THE BOOK--Playing The Percentages In Baseball

If strong favorites are likely to win by less than their talent indicates they should, this should probably already be accounted for in the betting lines.

Honest gamblers would assume that some % of games might be tainted and adjust their spreads accordingly.

Was there a previous discussion about the Wolfers’ paper (which is referred to in the Bernhardt/Heston paper) on this site?

You can try here:
http://sabermetricresearch.blogspot.com

Otherwise, do a search for “racial bias” for other possible interest.

King Yao:  Phil Birnbaum discussed the Wolfers’ paper and Bernhardt/Heston’s work here:  http://sabermetricresearch.blogspot.com/search?q=point+shaving.

thanks Guy.

If horse racing can do it, even at smaller tracks, why can’t sports books go to a para-mutual wagering system?  Seems like a good way to lock in your profit margin and protect yourself from huge plays from the point shaving crowd.
vr, Xei

Re: #6, I think it’d be an awfully tough sell to gamblers.  People who bet on football or basketball want to lock in their price and pointspread.  Any book that tries to go pure moneylines will get a lot less business and any book that tells customers they won’t know their price until the game starts will get a lot less business.

I don’t know the history of why horse racing is able to get away with this business model, but I will say they do have two advantages not applicable to hoops and football betting.

1. There aren’t a bunch of bookies competing with each other at the horse track, there’s just the track itself.  Therefore, the house is at less risk of losing their business to competitors by changing to a setup customers find less appealing.

2. There is something fundamentally attractive about 50/50 propositions.  People like betting on them.  I think this is a big reason that betting on football and basketball is more attractive to the general public than betting on baseball (where everything is odds-based).  Since horse racing is odds-based to begin, it’s less of a big deal to go a step further and make things para-mutual.  A bookie who tries this for team sports would be introducing a concept (odds) that simply doesn’t exist in football/basketball betting*.

* - Yes, there’s moneylines, and some places even shade their pointspread bets like -115/+105 or whatever, but by and large pointspread betting is the most popular.

#6 - sports bettors in general are not worried about point shaving, it isn’t a major issue except for those that have lost and want something to blame on their losing.  if they are worried, they can refrain from betting.

Yes, I second what King Yao said.  Serious gamblers do not worry about point shaving and recreational gamblers should not either. It is exceedingly rare in professional sports for obvious reasons, and it is probably fairly uncommon in college sports.

Anyway, about the Wolfers study and this refutation…

Isn’t this a “no shizit” moment when one discovers that point differentials in basketball around the point spread are not symmetrical and random?  That is because of “point shrinkage” which I talked about in the other basketball thread.

I have not read the Wolfers study in a while, but if they concluded that point shaving must be rampant because of the asymmetry of point differentials around large point spreads, they must have known absolutely nothing about basketball.

As I mentioned in the other thread, you are walking on dangerous ground when you do a study involving a sport about which you know little or nothing.  That is true no matter how good an econometrician or statistician you are.

I have not finished reading this study, but if the authors found exactly the same thing in the NBA, which apparently they did, that is all you need to know to confirm that the effect that Wolfers found is NOT due to point shaving, since there is NO widespread point shaving in the NBA.

It is a good paper - the new one.  Everything seems to be correct, more or less.

The “no shizit” moment from the paper:

In sum, the simplest and most plausible explanation for the patterns in winning margins and winning margins against the spread for both moderate favorites and strong favorites, is that all teams are driven by a common desire to maximize the probability of winning.

Economists must often resort to indirect methods and inference to uncover the level of illegal activity in the economy. Methodologically, our paper highlights the care with which one must design indirect methods in order to distinguish legal from illegal behavior. We first show how a widely-reported interpretation of the patterns in winning margins in college basketball can lead a researcher to conclude erroneously that there is an epidemic of gambling-related corruption.

... patterns in winning margins are driven by factors intrinsic to the game of basketball itself.

Would you rather pick your winners against the Vegas oddsmakers, or pick your winners vs the public?  Which do you think is smarter?  I am not saying one is better than the other for bettors or books, just throwing it out as a question.  Where could you find more value?  Sure, it’s nice to know your odds when you make your bet, but that doesn’t seem to make horse racing betting less popular.
vr, Xei

You want to pick against the public...yes I agree with that.  The problem is the huge percentage that the track takes right off the top, probably 10% to 18% range.  Meanwhile, if you shop, you can often find spreads less than 2% in major sports.

