THE BOOK--Playing The Percentages In Baseball

I admit to not making it through Gibbs’ paper yet, but unless I’m recalling incorrectly, the paper about point shaving in college basketball that came out a year or so ago never specified whether the author used the opening or closing line as the basis for his study. I’m not an economist and I’m not especially proficient at anything beyond arithmetic, but that seems like a rather important distinction to make.

I’ve only skimmed the actual article, so I’ll also make a disclaimer that I might be missing something ... but I am also skeptical that this should be considered evidence for point shaving.

My two main points ...

1. I think the author underestimates the chance that the big home dogs cover percentage is due to random chance or bettor bias.

There are all kinds of sports to look at and various ways to split the data.  You can look at whether NFL playoff favorites really cover 50% of the time.  You can look at whether away favorites in college football cover 50% of the time.  You can look at whether high total MLB games go over the total 50% of the time.  Or you can look at whether NBA big home dogs cover 50% of the time.  Even if all markets are perfect, just through dumb luck, we would expect to find some situations where we could “reject the null hypothesis”.

Further, the author is dismissive of the idea that bettors might have a bias against home dogs, citing the preference for longshots in horse racing.  But the more relevant pieces of info are that MLB and NFL bettors tend to (slightly) prefer favorites.

2. Even if we accept that big dogs cover “too much”, the article doesn’t seem to provide much evidence that it’s because of point shaving at the end of games.  Phil Birnbaum has already done most of the explaining here, but I’ll just add that there is a known and established “comeback tendency” in the NBA ... that is, final scores will be closer than you would expect if you assumed a random walk.  So it’s not really that shocking that dogs would often cover in the final minutes.

A couple other points ....

3. The Levitt (2004) article cited in the PDF is indeed a complete joke, and not just for the reasons described.  In fact, when academics write papers on sports or gambling, their articles usually are jokes.  I see two possibilities ... (a) academics don’t take sports and gambling seriously, and just like to write non-rigorous papers about them for fun or (b) the academics actually don’t know anything about anything, but I only notice this when they write about sports or gambling because they’re the only subjects I know enough about to see through their bullsh*t.  It’s probably (a), but sometimes I wonder .....

4. I will say that Gibbs shows some “real world” knowledge with his description of the differences between NBA and NFL betting.

I haven’t read the paper itself yet (seems to be a common theme), but Phil’s comments are spot on.  As someone who knows a “little” about sports bettting, it is common knowledge that, for example, a team that is actually 12 points “better” than another team is only going to be a 9 point favorite (or whatever number) because of “garbage time.”

I don’t know the source of the author’s historical betting lines, but accurate ones are difficult if not impossible to come by.  And there is a big difference between the opening and closing lines in the NBA.

Also, most sports have a favorite bias (the NFL the most), such that if you bet all dogs blindly, you usually can cut the juice down to a low number, but generally you don’t eliminate it completely.  The reason is that the public likes to bet favorites, so that if the linesmaker thinks that a team is really a 3 point favorite, they make the line -3.2 (or whatever - they only use half points in reality of course) in order to anticipate balanced action. I am skeptical of the author’s numbers though on large dogs and home dogs.  I wonder what his sample of games was.

Finally, as several people have already mentioned, if there were point shaving going on, it would be a very small percentage of games and it would be virtualy IMPOSSIBLE to notice with any statistical test because of the noise.

In general, in the NBA, the point spread (as a proxy for the relative strenghts of the teams) and the score has a gigantic influence on what happens for the rest of the game, at ANY point in the game, for various reason (mostly that teams play differently depending on the score, which affects the distribution of scoring hence), and it has NOTHING to do with point shaving!  In any case, the author should have (maybe he did - I don’t know since I did not read the article) consulted two very important sources before drawing any conclusions from the data - one, a sports betting expert, and two, an NBA expert, or someone who fits both bills (most NBA betting experts are NBA experts in general).

Ok, I’m reading it now.  The paper is here:
http://www.stanford.edu/~jmg52/NBA%20Analysis/JGibbs%20NBA%20Analysis.pdf

His data comes from here:
http://www.goldsheet.com/

You can start reading starting at the middle of page 22.  I’ll be back for more.

