Friday, July 27, 2007

Baseball, Gambling, and Lots of Nerd Talk

Log and I are attempting to do a comparison between Clay Davenport's Baseball Prospectus projections and the lines Las Vegas has created in regards to MLB teams winning their respective divisions. The projections BP produces give us the different probabilities each individual team has of winning their division or wildcard, and then sums those two totals to calculate an individual teams total probability of making the playoffs (presented as a percentage number.) I will focus only on the odds/projections of each team winning their respective division as those are the only bets Vegas allows for.

Baseball Prospectus gives us the ability to make predictions based on current cumulative statistics and future projections that are as accurate as any other baseball projections analysis tool used by statisticians(we know about). Using that information might enable us to find some holes in the lines of Vegas, which are actually lines the public creates. Once we know that the public may have missed the boat on a line, we can avoid it or bet against it, and consequently, increase our bets expected value as we aren’t basing our decisions on public perception but rather statistical projections rooted in fact

Please look at the spreadsheet and understand that the Vegas % you see for each team is essentially the public’s perception about each team winning their respective division. Then, look at the public’s perception and compare it to Baseball Prospectus’ projections. You can see that they differ a lot in some instances, and sometimes not at all. The spreadsheet indicates that the publics perception of a team and the most accurate projections of a team actually winning their division are sometimes completely different.

Throughout the rest of this article we will attempt to:
1) Explain how Baseball Prospectus arrives at their projections and prove their accuracy

2) Explain how an individual can accurately measure the public perception of an event by explaining how Vegas Lines are created and what they mean

3) Compare the results of the publics perception (Vegas betting odds) against the Baseball Prospectus projections that should be more accurate

4) Show you how you can use these comparisions to find holes in the betting odds Vegas produces

Let the fun begin!

1. First we need to convince you that these odds from Baseball Prospectus are legit and explain where they are derived from. Davenport starts with what’s called a team’s third-order winning percentage. W3, as its called, is derived from a team’s Equivalent Average or EQA which incorporates all offensive production into a single number that looks like a batting average. It is adjusted for park factors as well league factors. Adding each player’s EQA yields a new runs-scored total for each team and from this you can compute runs allowed using the total pitching line. After that strength of schedule is factored in and the results are used to calculate a Pythagorean record. It was originally developed by Bill James and has since been perfected. It has proven to generally be accurate to within three games.

If you’re still with us hold on because this will get a little more confusing before it becomes clear. Davenport now uses a Monte Carlo simulation, which, very simply put, takes a set of data and random simulates possible outcomes to find the most likely scenario. In order to take into account the random variance in the EWP the simulation uses a regression. Normally the regression would be to the mean (.500) but in this case Davenport uses the PECOTA projections from the beginning of the year. Davenport simulates the season a million times and the percentage of times each team wins the division is what we will use for our “odds”.

Baseball Prospectus is the most trusted name in baseball stastics. Part of Davenpor'ts projections use the aforementioned PECOTA projections that were 73.6% accurate for the 2006 baseball season. We think we can fairly assume that the predictive nature of Baseball Prospectus numbers won't deviate more than 10% from the actual outcome (i.e. which teams win their division.) No system is perfect, and Baseball Prospectus attempts to get us closer to perfect information. Basically, just assume we are right in suggesting that these projections are about as good as we can expect to do!

(If you want to see a more detailed explanation check out this, this, and this, as well as the actual projections, updated daily.)

2. Now we need to get rid of a common misconception many people have when looking at gambling lines. In order for us to compare the two systems, we must first understand the underlying "meaning" of any line Las Vegas creates.

Most see a horse or baseball team at 4:1, and assume those odds are the probability of a horse or team winning their respective events. In actuality, The 4:1 number is not a probability at all, but rather a "money ratio" of how much you have to pay to win. (PAYING ODDS!!!) To reiterate my point: the odds we see from Las Vegas are not "the chance an event will occur", but rather the amount a bookie pays if he loses or, collects if he wins. Please reread that section if you don't understand, because if its not grasped the rest of this article will look like it's written in Chinese. (It might even if you've understood me up to this point!)