Go to Matchbook.com.  There you will see incredibly tight spreads...no bookies, at least no official ones serving that capacity there.

I just re-read the Wolders point-shaving article.  He realizes that there are strategic changes in blowouts in basketball, discusses and addresses them. He makes some good points.  For example, he says that we should see “point shrinkage” (my term) in blowouts but that they should be independent of the spread.  That is true.  We should not see shrinkage around the spread - but in games that have high point differentials at some point towards the end, regardless of the initial pre-game point spread.

One problem with that assumption though, is that he is not taking into consideration the relative strengths of the teams in terms of the dynamics of point shrinkage.  For example, a 16-point lead with 5 minutes remaining in a game where one team is 14 points better than the other team is a lot different than one in which both teams are equal, and probably yields different strategies by both team.  For example, if my team is even with my opponent and I am 16 points up with 5 minutes left, I am probably leaving in all of my starters.  If I am already a much better team, I might put in lots of subs with a 16-pt lead since those subs are as good as their regulars anyway.

Wolfers also assumes that both teams should exert less effort in a blowout and that they should cancel one another out.  He is wrong there. For one thing, the winning team is likely to take out their starters and NOT the losing team, as the losing team NEVER gives up except for the last few seconds (or whatever).  That should be obvious.  In addition to that, there are other strategies that happen in basketball that make for a non-symmetrical distribution of outcomes around some mean.  For example, late game fouls by the losing team, which this “new” author mentions, but Wolfers does not.

Anyway, the strongest evidence that Wolfers did not in fact find evidence of widespread point shaving is the “controls” that this new study used, which were games in which there was no widespread betting (and therefore point shaving is unlikely).  And, as I said, if you do the same analysis in the NBA and find similar patterns (although it is much harder to get a large sample of large faves in the NBA), that is also evidence that those patterns are “normal” in basketball, absent point shaving, since almost no point shaving goes on in the NBA…

Personally I’d be a lot more woried about “points manipulation” (both points shaving and running up the score) in large spread college football games than in basketball.

There seems to be a lot more changes in strategy possible in football with regards to clock management and in going for FGs vs TDs etc once the points difference gets large in football compared to basketball.

Plus the fact that as a matter of “etiquette” it is considered bad form to “run up the score” in football in a way that is never or at least almost never mentioned in basketball.

I mean if it is considered “standard” that teams to some extent “show mercy”, take their foot of the trottle and just run out the game when up by a safe margin, who is to say if there is any foul doings if they do so slightly earlier or later? Plus, in one sense you only need to get to one guy, the one sending in the plays.

That is the other thing that has not been mentioned so far.  It is NOT easy to shave points in basketball without making it fairly obvious and it is not easy for one person to do so.

Not sure if this has been mentioned before (I didn’t read the paper, just skimmed through the comments), but I’ve heard that bookies often institute a premium on the favorites, reflected in the point spread. This is because bettors tend to wager on the favorite more than the underdog. Bookies also tend to charge a premium on high-profile teams, like Duke, North Carolina, Kansas, etc.

For instance, let’s say a bookie is considering the line for Duke vs. Rutgers, and the bookie believes that the “fair” line is Duke -20. The bookie knows that more money will get wagered on Duke than on Rutgers, so he can set the line higher, perhaps to Duke -24. Thus, he’s giving himself 4 extra points over the “fair” spread.

The bookie wants to receive equal action on both sides of the bet so that he can just collect the vig and have a riskless position. But absent that, he wants lopsided action on a spread that’s in his favor, which I think often happens with heavy favorites

I don’t see how that can work, as that would be a classic arbitrage opportunity.  It’s not as if there is only one bookie in the whole world.

Bookies goal is to make money not necesarily split the action.  If a bookie believes the true line is Duke -20, why would he want to move it to Duke -24 just to split the action.  If it’s truly Duke -20, then he’s got a good chance to make a heavy pay day off of the Duke homers, by leaving the line at -20.  If he moves it to Duke -24 just to halve the action, he is in danger of a big player coming in and plopping down a large chunk on the dog.
vr, Xei

Tango mentioned that one of the authors may be monitoring this discussion.  If so, I’d be interested in hearing his response (and others here) to Wolfers’ comments made at Phil’s site. I’m copying the text here (hope this is OK with Phil and Tango).