What the author concludes as “point shaving” is in fact “point shaving”, but not necessarily betting-driven point-shaving.

You can shave points by having garbage time players, or quality players playing as if they are garbage time players, etc.  But, they can be doing this without knowledge of the betting line.
The real question is: are players influenced by knowledge of the betting line?  I don’t see the author as answering that specific question.

And my proposal at the top of this blog would seem to answer the question.  Take a group of games where the team leading after 46 minutes by a substantial margin and then split them into four: those that are just over covering the line, those that are way over covering the line, those just under to cover, and those that are nowhere near to covering.  What happens in the next 2 minutes?  Are the points scored and point allowed similar for all 4 groups?  What percent of the just under group goes over, and what percent of the just over group goes under?

I’m going to guess (and I don’t follow basketball other than the finals) that teams that are substantially leading after 46 minutes will end up scoring 45% of all points in the final two minutes, regardless of where they stand relative to the line.

The problem with your proposal, Tango, is that the point spread is still a proxy for the relative strength between the 2 teams, so that whatever the result of the last couple of minutes in a blowout among all 4 groups, you don’t know how much may be due to point shaving and how much is due to differences in strength between the 2 teams.  In any case, you just ain’t gonna “find” point shaving in the data even if point shaving exists.  There is just no way that if it exists at all that it would show up in this kind of study or any study at all, as the incidence, at best (or at worst I guess), is going to be EXTREMELY small.

My original proposal called to only look at teams that were heavily favored.  That should satisfy your requirement.

So, heavily favored, and leading in a lopsided game.  One group just below the line, and the other just above it.

I agree with MGL, that point shaving would have to be pretty widespread for it to show up in the data.  Of course, Gibbs is suggesting 6% of unbalanced games, 1% overall.  That would be easy to find.

Look at it this way: suppose you took a normal distribution centered around zero (points against the spread), and selected 10,000 random points.  You’d get a bell curve.  Now, take 1% of those points—100 points—and move them from +1 or +2, to -1 or -2.  Look at the curve now.  It would be obvious there’s something going on.

1% is so big, I think, that it should be easy to disprove.  Whether there’s ANY shaving going on ... well, I think MGL and Pizza Cutter are right when they say that if cheating is rare, we’ll never find any through analyses of this type.

I remember reading an article in SI a few years ago, from a college kid who admitted to point shaving.  And consistent with the way that Nick Nolte movie showed it ( http://www.imdb.com/title/tt0109305/ ), it wasn’t a case of “lopsided end of game” scenario. 

That college kid said that he’d have his best scoring game because he wanted to show that he was really trying to win, but would let his defense slide, letting guys be able to get by him.  Essentially, he’d have a poor “plus/minus”.

Here’s the story:
http://robots.cnnsi.com/basketball/college/news/1998/11/04/shaving_story/

As for his point shaving, Smith said he cheated while playing on defense. In one such game in which he scored a career-high 39 points against Oregon State, he said he just “stepped back a half step” from the player he was guarding “and he had the room he needed.” The Sun Devils won but only by six, meaning the Beavers covered the spread.

Smith admitted having agreed to fix four games for $20,000 a game, in part to erase a reported $10,000 gambling debt.

I read the first half of the paper which is essentially the background.  I am quite skeptical of his argument as to the incentives that NBA players have for cheating.  For one thing, he says that the chances of getting caught are near zero.  I disagree.  I think they are quite high, and that the reason that there has never been a player cheating scandal in the NBA is because virtually no one cheats.  It is not THAT easy to bet a lot of money on an NBA game without attracting some attention.  Even if it were difficult to get caught, I find the idea that players making millions of dollars would jeapordize their careers and reputations (and their freedom as they might end up in jail) pretty far fetched.

I’m not sure that I will be able to understand the math, but I’ll read the rest of the paper and see what I think.  The guy does sound pretty smart.

MGL, what would your feelings be if you were living in Italy?  Hard as it is to believe, betting scandals involving top-end sports do happen in the rest of the world. I don’t see why North Americans would be immune to it.

