretty well mirror 1st down conversion rates.)

Drives Chart

As you can see, the three-and-out percentage has remained pretty steady the past few years but has dropped about half a percentage point from the early 2000s.

What has steadily risen over the last five years, though, is the total number of drives per team. This leads me to believe that offenses aren’t improving because teams continually pick up first downs but rather because they are scoring more quickly. This increased pace could be due to a few things: more yards per play, more passing plays (so the clock stops), or simply wasting less of the play clock.

I doubt the third reason (clock wasting) has much weight, but it certainly seems the first two (increased pace, more passing plays) play a big role in the increased number of drives.

So with this knowledge, how would I propose fixing this issue?

Probably just lengthen the field to 110 yards rather than change the distance necessary for a first down. Or conversely, I might suggest narrowing the field from 53 yards wide to 50 to combat the effects of spread offenses. (I remember seeing an argument somewhere recently that the spread offense has led to fewer injuries. I’d probably disagree… Sure, more players can find space and avoid contact, but the spread also allows both offensive and defensive players to use that space to gain more momentum and allow for bigger hits.)

So… Is this even an issue that needs fixing? Probably not. As long as there’s a solid balance between scoring drives and non-scoring drives, and it’s not skewed too far in either direction (i.e. making punting irrelevant), then the (slight) rise of offenses is fine by me. Sure, it might skew the data and make simple aggregate yard historical comparisons difficult, but that’s what z-scores are for.

Eliminating NFL Overtime


Realistic rating: 4.5

After the Week 12 Packers-Vikings game ended in a tie, making 2012-13 the first back-to-back seasons with ties since 1988-89, there was again much consternation about games ending in ties and how THIS IS AMERICA. TIES ARE FOR EUROPEAN PUSSIES.

Emerging from all the noise condemning the NFL’s OT rules was a very reasoned response by AdvancedNFLStats’ Brian Burke, who argued that the NFL’s current rules were poorly structured because they are contradictory to the extra period’s goal of avoiding ties while also prolonging the additional period.

This seems like a bit of a tautology, though. “______ is bad because it doesn’t deter the likelihood of what we’ve defined as bad.” But why are ties or prolonged OT periods something to avoid? (For a much less nuanced take on this debate, the increasingly irrelevant Sporting News offered a #HotSportsTake that basically says, “The current OT rules are bad because ties are bad,” and then goes on for many more paragraphs to basically say, “Ties are bad because teams don’t want to tie.”)

While everyone seems to focus on how to simplify the NFL overtime rules, here’s my proposal for the most simple solution: Not have overtime at all. Just end the game in a tie if it’s deadlocked after 60 minutes.

Because the NFL season is only 16 games (i.e. each game represents 6.25% of the season), it is the only sport that can accommodate (and in my opinion, should welcome) ties without significantly diminishing game-to-game excitement. In the NFL, a large swath of teams routinely miss the playoffs, earn first round playoff byes, are assigned different playoff seeding, or see major shifts in draft position by a difference of a single game, and not all games are created equal. The Cowboys’ Week 8 final possession nail-biter loss to the Lions counts the exact same in the standings as their 49-17 blowout loss to the Saints two weeks later.

The fact is that wins and losses are binary outcomes that are not nearly granular enough to truly determine the better team in a season that only produces 16 such outcomes. (In 82- and 162-game seasons, this binary outcome is not only tolerable, but necessary, as any more granularity would further sap the already-small level of game-to-game excitement.) There’s a reason statisticians don’t really look at wins and losses when analyzing teams. (Sadly, many fans and “experts” don’t even use wins and losses, but something far less granular to evaluate teams: championships.)

Now for those concerned about seeing a standings filled with records like 10-3-3 and 7-5-4, that hysteria is very overblown. Only about 7% of all NFL games go to overtime, or roughly one per season for every team. While relatively rare, ties would have the benefit presenting the standings as a slightly better depiction of a team’s actual body of work for each season.

The other big thing to consider here is injury risk and fatigue. Is it fair for a two teams to have to play an extra period, risking injuries to all their players and also further wearing them out for next weeks’ game? Overtime in a sport as violent as the NFL is almost a prisoner’s dilemma situation in which it would be mutually beneficial for both deadlocked teams to simply agree to a coin flip to determine the winner rather than for each of them to risk incurring negative effects on their respective futures.

So rather than trying to fix the OT rules many people seem to despise so much, let’s just leave them for this weekend’s games and the rest of the postseason.

Bottom line: This likely wouldn’t happen because of the heavily ingrained cultural aversion to dreaded ties. The only foreseeable way the NFL would eliminate OT is if the sport became so dangerous that any additional time playing the game was thought to be reason to avoid it.

Sports Gambling Stock Market


Realistic rating: 8.0

Today marks the one-year anniversary of one of my favorite websites, Intrade, closing all American accounts thanks to the friendly folks at the Commodity Futures Trading Commission, so what better occasion than to take a page from their brilliant idea and apply it to my favorite professional sport: gambling.