WOLFERS’ COMMENT AT SABERMETRIC RESEARCH:
Phil:
I like the Bernhardt and Heston study - a lot - so I’m reluctant to say anything critical. But I think that they oversell their results a bit, and your posting oversells their results a lot.

Their key point is the first one you make: That if point shaving is occurring, one might expect it to be more prevalent in games in which there is heavy betting on the underdog. So they take the sample, and split it into two. In particular, they create a “shaving” sample, in which betting line movements suggests strong betting on the underdog. And indeed, they find stronger evidence of point shaving in the “shaving” sample (see their Table 1). That is, they were able to locate a sample in which (logically enough) the effects I pointed to earlier were even stronger.

But they actually say something a bit stronger: “when the closing line does not exceed the opening line, point shaving is implausible.” That is, they treat the alternative sample as a “control” sample as if they know that there is no point shaving going on. Thus, rather than look only at the absolute level of the “Wolfers discrepancy”, they look at how it differs across the two samples. They find that it is indeed greater in the “shaving” sample, but not statistically significantly different. And this is the evidence against shaving.

But note the problem here: They are assuming zero point-shaving in those games in which the betting line doesn’t move as predicted. If this is false, then the test is problematic. To see why it is false, just think about Tim Donaghy. There is no evidence that the outcomes in games in which he ref’d are at all correlated with line movements. That is, Donaghy likely cheated as much when the betting line moved as when it didn’t. In fact, if you look at the history of known point-shaving episodes over the past century, you will often find that the betting line didn’t move. There are two reasons for this. Some point shaving episodes are just half-assed - a college kid betting a few hundred dollars on the opposition, and this doesn’t move the betting line. And second, only a very very small proportion of gambling on NCAA basketball occurs through Las Vegas, the source of the betting line movements relied on by the authors.

If instead you thought - as seems plausible from historical experience - two-thirds of point-shaving episodes appear in the “shaving” sample, and one-third in the “control” sample, then this would fully explain why they find a noticeable, but not large difference in point shaving across the two samples. All told, I regard these results (truly!) as supportive of my analysis.

The second test is also quite interesting: they narrow the game-margins in which to look for point shaving. In fact, they find greater evidence of point shaving when they modify my results to looking at a 12-point window; it is only a 6-point window that yields less evidence. And I think that makes sense: If I had bet $1000 on a game, I might be unwilling to shave enough to just win my bet by, say, 3 points, because then a fluke at the end of the game might mean I lose my bet. So perhaps the 6-point window is just too narrow to find all of the point-shavers. (Certainly a two-point window would be too narrow, so I’m not sure where to stop.)

The third point you note is actually supportive of my results: The data you cite show that the more betting there was on the underdog, the stronger the evidence of point-shaving. Look again at your numbers, but don’t focus as much on what is or isn’t statistically significant different from zero, but instead on whether the pattern is statistically significantly different from what you would expect if point shaving were occurring. The more the line moves, the greater the evidence of point-shaving.

I find their fourth point most interesting: that in games in which there is no point spread, the authors find similar evidence of point-shaving. That worries me a lot. But the problem is that in games in which there is no point spread, there is no point spread, and my test can’t actually be performed! The authors sidestep that neatly by “predicting” a point spread, but then one is left to wonder whether we are learning something about their predictions of what the point spread would have been, rather than about point shaving. Betting markets are a lot smarter than econometric models produced by even very clever economists, and so I suspect that some of this result reflects them mis-predicting what the spread would have been.

But lest this sound defensive, let me just note that I describe my own research as providing a “prima facie” case that point-shaving may be occurring. Forensic economics can’t do more than point out suspicious patterns. Bernhardt and Heston do a nice job in extending the analysis, but arguably strengthen, rather than weaken the case that there is something fishy in the relationship between outcomes in basketball games and betting lines.

Tango, I see your point about it being arbitraged away. But all bookies want the riskless position of having equal wagers on both sides. Trying to arbitrage away the difference between the listed point spread and the fair spread means you’re increasing your risk of a big loss.

Xei, you say “he’s got a good chance to make a heavy pay day off of the Duke homers”. It’s actually a 50% chance if the line is fair. He also has a 50% chance of a huge loss if Duke covers. If he moves the line a few points, he reduces his risk.

