Friday, October 15, 2010

Is the NFL Betting Market Efficient?

So the guy running The Money Line Journal has entered the Las Vegas Hilton Supercontest. That is the contest where for $1500, you pick 5 NFL and only 5 NFL games a week, over the course of the regular season. The payout is something like the WSOP, with the top prize being well into the six figures.

RyanHojo (the name of his entry) has postulated that the NFL betting market is efficient. Meaning that people more or less have the lines figured out right, and if a line doesnt move that it is a 50-50 out come as to which side covers their side of the bet.

If the line moves after you bet, your odds go up in something rsembling a normal curve pattern, with some allowances for odds of a push.

Therefore RyanHojo has made his entire wager, and thus $1500 trying to catch line moves, or bet based on arbitrages between the LV Hilton line and the pinnacle line (which is one of the biggest online bookies).

This concept would be fun a a science experiment; Lighting things on fire and blowing the same things up also made for fun science experiments, and that is how I will spend the rest of this post.

Simply put, the theory kind of sucks.

First lets take a look at his initial post for this year, the chart that is attached shows the arbitrages he is trying to take advantage of.

Now, lets take a look at after week 5 and where he stands.

That chart is instructive. In it, he shows his expected value for each week based over 5 picks, and tabulates everyone's entry that way.

Now let's see where his theory might be plausible.

For starters, one of the few players ahead of him in RyanHojo's calculations of who should be top table each week is Steve Fezzik, the TWO TIME defending champion of the contest (which by the way is an absurd achievement on so many levels.)

So in that sense, Fezzik is probably running a strategy at least partially similar to RyanHojo.

Now where does this strategy break down?

As you can see in the 2nd post, the top expected value bettors in RyanHojo's eyes shouldn't even expect to win 55% of the picks (Ryan himself is at 54% per pick).

So let's just say that the best gamblers do use a system similar to Hojo, and the market is efficient. Lets say they can pick at 55% winners. Over 85 games that means someone should be able to score 46.75 points.

The standard deviation on such a result is easily calculated. SQRT (85*.55*.45).

The standard deviation is about 4.6 wins over a season.

For a 50-50 better the standard deviation is about the same. So why does this matter?

Let's say there was no skill at all in picking NFL winners. Lets take a look at the top score form last year.

Steve Fezzik scored 54.5 points. If the result was based on luck, then his result would be almost 3 standard deviations from the norm (he finished 12 games over .500, which would be about a 1/250 occurence if it was pure luck)

Now lets say he he could pick at 55% per win. He would be lucky by an order of only 1.8 standard devaiations (closer to a 1/35 occurrence)

Was steve 1/650 lucky or 1/35 lucky last year? Or was he less lucky than that even, picking games that were truly closer to 60% than 55%

Well the answer can be determined in part from looking at his results from last year... When he won again. His win in 2008 was even more impressive, going 56.5 out of 85 games.

170 games is a better sample size to deal with.

Over two years fezzik was 111 out of 170, better than 26 games over 500.

THe standard deviation of someone's results over 170 games is 6.5 games. So if fezzik was picking blindly he'd be an outlier on the order of 4 standard deviations away, or a 1/30,000 chance over 2008 and 2009.

Even with his relatively craptacular 2010, it's clear he's on a run that is either extremely lucky (unlikely) or he has a system.

Now the question is could that system be the same one RyanHojo professes to use?

Let's say the efficient betting market hypothesis clearly yielded 55% winners.

Over 170 games Fezzik should be at 93.5 wins. He won 111 games as we know, which is still 2.7 standard deviations away. The years he won it there weren't even 1000 entries. Some of them are clearly amateurs, and some are just big fish. The question then is, how many sharps are there, and what are the odds that a 2 year run for one of these sharps would be lucky on a 250-1 scale?

That depends on if you think there are even 100 people in the contest that can pick at 55%. Through 5 weeks according to RyanHojo, none can pick that high, and very rapidly the best pickers by his system are only at 53% or so cumulatively (across the top 50 or so)

WHat does that tell me?

That much like the stock market, the NFL betting market is not 100% efficient.

That makes the allegedly egregious pick of Chicago last week defensible. It also reminds me of one of my favorite blogposts from one of my favorite bloggers ever

After reading that, you may think less of efficient markets as well.