So, when public perception of a team is high, a bookie starts getting a lot of bets for that particular team. In an attempt to protect his ass and minimize his loses (in the case that the public favorite does actually win) he has to start adjusting his “paying odds” ratio so that more action is giving to the other team (the public dog.) Remember we are talking about money and not probabilities. Hypothetically, if a bookie was sure about the probability of a random event, a natural line would be created, and he'd only take action if the public produced a "paying odds" line that gave him positive expected value. If they wouldn't, he would simply avoid the action and wait until the public bit, and produced a favorable line. In the long run, he would win every single time!

For example, if people were paying a bookie $50 dollars to win $1 on coin flips, he would never move his line because the "public perception" was that heads was the "hot" side of the coin and "it could never be beaten". The true odds would be 1:1 and people would be paying 1:50!! He would be as rich as Bill Gates. That's why a flip of the coin bet will always be even money, unless you are a degenerate like me and would give someone 13/10 odds on one side just so you could get action. (Yeah I've done that a couple times). If the public thinks the tails side of the coin, for whatever reason, didn’t have the same expectation of “winning” as the heads side, and wouldn't bet it, he would have to wait until those perceptions shifted back and created at least an even money bet. He would only be willing to take action if one side of the coin was perceived as being a better bet then the other side of the same coin. In that instance, he would win every single time over the long run!

3. Saying all that, I think that the "paying odds" ratio for random Team A, (expressed as X to Y, X:Y or X/Y )do in fact correlate to the actual probability of random Team A winning or losing an event.

Inherently, a "futures" bet involving playoff projections is different than the flip of a coin. Based on information (PECOTA), one can start to predict probabilities that move the "paying odds" ratio away from 1:1(even money.) Remember, the "paying odds" should tend to correlate with the true probability odds of an event because as a large number of people start betting, the "paying odds" ratio (X :Y) actually becomes the public ‘s perception of the likelihood of a team either winning or losing. We, as a betting public, have the ability to somewhat predict the likelihood of an event by creating the very lines we bet on.

Say this with me: We create the lines we bet on! Those lines we create indicate our future probability projections. We wouldn't be willing to put up a $100 to win $1 if we didn't think we knew something was almost guaranteed to happen!

Would anyone bet that the Red Sox are making the playoffs if they had to pay $3000 to win $1, with their current standing atop the AL East? Definitively, the answer is no. However, people are willing to pay $50 to win $1 dollar because that's where the line is it. The public created that line and it suggests that the Red Sox have a very, very, good chance of making the playoffs. Basically, that large a pool of bettors can't be wrong, so Vegas is only willing to pay out $51 on your 50$ risk! IF the public perception of the Red Sox started declining, the line would move down and we would have to pay less up front to win that mighty dollar. Are we smart enough as a group to predict probabilities? Well, Vegas sure thinks so. I'll attempt to explain why.

I first took the "paying odds" ratios and created a makeshift percentage which looked something like this:

Percent of future win paid= Y/ (X+Y) where the "paying odds" ratio is set up as X:Y or X to Y. (i.e. The Orioles "paying odds" ratio is 250:1 or 250 to 1)

This formula, which attempts to show the public's perceived probability of success, calculates the amount of money one has to pay in a "paying odds" ratio and compares it to the total amount of money earned from a future win based on that same ratio. So, in the Red Sox example, the "paying odds" ratio was 1:50, which means someone has to wager $50 to win $51.

The formula looks like this: 50/ (50+1)= 50/51=98%.

We have to pay 98% of any future win initially if we even want to take any action. So, anyone who takes this bet must believe that the perceived probability of success (the Red Sox making the playoffs in this example) is close to 98%, because that person is willing to put up 98% of any future win just to take the action. Along those lines,, this example suggests that Vegas thinks there is an extremely high probability that the Red Sox are going to make the playoffs (or the line would move to a lower number to get proper action). The Royals aren't viewed quite so highly as the "paying odds" ratio is 250:1, which means we have to pay $1 to win $250.