As an example, let’s say he sets the line at -20 and he gets $10 million wagered on Duke and $2 million wagered on the underdog (I’ll use Rutgers, as an example). There’s a 50% chance that Duke covers and the bookie loses $7 million (payouts equal .9*$10 million = $9 million. Receives $2 million from losing bets). There’s also a 50% chance that Duke does not cover and the bookie wins $8.2 million (The bookie pays out $1.8 million to the people who bet on Rutgers). Thus, the bookie’s expected profit is (8.2-7.0)/2 = $.6 million. This is 5% of the total amount wagered.

Now, let’s say he sets the line at -24 and gets $6 million wagered equally on both sides. He pays out $5.4 million to the winners but receives $6 million from the losers, no matter who covers the spread. The bookie has the same expected profit ($600,000) with no risk of a loss. Once again, the expected profit is 5% of the original amount wagered.

That’s why the lines move in accordance with betting patterns. The bookies want to limit their risk as much as possible. When a lot of money comes in on one side of a wager, they don’t just sit back, cross their fingers, and hope their position wins. They move the line in order to cause increased activity on the other side of the bet.

That’s why arbitrage doesn’t really happen among bookies. To gain more market share, you have to substantially increase your risk, with no increase in expected profit as a percentage of wagers received.

It’s possible that I’m wrong, but I remember reading an article online (I think it was ESPN.com) where a writer got to see the inner workings of a Vegas sportsbook. One of the sportsbook employees mentioned the “favorite premium”, as well as the “popular team premium”. I’ll try to find a link, but it was a few years ago and I’m having trouble digging it up. Until I find it, I understand if you guys are still skeptical…

Actually, I thought of it in another way that might make more sense.

The sportsbook industry is an oligopoly. It is not a pure monopoly, but it is not purely competitive either. There are severe barriers to entry which result in a less-than-perfectly-competitve market. There is strict regulatory control of the industry, so not every Joe Schmoe can open his own sportsbook. You can run an illegal sportsbook, but there are obvious risks to doing this. Also, you need to be very well capitalized to start, or you run the risk of blowing all your capital the first time you hit an unlucky stretch.

Now, think of it from a game theory point of view. If everybody sets the line at -24, every sportsbook will receive roughly equal amounts of money wagered on both sides, so they’ll all get a guaranteed profit.

Now let’s say one sportsbook decides to undercut the others. Every other sportsbook will undercut also, until they all reach the “fair” spread of -20. Now, they will once again be splitting the same total pot of money wagered. However, they will have a lot of money on one side of the bet, resulting in the risk of a big loss. They will all have the same market share and expected profit as they had when the line was -24, but now with a much higher risk level.

Thus, they choose to cooperate with each other, and not undercut each other. The spread remains at -24, and each sportsbook receives 5% of the total money wagered with them.

Wolfer’s response is a decent one.  Most of his arguments are good ones.  It is true that that the new authors’ assumption that point shaving in games where the line does not move towards the dog is “implausible” is a bad assumption. It is also true that, interestingly, there is evidence that the the asymmetry is greater in the games where the spread does move more toward the dogs.  The (new) authors just write this off as “not statistically significant.” That is poor (statistical) logic.  You don’t just write off all differences that are less than 2 standard errors, especially when you are looking at many different data sets (a bunch of small, statistically insignificant results can add up to one statistically significant one, PLUS the fact that ALL differences are evidence of something, whether they are technically significant or not).

It is true that since there ARE no lines on games that are not bet on - the control group in the new study - and they have to construct a line from Sagarin ratings, their analysis of that data set is suspect.

However, his argument that he only found a “prima facie” case of point shaving is weak.  It is his responsibility to make sure that there is no other explanation for the pattern he found before he even talks about point shaving, as that is a very serious accusation and one that should not be taken likely.  And he (Wolfers) is very clear in his study that he is indeed suggesting that point shaving is fairly widespread in NCAA basketball, not that “point-shaving is just one possible explanation for the effect we found,” which is the correct thing to say.

At the risk of offending those people who are sick of my Bayesian probability rants, I think that the point-shaving explanation is a weak one, as we should intuitively think that the prevalence of point shaving that Wolfers suggests (6% of high lines games) is unlikely (without looking at the data) - hence the a priori probability of that is low. 