Futures (i.e. odds on something like a team winning its division, conference, championship, etc.) are becoming a more and more popular bet at Vegas sportsbooks, so popular that the books usually release the odds for next season within 24 hours of the current season’s champion being crowned. As futures currently work, the books open odds on a team winning a division/conference/championship, and gamblers can place bets they can later cash if their speculative outcome comes true.

Futures are typically a bad investment that only get worse the longer you down the road you speculate. Take a look at the NFL odds going into Week 16. Totaled are the sums of the win percentages Vegas estimates for all the potential outcomes of each event.


Total Win Probability

Number of events

WP per event

Individual Games




Division Futures




Conference Futures




Super Bowl Futures




As you can see, in each individual game, the average sum of the two teams’ winning percentage is only 3.74% over 100%, so the house edge is relatively minor. This edge grows a bit when looking at the seven division futures still on the board (the Colts already clinched the AFC South) but takes takes a massive leap once you start looking at conference and Super Bowl odds, with the sum of all the teams’ winning percentages each coming out to over 125%.*

*This also doesn’t include the fact that with futures bets, the sportsbooks get to hold your money for a long period of time and gain interest on it, so there’s also an added opportunity cost to bettors.

Ignoring the house edge, there are are two slight inconveniences to bettors under the current futures betting marketplace:

1. There’s no way to buy and sell futures after purchase. There are only two available exchange times: Initially purchasing a ticket and cashing it out should it win.

For example, about six weeks ago, I purchased a futures ticket on the Texas Rangers to win the World Series at 25-1. (For the gambling unaffiliated, this means $25 payout for each $1, so 1-in-26 total odds. These odds can also be expressed as +2500.) Since that purchase, the Rangers have traded for Prince Fielder and signed Shin-Soo Choo, bringing their odds down to 12-1 and effectively doubling the value of my initial investment. While I thought the Rangers were better than 25-1 odds six weeks ago, I think 12-1 might be a bit low today. If this were a stock market, I could sell my “shares” of Rangers stock for double my initial investment, but I don’t have that opportunity with current sportsbooks.

2. There are no opportunities to “short” teams if you think its odds are too low.

For example, I think the Denver Broncos’ current odds of 5-2 to win the Super Bowl are far much too low, but there’s no way to invest in belief other than betting on every other team’s Super Bowl odds, which as shown above, is not a very good investment.

There’s an easy way to fix these issues: The Intrade model.

Intrade is—I mean, “was”— a betting site that that allowed users to purchase shares of the an event occurring with the price of those shares constantly fluctuating based on the market’s estimation of the event’s probability of occurring. The payout for each share was $10 if the event occurred and $0 if it did not. So for example, if the market said that Mitt Romney had a 35% chance of winning the presidency in 2012, then his shares would sell at $3.50, and if he won, their price would rise to $10.00 per share. Not only does this model allow for investors to sell their shares if they’re currently bearish on a previous investment, it also allows investors to short outcomes they think the marketplace is trading at too high a price.

Now, here’s the big question: Why would the sportsbooks want to change their current futures market models to an Intrade-style marketplace? The books already make huge profits on futures, and the last thing they want is betters taking money off the table and cashing out.

To answer this question, let’s look at two ways the Intrade model could be applied to Vegas sportsbooks:

1. The sportsbook could sell a set number of shares at an opening price, and then after they are all bought up by bettors, simply serve as an exchange marketplace charging a small commission or broker’s fee for every transaction.

This is is pretty much exactly how Intrade worked, but the books would likely eschew this kind of model due to the fact that they would never want to create a self-imposed limit on the number of bets they can take in. However, this could be solved by…

2. The books would have an unlimited number of shares available to sell and could have two prices on the board: the bettor buying price and the bettor selling price.

The bettor selling price (i.e. what bettors can sell their shares back to the books at) would be slightly lower than the buying price, which would allow the books to make a slight profit.

For example, with the Broncos’ current 5-2 Super Bowl odds, they would be selling at $2.86 on a $10 scale or $28.57 on a $100 scale. (It’s probably more appropriate to make this a $100 since Super Bowls futures markets aren’t binary and have a multiplicity of outcomes that require a more granular scale.) Sportsbooks could make the selling price, say, 95% of the buying price, so if you wanted to sell your $28.57 Broncos shares, the book would buy them from you at $27.14.

(This also opens up the opportunity for a secondary marketplace that will by and sell these shares at different rates from the books, further mirroring the stock market.)

These methods would still allow the books to make huge profits, albeit likely a bit less than they currently make with their aforementioned 25%+ house edge. (However, the vast majority of bettors likely wouldn’t even exercise their right to sell back their futures ticket, as the public is usually just looking for a thrill and not interested in using sports betting as an investment.)