#12, I don’t know.  I am not familiar with betting scandals in other countries.  And of course, my comments about the prevalence are mere conjecture.  I would not be shocked or even surprised if there were some point shaving going on that has not been detected.  I just think it is rare, but I could be wrong.

Tango, the problem with your “4 group proposal” is that in each group while you might have the same large lead which would suggest that the winning team should score around the same percentage of points in the last 2 minutes (say, all teams with a 10-12 pt lead score 45% of all points in the last 2 minutes), you have different team quality differentials in each group, which can cause all kind of weird dynamics.

For example, your 4 groups might be:

1) winning team is a 16 pt fave.
2) a 12 pt fave.
3) an 8 pt fave.
4) a 3 pt fave.

And let’s say that they are all winning by around 12 points after 46 minutes.  Now, you would not expect team #1 to shave much, you would expect team #2 to shave a little to make sure they don’t outscore their opponent in the last 2 min., team #3 should shave a lot as they are covering, and team #4 would probably not shave as they are covering too much and you don’t expect any polint shaving in a game where the fave is only 3 points anyway.

So if there were shaving:

You would expect group one to score what they usually do with a 10 pt lead, say, 45% of the points.  Group 2 would shave a little and score 42% of the points.  Group 3 would shave a lot and score 40% or less, and group 4 would not shave at all and also score 45% of the points.

If there were no shaving:

You would expect everyone (al groups) to score 45% (or whatever they normally do with a 10 point lead), but....

In group one, the winning team is a large fave.  Maybe with large faves, they have lots of superstars and take them out of the game with bog leads, so maybe they will only score 40%.  OR maybe they would normally score 47% even with garbage time, because they are so much better than the other team, but when they take out their stars, they only score 45%.  And with group 4, they are not a big fave, so maybe even with garbage time (and no shaving of course), they only score 40% of the points.

I don’t know the dynamics, but the problem with your scenario, Tango, as I already said, is that while you are trying to control for point ahead and then vary the scenarios where one group would be trying to shave more or less than another group, in order to do that, you have to vary the relative strengths of the teams, and that creates all kinds of weird dynamics which you cannot predict which might change the outcome of that last 2 minutes.

Not to mention the fact, that if you try this in practice, you will NEVER have anything but a very small sample of games to analyze because relatively few games are when one team is winning by a lot with 2 minutes to go AND you can find teams that are favored by a little to a lot.  So even if there were shaving or no shaving, I don’t think you would ever get a nearly large enough sample to “prove” it one way or another, using your “4 group proposal.”

MGL: In Tango/7, I said to only look at heavily favored teams that were leading big.

Tango, in any case, you’ll have literally like 10 games per year in each group…

OK, in 05-06, there were 302 games in which one team was favored by 10 or more. Of those games, there were 33 in which the favored team was winning by within 4 points (plus or minus 2) of the spread.  If you want to be withing 8 points of the spread, it is 63 games.

MGL/16, when you say “was winning,” you mean “won,” right?  i.e., after the full 48 minutes.

Could you give the breakdown of those 33 games by sign? 

If there’s point shaving, the -1/-2 should be larger than the +1/+2, right?  And if there’s no point shaving, they should be equal.

Phil, I think he means was winning after 46 minutes.

What is interesting, to me, is that only 11% of the games are “shaveable”.  That is, if we consider only games with a 10pt lead as ones that will attract collusion, only 11% ended up close enough with 2 minutes to go, where a player could have an impact.  (Unless of course the player did the damage way before the 2 minute warning.)

MGL, can you show the percentage of games for all the betting lines, to extend your post 16?  That is, you have 302 games line of 10+, 33 of which favored within 4 points of the line (11%).  How about the 6-9 games, the 3-5 games, and the 1-2 games?  Ideally, all games are equally shaveable.  But if they are not, it may show that there was some shenanigans going (whether intentional, like the college kid, or more garbage time play).

The thing is, even if we did get a big enough sample and satisfied everyone that we were controlling for external factors and the study did show a “statistically significant” difference ... would you actually believe that there is shaving in the last two minutes?  I wouldn’t.

Who can engage in this last minute point shaving? 