As I said, all either authors have to do is to check a data set of NBA games.  If they find the same thing, then voila - it is overwhelmingly likely to be a part of the structure of the game, as there is NO point shaving in the NBA.  That is your ultimate control group.

Finally, the new authors’ explanation of how and why you would find this asymmetrical pattern of point differentials in basketball is right on the money and well-known to anyone who follows basketball.  That alone shoots the point shaving explanation out of the water and is what Wolfers should be addressing in his refutation!

MGL:  why do you view no point shaving as a certainty in NBA?  (Not disagreeing, just wonder why you feel this is a near-certainty.)

I found Wolfers response somewhat disingenuous.  Yes, he raises legit concerns about this paper.  But he cherry-picks some findings that show point shaving is possible, while just ignoring the fact that the new authors basically prove it can’t be happening on anything like the scale Wolfers claimed (and, as you say, also offering a simple, plausible explanation for the patterns that worried Wolfers).  If Wolfers had only claimed that “point shaving might be going on,” his response would be appropriate.  But in the context of what he actually wrote, to claim this study as validation of his work is chutzpah at a pretty stratospheric level.

Wolfers was equally cavalier, you’ll recall, in making a much more serious charge of racial bias against NBA refs a couple years ago.  (I say much more serious not to rate the relative badness of racism and cheating, but because the small number of NBA refs effectively singles out real individuals as bad actors, while saying 6% of NCAA games feature point shaving doesn’t do the same to any particular players).  But when you dig into his data, what you find is—at most—a tiny amount of bias, with virtually no effect on game outcomes.

Excellent point by MGL, and one worth repeating.

If you flip a coin and you get 20 heads in a row, what is the chance that you have a weighted coin?  Well, if you KNOW that the coin is NOT weighted (that’s your prior), then the chance that you have a weighted coin is zero.  This is a tautology of course.

In the NBA, what is the chance that there’s point-shaving?  As MGL notes, it must be so close to zero that it is zero.  The players in a position to shave points are those earning the most money already.  And they won’t risk that money by making small sidebets would they?  So, as MGL notes, the control group is the NBA.

If there is something about the structure of how points are made in basketball, the NBA provides the great context to determine that.

The key point is that you must start with a prior.

Refereed publications are a better forum to debate Wolfers specifically.  Wolfers mainly responded that point shaving may occur without betting enough money to alter the pointspread.  So absence of evidence is not evidence of absence.

Stanford student Jonathan Gibbs found comparable results with N.B.A. data.  I found a larger effect in old N.B.A. data from an era with bigger pointspreads.  If you believe that point shaving is not widespread in the N.B.A. then these results must be caused by something else.

The effect exists in baseball.  Teams that are 1.5 run favorites win games by exactly 1 run more often than they win by exactly 2 runs (especially home teams, ).  Of course there are other statistical explanations besides point shaving!  Skewness also occurs in baseball totals, hockey margins of victory, and other sports.  So an asymmetric distribution is not “prima facie” evidence of anything sinister.

#21: “Thus, they choose to cooperate with each other, and not undercut each other. The spread remains at -24, and each sportsbook receives 5% of the total money wagered with them. “

Please just go to Matchbook.com, click NCAA Basketball and click Michigan State at Connecticut.  It doesn’t matter what time as long as it is at least a few minutes before the game.  I imagine you’d throw away your previous assumptions about competition in the sports betting market after seeing the tight, liquid markets...and that’s only one “casino”.  Not all places have lines that tight of course, but once you put them all together, its pretty darn tight.

NBA players make too much money to be point shaving.  That is not to say that somewhere, sometime, some player with gambling, money, or other personal problems has not done something like that, but the likelihood that at any given time that the incidence of point shaving is close to 0% is very high, in my opinion.

If that were my study (Wolfers) and I got the results that he did, the absolute MOST I would say with regard to point shaving is, “The results are consistent with what one might expect if a certain proportion of games involved point shaving, however, there may be other, more likely, and less sinister explanations.”

And then, why he didn’t postulate or consider what those other explanations might be (like end game strategy) is the $64,000 question.  Had he asked any person who knows about basketball, they would have given him THE likely explanation which has nothing to do with point shaving.  That is one of the problems with doing sports research when you don’t know much about the sport.

