How well do Vegas futures predict playoff results in each sport?


Spurs and Heat… again.

On Friday, I wrote a post for FiveThirtyEight discussing the rampant inequality and predictability found in the NBA. I have a few more thoughts on that subject…

While the NBA has successfully suckered tens of millions of fans into believing the 2014 playoffs have been thrilling and unpredictable, with the LA Times even declaring, “March Madness suddenly seems like such a bore by comparison” (this is a pretty odd comparison considering the Final Four concluded with a No. 7 seed beating a No. 8 for the title), I’ve had a much different opinion, and this year’s predictable results simply fall in line with recent history.

While my original post mostly analyzed the odds distribution in each sport, I didn’t much consider the actual results, and it got me wondering… How well do those futures odds predict what actually happens on the court, as well as in other sports?

To analyze this, I ranked all the teams in each sport according to their preseason championship odds* (i.e. for 2014, Miami is No. 1, Bulls No. 2, etc.) I then plotted this rank against their eventual playoff results (0 = missed playoffs, 1 = lost in first round, 2 = made conference semifinals, 3 = made conference finals, 4 = made finals, 5 = won title) over the last four seasons. For comparison, I also included the NHL, a league that also has an 82-game regular season and four rounds of best-of-seven playoffs:

*Because any betting odds will add up to greater than 100 percent, I simply divided all the futures by the sum of all the teams’ odds to scale them down to 100 percent.

nba presason vs results

nhl presason vs results

The NBA has a clear strong correlation between preseason championship probability rank and playoff results, while the NHL is much weaker. Over the last four years, no NBA team ranked lower than fifth in preseason championship odds has made the finals. Compare that to the NHL, which has had six of eight non-top five finals teams in that time.

Here are the NFL and MLB distributions too:

NFL preseason vs results

(0 = missed playoffs, 1 = lost in wild card round, 2 = lost in divisional round, 3 = lost in conference championship game, 4 = lost Super Bowl, 5 = won Super Bowl)

MLB preseason vs results

(0 = missed playoffs, 1 = lost in Wild Card game, 2 = lost in LDS, 3 = lost in LCS, 4 = lost World Series, 5 = won World Series)

It’s easy to see how these other leagues’ plots differ from the NBA’s. Here are the correlations for each graph:

NBA = .647

NHL = .523

NFL = .440

MLB = .371

Clearly, the preseason favorites go further in the playoffs with a much higher frequency in the NBA than in any other sport.

Dominance of Miami

Much of the predictability in the NBA is due to the havoc the Miami Heat have waged on the wagering markets. To put Miami’s sports book dominance during the LeBron-Wade-Bosh era in perspective, here’s a scatter plot of the all the seasons in the MLB, NHL, NBA, and NFL over the last four seasons, plotting each team’s championship odds at the start of the season against their odds at the start of the playoffs.


(Sorry, no pretty graphic with this one—just a screenshot of an R plot. Chartbuilder doesn’t take to kindly to doing scatter plots with multiple series.)

Only once in the last four years have the Heat not been favorites to win the title—the start of the 2011 playoffs, following the Big Three’s underwhelming debut regular season. Now, to really see how Miami’s recent run stands out, here are those odds when the four years for each team are averaged together.


Over the last four seasons, the Heat have averaged 24.6 percent and 28.4 percent chances of winning the title at the start of the regular season and postseason respectively. Compare that to the Sacramento Kings, which have averaged 0.3 percent and 0.0 percent respectively over that time.

Another interesting takeaway from this chart is that the Patriots have often wildly outperformed preseason expectations during the regular season, accruing more than double the title odds by the time the playoffs start. The Lakers, on the other hand, wildly underperform (or are simply very overvalued at the start of the year), nearly slicing their preseason title odds in half over the course of the regular season.

Odds Distributions

Probably the most striking image from my FiveThirtyEight story was this line chart of the distribution of championship odds at the start of the season in each sport.

Pre line chart

When you zoom in on the bottom two thirds of the chart, you can really see the near-zero odds of the barren bottom 50 percent in the NBA.

Pre line zoom

This NBA inequality is still apparent come playoff time. (I separated the MLB data into the years in which there was only one wild card per league and years in which there were two.)

Play line chart

While the NBA may look like it’s made up some ground here equality-wise, it’s important to note that the NFL and MLB have byes and play-in games, a structural advantage that automatically adds greater disparity in championship odds. The average top NBA playoff team, which has to win four rounds for the championship, still has better title odds than the average top MLB and NFL teams, which only have to win three rounds.


The day after my FiveThirtyEight story ran, the NY Times published a story that touched on very similar topics. Most interestingly came a quote from former Stanford professor Roger Noll, discussing one of my most despised regulations in sports:

“If you didn’t have an individual cap,” Noll said in a telephone interview, “if LeBron James was in a position to sell himself to the highest bidder, his salary would be much higher and you wouldn’t have a small number of top teams with more than half the superstars in the league.”

“It’s a big mistake, and the N.B.A. hasn’t adjusted. So if you have as many as 25 teams that know before the first game is played that they probably won’t even be in the conference finals, doesn’t that make the regular season seem almost meaningless, more of an exhibition than a pathway to a consequential championship?”

I couldn’t agree more (and plan to write more on this in the NBA off-season).

In previous posts, I’ve argued against the randomness and extreme parity of college basketball, much of which is due to the 68-team single elimination playoff format—a huge contrast to the NBA’s best-of-seven series. If that sounds like the complete opposite of my above criticism of the NBA, then you’re right. The NCAA lies too far toward the extreme randomness/parity end of the spectrum, while the NBA goes too far to the extreme predictability/inequality end.