No individual player can be confident that he’ll be in the game in garbage time even if the pointspread is in doubt.

The refs?  Maybe, but as has been discussed in recent news articles, if you find a corrupt ref, you’re best off dealing with over/unders.

The coach?  No, because his selection of which players to use in the final minutes won’t make that much of a difference to the chances of covering.

Maybe a combination of coach and players would work.  That way, the “tankers” could be assured that they would be in the game when it mattered for pointspread purposes.  But do you think this really happens?

This is a shortcoming of classical statistics.  You can’t just run a test and say, “oh, look, that’s statistically significant” ... you also have to factor in that there is no f-g way this type of cheating is widespread among the players. 

I’m reaching here, but sometimes I feel like articles like this are the reason people get fed up with statheads and sabermetrics.  They read a newspaper article about how someone did a bunch of complicated-sounding statistical stuff and reached a conclusion that made no sense ... in their minds, this supports their notion that “you can prove anything with statistics”.

On the other hand, I now see that this was an undergraduate thesis (not a research paper), so perhaps I should not be as disgusted with the academics as I previously indicated.

Sorry, these were the final score.  I don’t have access to in-game scores.  I am using the same betting logs as the author (The Gold Sheet), which just gives the spread and the final score.

DFL, it is not a shortcoming of statistics.  It is a Bayesian problem.  It is a combination of what we find in the sample data and what our a priori estimate of cheating is.  That should definitely be mentioned in these kinds of studies.  For example, what if we want to find out if we have a biased coin so we flip it 100 times and come up with 65% heads.  Do we conclude that we have a biased coin because we are 3 SD’s above what we expect from a fair coin?  No!  Because we have an a priori probability which is that there are virtually no biased coins.

Now, in studies like this, I don’t know when you use a Bayesian scheme and when you don’t.  I guess for one thing it depends on how well you can estimate the a priori probability.

Right, Bayesian is the way to go ... I’m only saying it’s a shortcoming of classical statistics (i.e. hypothesis testing, publish if you get a p-value less than 0.05)

DLF, sure I agree and sometimes researchers neglect Bayesian analyses (when it is appropriate) and can lead them to erroneous conclusions (accepting or regecting a certain H based upon a certain P-value).

Not only that, but I have always said that it is silly and arbitrary to categorically reject or accept an hypothesis just because it is above or below a certain P value. I know that is what social scientists tend to do, but I think that it is a bad habit. That is especially true when we have an “idea” as to what an a priori probability might be.

I prefer to simply give the result of an analysis (of sample data), give the confidence intervals (the standard error or whay have you), and let the readers make up their minds.  What else can you do?

Thinking about this some more, wouldn’t the larger lines tend to be less accurate for purposes of predicting the final score?

I don’t know the relative volume of casual vs. professional bettors and their respective degrees of impact on line movements. Is it incorrect to assume that a bookmaker would take, over time, more action on heavy favorites than heavy underdogs and the line would reflect this reality?

Bad teams rarely have bandwagon fans.

MGL: Agreed.  Even without a formal Bayesian approach, you should just be able to say “while the frequency with which the coin landed heads is significantly different from 50%, the fact that biased coins are so rare requires us to take this result with a grain of salt.”

Although, perhaps, the referees would reject any article that did that.

It also works the other way.  I reviewed an article that rejected a hypothesis that did not show statistical significance, even though rejecting it *contradicted* a hypothesis they accepted!  IIRC, it was the Massey/Thaler study: they argued that an earlier NFL draft choice is more likely to get you a Pro-Bowl quality player, and is also more likely to get you a regular than a sub. 

But they said it was NOT more likely to get you a better non-Pro-Bowl regular player than a worse non-Pro-Bowl regular player, because the coefficient was only 1.5 SDs from zero, or some such.

That’s what happens when you blindly follow the “5%” rule—or indeed, any other rule of thumb in any field.  You have to use your brain to think about whether what you’re doing is appropriate, and what it means.

I haven’t read the original paper yet that Phil is analyzing, but an academic drops by to blog about his research paper in Phil’s comments:

http://sabermetricresearch.blogspot.com/2007/08/ncaa-point-shaving-study-convincingly.html