Given that we have some extremly knowledgable sports betting insiders in this thread and that the subject has been sort of mentioned there is something I would like about how sports books handle their odds.

As I see it there seems to be two main mechanisms they can use.

One is to use the “wisdom of the crowds” to set the odds or point spread and thus guaranteeing roughly equal action and getting a risk-free profit from the vig.

The other one is to try to estimate the “true propabilties” of the different outcomes of a game and set the odds or spread accordingly.

Now to my question, do they use both equaly regardless of how “big” the game is? And by that I mean how much action they expect to get on it.

While many internet sportsbooks have many 1000’s of availible objects every day I would guess that something like 50-100 of those are responsible for a percentage of all action that is somewhere in the high nineties.

#26: I’m not really familiar with Matchbook, and I guess it’s a strong possibility that Internet betting has eliminated whatever competitive advantage the Vegas sportsbooks used to have.

Just wondering, do the point spreads on Matchbook tend to differ from the Vegas spreads? Right now, matchbook.com and Vegas both have UConn at -4, and I’m wondering if it’s going to change as it gets closer to the game.

Also, just to clarify, I know the casinos don’t ALWAYS adjust the lines according to betting patterns, and they’ll occasionally take bets against the public. Apparently, the Vegas sportsbooks took a huge hit on Super Bowl 42 (Giants vs. Patriots), suggesting a greater proportion of money was wagered on the Giants, but I don’t remember the line moving much, if at all

Oh wait...I misunderstood how Matchbook works. I see now how the lines move. Very interesting.

Steve/25:  I can certainly understand why it may make sense professionally for Steve to engage Wolfers only through journal articles, and not on a blog.  But from our vantage point, as consumers of these articles and ideas, that’s not terribly satisfying.  First, it literally takes years to litigate an issue through the forum of refereed journals (business slogan we’ll never hear:  “At the speed of peer review.") Second, Wolfers isn’t waiting for that process.  He widely publicized the findings of both his point shaving and referee bias articles in the mainstream media.  The public will never hear about the rebuttals if they come years later in refereed journals, so the original claim effectively stands uncontested in the public arena.  I’m sure thousands of basketball fans now believe they learned that “refs are racially biased.”

I’m not necessarily criticizing Wolfers for going public with his ideas prior to publication, or anyone else who chooses to do that.  He feels he has something important to say and he’s very productive, and I can appreciate his not wanting to wait for full academic vetting.  And frankly, given the poor performance of peer review in many cases, it’s hard to justify the delay it creates.  But if some authors are willing to go public, while those who disagree play by academic rules, then the public will often hear a very one-sided presentation.

I think the academy is going to have to adapt to the Internet age, perhaps by creating online publications in which academics can post criticisms and responses to articles without waiting for peer review.

I found an academic paper that looked at betting behavior. I think it’s by the guy who wrote Freakonomics. Clicking my name should link to the paper. The general results were this:

Bookies are at an informational advantage over the public. They know more than the betting public, and they have a better grasp of each team’s odds of winning each game.

Bookies do, in fact, exploit bettor tendencies, such as the tendency to bet on the home team. However, bookies do not try to equalize the money on both sides of the wager. By “shading” the line away from the true 50/50 spread (which was my original point), the bookie takes an active position (as opposed to the passive, no-risk position I previously stated) against the public.

To put it even more simply: the bookie sets the line such that the favorite covers the spread less than 50% of the time, but more than 50% of the wagers are placed on the favorite.

He found that when the favorite is the home team, 56.1% of bets are placed on the favorite, but they only cover the spread 49.1% of the time (there is a push .5% of the time). When the road team is the favorite, 68.2% of wagers are placed on the favorite, but they only cover 47.8% of the time.

In total, the favorites were picked 60.6% of the time, but they only covered 48.5% of the time. If the spread was “fair”, they would cover 50% of the time. The sample size was 19,201 wagers by 285 different gamblers

Tom referenced a paper by Steven Levitt.  It measured entries in a free promotional handicapping contest.  But bookmakers presumably set pointspreads based on real wagers, not contest entries.  Smarter, richer, and more motivated people can bet more and presumably have more influence on a real market.

Haven’t read the paper but if it is based on a handicapping contest, the results are NOT applicable to “real” betting. Not even close. 