You don’t want seasons to feel like they’re extremely predictable like the NBA, but at the same time, you want the true best team to win with a relatively high frequency so that it feels like teams are justly rewarded. It’s critical to have a good balance between the two, and finding that equilibrium is something sports leagues have wrestled with—and will continue to wrestle with—for decades.



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.

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.

Welcome to Lower The Mound

Anyone in my fantasy football league will readily tell you that I’m never satisfied with the status quo. Every summer at our annual owners meeting (we take our league rather seriously), I present a point-by-point list of twenty or so league changes I’d like to see implemented for the coming season. Because we use a website that allows us to customize just about every facet of the game, I often view our league as my own personal laboratory to tinker with things to create the best possible game experience.

This fascination with game design naturally spilled over into real sports, and I’m not alone. I find more and more frequently that when people talk sports, they talk about everything but the sport itself. Almost no casual (or even relatively serious) fans have substantial discussions on Justin Verlander’s devastating curveball against lefties or Andrew Luck’s recognition of zone blitz schemes, but you’ll hear hours of conversation (and endless columns) on the Redskins’ nickname controversy, the addition of a second MLB wild card, or the NFL overtime rules. Like it or not, the modern sports discussion is shifting from what happens on the field during games to virtually everything around it, and that’s what this site is trying to capture.

The Premise

Lower The Mound will be my platform to present changes I’d like to see in modern sports. The topics will have a sharp statistical focus (bell curve alert!) and mostly focus on the four major North American sports (NFL, NBA, NHL, and MLB), but the coverage range will likely expand with time. Anything and everything is up for discussion, ranging from basic rules of the game (such as MLB lowering the pitcher’s mound in 1969), to standings procedures, schedule design, and league financial structure.

First I want to set a few guidelines: These ideas all have to be somewhat realistic, and by “somewhat realistic,” I mostly mean, “won’t cost the leagues millions of dollars” and “won’t cause massive class-action lawsuits.” So no, there can’t be any “eliminate TV timeouts” or “allow broadcasters to curse on air” ideas—wait, actually hold that thought on that last one. Every Tuesday, there will be a new original idea post, and throughout the rest of the week, there might be occasional shorter posts responding to new ideas proposed by other writers. Other fun related sections such as “how to cheat at sports” (one of my favorite topics to mull over) could likely appear.

A big model for everything will be the NFL. Over the last decade, it’s hard not to notice how the NFL has revolutionized the sports-watching culture of America, taking numerous slots for the annual highest rated shows and completely monopolizing viewership for three nights a week in the fall. Like most other Americans, I’ve also been swept up in the national NFL hysteria, so while it’s certainly my favorite major sport, there won’t be as many posts about it here, as I personally think that compared to other leagues, there are very few major errors with what I’m inclined to say is a relatively flawless league (other than the whole widespread debilitating brain trauma thing.)

The most finely crafted “game” setups in American culture today are not found in massive stadiums or nationally televised broadcasts, but rather in your living room in the form of board games. The principles that make great board games—a good balance of parity while still ensuring the best players succeed a high percentage of the time (what I call the fairness-excitement spectrum—more on that later), a length of time that doesn’t drag on too long, and an even starting playing field for all competitors—are all-too-often missing from the realm of sports.

Why Change?

Of course, bringing about change in professional sports isn’t as easy as shifting Madden from “pro” to “all-pro.” Leagues are run by dozens of owners and hundreds of corporate bureaucrats, and if history has told us anything, they are extremely adverse to taking risks or trying anything new. In fact, the boldest move any pro sport has made over the last decade might be… NASCAR implementing a playoff? (If NASCAR is your most progressive sports league, it might be time for some more changes.)

And in their defense, it’s a fair question to ask why should they change? Pro sports are a multi-trillion—yes, trillion with a “T”—dollar industry. Why shouldn’t they be happy? Because as Don Draper told the dominant Dow Chemical, happiness is simply “a moment before you need more happiness.” Just look at how unsatisfied NFL owners are with only taking in a paltry (tax-exempt) $10 billion in annual revenue. There’s always room for growth, and it doesn’t have to just be in the form of financial gains in the owners’ wallets. There’s certainly a lot of room for improvement that benefit the players, fans, and game itself.

Fans themselves usually aren’t particularly open to change either. I’ve found that a lot of the things that suck about sports are simply in place due to the hallowed grandeur of “tradition.” “Oh, we can’t change that. We’ve always done it that way,” is a common refrain from fans when new ideas are suggested.

This isn’t to say that tradition is entirely meaningless. It certainly has some (somewhat) quantifiable value for the sake of historical records, familiarity, and branding. But it’s certainly not an end-all, be-all dealbreaker, and many leagues have made great strides since “breaking tradition” with their past m.o. (Anyone still wish there were no three-point line or free agency? Ok, Dan Gilbert probably wishes there weren’t free agency.)

My Perspective

While the media likes to paint pro sports owners as greedy fat cats with no care for the fans, in the grand scheme of things, this narrative is mostly false. Sure, in some instances owners certainly do slight the fans for some extra dough, but in the big picture, fan experience and owner profits are highly positively correlated. It’s simply bad business to produce a product your customers don’t enjoy (or in the NFL’s case, are scarily addicted to). So in proposing these ideas for how to improve sports, I try to take the perspective of a McKinsey consultant, primarily having the sports’ best (i.e. financial) interests in mind, with a better fan experience simply being a side effect.

Anyways, thanks for being a part of this early stage, and I hope you stick around. Exciting things are on the way!