The formula looks like this 1/ (250+1)= 1/251= .04%.

We only have to pay .04 of any future win initially if we want to take the action.

After I calculated this P% of future win paid (perceived probability of success) and then compared it to the projections Baseball Prospectus created. A quick observation suggests that the "paying odds" ratios, when broken down into a P% of future win paid, are extremely similar to those probability odds of BP. The long shots shouldn't even be considered. Vegas, as well as the public, know that these teams have no chance of winning a division. The chance of a team like KC winning their division becomes almost as predictable as a flip of the coin and Vegas doesn't have to move their line from an optimum point. Believe it or not, even these teams are over valued!

Think about it, if you agree that the public sets the line, and that the line is a pure "money odds" ratio, we would have to see if that ratio is similar to the % projection probabilities BP creates. The only way to do that is by creating a Percent of future win paid #, which would suggest our perceived probability of success for any given team and comp, and then comparing it to the probabilities generated by BP.

4. Taking the average difference between our perceived probability and that of the lines of Vegas, one can see that our probabilities and those BP are very similar. Over the entire league my "Probability of Success" % is only 6% different than that of Vegas. (see chart)

The 6% difference is due almost entirely to "public plays" that are statistically (based on our PECOTA projections) awful.

Ten Teams were +4% or more away from the mean.

NYY- 10%


SEA- 12%


SDP- 13%

MIL- 14%

CLE- 15%

ARZ- 15%

PHI- 18%

The Yankees are projected to make the playoffs 6.50% of the time based on our BP projections, while the public suggests they will get there 16.66% of the time.

The Phillies deviate furthest from the mean, as BP's statistical projection has them making the playoffs 7.45% of the time, but the public sees them getting in 25% of the time; creating the 18% difference. (See chart) This makes the Phillies the most "public Play", and statistically the worse bet one could make this year when considering MLB division futures. I find this very interesting, and if not for "public plays", that are based on nothing more than a feeling, Vegas would only be collecting the juice. They are content with taking action this far away from the mean because they are going to win more than they lose.

I found one interesting case where the public's perception (the Vegas Line) was less than that of BP's playoff projections. The Mets, under BP, are supposed to make the playoffs almost 80% of the time, but the public is only willing to put up 75% of any future win (perceived probability) to take action. This suggests that they are a public dog, and would be the best bet. I guess this turns into the contrarian theory of betting, but statistical projections suggest they are undervalued by 5%in the eyes of the public, whereas the ten teams listed above are extremely overvalued. The Sox are right at the average, but are also overvalued as a team.

Remember, the BP projections are historically around 70-75% accurate, so a better system could certainly be created that would produce better probability projections. However, it is a start. I've learned that this tool could be more valuable in preventing people from making stupid, public bets then in finding teams Vegas has really missed the boat on. However, saving bets is important in any form of gambling. Money saved is money earned.

We hope you were able to follow this article at least somewhat. Our findings were anything from earth shattering, but you know who to stay away from with any 'futures' betting you might do this year. GO METS!!!


Buzzsaw said...

Holy shit

Daris said...

hahaha ya

Buzzsaw said...

My eyes hurt ... there might be a problem with the Phillies though, when'd you get the PECOTA stats? Today? Wouldn't they have changed with Utley going down, while the betting odds may not have yet? That would definetly cause for that big of a shift.

Buzzsaw said...

That's like 100% what the problem is, there's no way the Phillies would only be 7.__% with Utley. Right?

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Buzzsaw said...

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Daris said...

ya those statistics are now a few days old. in fact, Vegas stopped taking action on the AL East last night and i'm not sure if its up yet. I'm sure they pulled the PHI line for awhile until they figured out what they wanted to do.

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Buzzsaw said...


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