Bookmakers are looking to make as much money as possible, like almost any other business.  That being said, they also don’t like to take too much risk.  That varies among book makers of course.  And what they did 30 years ago is a little different than what they do now.  In general, the opening line is a combination of what they think the public will do (trying to split the action) and what they think the true line should be.  There is also a little game theory involved in setting a line.  If I think that -3 in a football game will split the public action, but I think that the true line should be -2, then if I put out -3, I risk the likely fact that smart betters (good handicappers) will pound the dog.  If I put out -2 to keep the sharps from betting, the the public will pound the fave, which is fine, but I am losing out on making extra money from the public.  So I put out -2.5, which wins me extra money from the public, who will still bet disproportionately on the fave (at a bad line for them), and some of the sharps will bet the dog, which loses me some money.

To really know how lines are set, you have to ask a bookmaker or a linesmaker. However, if you did, you would NOT be satisfied with their answer, because the answer varies from game to game, from sport to sport, and from bookmaker and linesmaker to linesmaker, AND they can’t really articulate why they do what they do.  Sometimes people do things that “work” and they don’t really know how and why they do it.

The bottom line with lines is that any old line can be put out and then a smart bookmaker will know how to move the line once it comes out in order to maximize his profit, minimize his risk to some extent, and minimize the impact of his mistakes.  There are many ways to do that.  One is to take limited action on opening lines to get a feel for which way the public and the sharps are leaning and betting.  Another way (or an additional way) is to monitor the action, such that you try and tale advantage of sucker action (if lots of people - suckers - are betting on one side and you think you have a fair line, you can move the line to “rip off” those people), and you try and learn from the smart bettors (you move the line if the sharps are “telling you” you made a mistake in the line, etc…

Here are some numbers from the NBA (King Yao’s NBA database with point spreads):

I broke games up by pointspread from 1-3, 4-6, 7-9, 10-12, and 13 or more.  So, 5 groups, group I, II, II, IV, and V.

I looked at how often teams won by X more than the spread versus X less than the spread, essentially the same thing as Wolfers and the NCAA data.

Here is what I got:

Group I

N 2478 games
Average spread: 2.11
Win by 1 or 2 less than spread: 3.4%
Win by 1 or 2 more than spread: 4.7%
Diff (more minus less): 1.3%

Group II

N 2709 games
Average spread: 4.98
Win by 1, 2 or 3 less than spread: 5.6%
Win by 1, 2 or 3 more than spread: 7.7%
Diff (more minus less): 2.1%

Group III

N 1828 games
Average spread: 7.89
Win by 1, 2, 3, or 4 less than spread: 7.5%
Win by 1, 2, 3, or 4 more than spread: 8.2%
Diff (more minus less): .7%

Group IV

N 796 games
Average spread: 10.8
Win by 1, 2, 3, 4, or 5 less than spread: 9.7%
Win by 1, 2, 3, 4, or 5 more than spread: 10.0%
Diff (more minus less): -.3%

Group V

N 307 games
Average spread: 14.0
Win by 1, 2, 3, 4, or 5 less than spread: 14.3%
Win by 1, 2, 3, 4, or 5 more than spread: 12.4%
Diff (more minus less): -1.9%

So we see a similar pattern as Wolfers and the NCAA data, I think, although we have smaller differences at the high end. The samples are small at the high end, so we really have no reliable numbers, I don’t think.

But the pattern of point differentials around the spread seems to suggest that the higher the spread, the more that teams tend to fall short of the spread than exceed it, for the same differential.  At least with this small sample of games.

Again, suggesting that that is how teams play with a big lead rather than evidence of point shaving, if we assume that little or no point shaving is going in the NBA, which I think is a very good assumption.

Just for fun, here are other numbers:

Group I
avg. spread 2.1
avg. wp .556
avg margin of victory (including losses): 1.4

Group II
avg. spread 5.0
avg. wp .669
avg margin of victory (including losses): 4.6

Group III
avg. spread 7.9
avg. wp .765
avg margin of victory (including losses): 8.0

Group IV
avg. spread 10.8
avg. wp .867
avg margin of victory (including losses): 11.7

Group V
avg. spread 14.0
avg. wp .941
avg margin of victory (including losses): 14.7

Just to specify, the handicapping contest had an entry fee and actual cash prizes. The top prize was something like $40,000.