But still, is that enough for the books to want to revert to this model? They might not have a choice.

This marketplace improves the customer experience, and at a microeconomic level, market forces say that at some point, a firm will take a risk at reduced profit margins if they can appeal to more customers and thus take a bigger market share. While this book’s profits margin per bet may not be as high as under the previous system, that will likely be offset by the higher total number of bets they receive. This would create a domino effect on the other books.

At a macroeconomic level, this new model could also benefit the the entire sportsbook industry, as the “stock” price of futures could be an easily circulated figure. Now, not only could ballparks and sports networks flash scores on a video screen or bottom line, they could also have a live stock ticker listing all the current teams’ prices and net changes they made after games. The stock figures would become ubiquitous, thus raising public interest in the sports gambling industry and bringing in more bets.

Bottom line: This really wouldn’t be too drastic an overhaul of the sportsbook industry and wouldn’t take very look for bettors to get used to the new pricing method (especially if the old odds format was printed right next to the new stock price format). Market forces say that one day, a struggling sportsbook will break from the norm, try the Intrade model (or another more customer friendly model), and reap the benefits of a larger customer base. It’s really only a matter of time.

Can the best college team really challenge the worst NFL team? Let’s find out!


 Realistic rating: 2.5

Every year, the question always comes up from talking sports heads, writers, and fans: “Could the [best college football team] beat the [worst NFL team]”? All the questioning is mostly facetious, but it’s become so prevalent, and such a matter of intrigue, that it begs the question… Why not actually do it and once and for all find out?

The biggest reason it wouldn’t happen (or be worthwhile) under current circumstances? The NFL team would have no incentive to play. Why risk injury? Plus, there’s no upside. If they win, they only do what they’re expected in crushing a bunch of college kids. If they lose, they’re eternally humiliated.

These aren’t unfixable problems.

Let’s say the NFL were to propose a rule in the next CBA that the worst team in the league must play the BCS National Champion in a game held the Saturday between the conference championship games and Super Bowl (i.e. the day before the Pro Bowl.)

The game would be held at the recently crowed BCS championship team’s home stadium. This location would be because the college team’s fans would be the ones most willing to come out and cheer for a team to win in such a game (don’t think many Texans fans would be pumped to cheer on their team to avoid a humiliating loss), and it would also give the college fans a kind of de facto homecoming celebration for the returning conquerors, as the BCS National Championship Game could easily have taken place across the country.

Here’s the kicker to incentivize the pro team to win*, though: If the NFL team loses, its No. 1 overall pick in the upcoming draft moves back five slots and becomes the No. 6. It’s a penalty significant enough for the team to prepare for the game and play hard while really not being draconian, especially considering the somewhat crapshoot nature of the NFL draft and the a recent quantification of draft pick value by the Harvard Sports Analysis Collective.

*Players on the NFL team will be paid a pro-rated stipend based on their salary that season for their extra week of work. (Players on the NCAA team will continue to be “paid” with, well, more textbooks and knowledge.)

The NFL and NCAA could split the ticket, merchandising, sponsorship, and TV revenue 50/50. (A bulk of each league’s half would go to each representative in the game.) One could imagine such a game generating quite a lot of viewership, especially compared to the Pro Bowl audience the next day. Given the event-ization and unique nature of such a contest, it’s quite reasonable to suggest its ratings being on par with a typical NBC Sunday Night Football game, which sells ads at a rate of $500,000 per 30 seconds. One of the NFL’s many broadcast partners would probably pony up quite a bit for those kinds of figures.

The other wrinkle in this idea is that, due to the humiliation of playing in such a game and also the risk of downgrading a draft pick, it de-incentivizes NFL teams from tanking to get the No. 1 pick. (Although it should be noted that this side bonus is pretty minimal, as tanking in is nowhere near as prevalent in the NFL as it is in the NBA due to the fact that so many more NFL players are on shorter non-guaranteed contracts, and playing for that next paycheck.)

The thing to remember here is that the NFL team is going to win the vast majority of the time, so the draft pick penalty will come into play only once every couple of decades. (Although we can’t know that for sure since, you know, this game doesn’t exist yet.) Plus, if the NFL team is leading by a few scores early (a very likely possibility), they can just sub out their highly paid starters and minimize their injury potential.

**Addendum: This idea might work better for basketball, where the relative injury risk each game isn’t very high compared to football. All the principles are still in play, though. (Although since high draft picks are much more valuable in the NBA, the penalty for losing would have to be more along the lines of only 2-3 draft spots back.)

Bottom line: This idea will almost certainly never happen due to complaints from the NFL player’s union as well as some hypocritical NCAA stance on having “amateurs” be tainted by playing on the same field as “professionals.” That doesn’t mean this idea wouldn’t work in theory (and also be a profitable investment for the NFL and NCAA), though.