MGL, I think your explanation in #34 is probably the most reasonable of anyone in this thread (including myself).

I think that the assumption that bookies always select a “fair” line (which basically everybody besides me and MGL seems to believe) requires at least one of the following assumptions to be true:

1. There are bettors who have as least as much information and analytical capability as the bookmakers. Thus, they can arbitrage away any mispricing in the point spread.

2. The betting public does not display certain tendencies (disproportionate wagers on favorites, for instance)

3. If the betting public DOES display certain tendencies, the bookmakers do not to adjust the lines to take advantage of this. They just stick with the “fair” spread.

Assumption 1 MIGHT be reasonable (but I doubt it), but assumptions 2 and 3 are simply too unrealistic for me to believe.

One very noteworthy thing that Levitt shows in his paper is that from the years 1980-2001, favorites covered only 48.2% of the time, in 4793 games. In particular, road favorites only covered 46.7% of the time, in 1483 games. Those are both large enough samples to reject the hypothesis that favorites had a 50% chance of covering the spread.

Perhaps the increase of Internet betting has changed this, but for an extended period of time, bookies were definitely “shading the line”. Levitt does mention on his New York Times blog that road favorites did MUCH better in 2007 and 2008, so it’s possible that the betting landscape has changed enough to eliminate the bookmaker’s ability to take advantage of betting tendencies

If you want to compare NBA to Wolfers NCAA results then it is critical to use identical measures.  Bernhardt and I tried varied the point shaving interval and strength of favorites, but Wolfers’ choices always gave the strongest results.

Maybe you can link to Jonathan Gibbs’ NBA paper.

What do you mean “link to the paper?” Do you mean I should read it?  Put a link to it in this thread?  I don’t know what you mean by using “identical measures.” One of the problems with the NBA data I have is that there is not enough to carve it up and get anything meaningful in the resultant pieces.

Tom, yes there is no doubt that there used to be plenty of biases in betting lines that took advantage of the public and to some extent were designed to split the action (before there was much information available to anyone, including the bookmaker, AND because the bookmaker used to be afraid of inside information, the bookmaker used to be satisfied with just splitting the action, so all he had to do was handicap the public) and only accidentally took advantage of the public.  All of those biases, including the favorite bias, at least the obvious and not so nuanced ones, have disappeared or are disappearing for obvious reasons…

"[S]hould [I]… link to it in this thread?”

Yes.  I have a copy but can’t find it online.  You and other readers might find it interesting.

I think you wanted to compare your NBA analysis to Wolfers’.  To compare magnitudes you need to use the same measure as Wolfers, i.e., the fraction of games landing between the pointspread and twice the pointspread.

How can I learn more about those historical biases (in MLB or NFL)?

Steve, how would I link to it if you can’t find it on the web?

Here is an article that summarizes his findings. That is all I could find.

http://sportsgambling.about.com/od/basketball/a/nbafixed.htm

OK, I looked at how often the favored team won by more then the point spread but less than twice the spread, versus how often they won, but did not cover the spread (and did not push).

For example, if the spread was 5 points, I looked at how often the favored team won by 1 to 4 points (won but did not cover) versus how often they won and covered by less than 10 points (won by 6 to 9 points).

As you can see, the pattern is exactly the same as Wolfers found in the NCAA.

Group I (2.1 average spread) N=2478

won no cover: 6.24%.  Covered but by less than twice the spread: 8.48%

Group II (5.0 average spread) N=2709

won no cover: 19.6%.  Covered but by less than twice the spread: 25.6%

Group III (7.9 average spread) N=1828

won no cover: 29.6%.  Covered but by less than twice the spread: 33.2%

Group IV (10.8 average spread) N=796

won no cover: 42.6%.  Covered but by less than twice the spread: 38.8%

Group V (14.0 average spread) N=307

won no cover: 46.4%.  Covered but by less than twice the spread: 40.5%

Oh no, it looks like there is massive point shaving in the NBA as well!

Steve, I don’t know how you can learn about the biases. I guess get involved in sports handicapping and betting for 5 or 10 years. I was referring to things like the line and public shading the favorite in most sports, the same thing for “hot” teams, totals in the NBA used to be never that high or low (they didn’t understand how “pace” dictated the totals in basketball 25 years ago), etc.  These (and more) things no longer exist to any degree.