The effect of music is so very much more powerful and penetrating than is that of the other arts, for these others speak only of the shadow, but music of the essence.
- Arthur Schopenhauer
In 1906 Sir Francis Galton came across a contest at a fair in which people were guessing the weight of an ox that had been chopped up to eat. The person who produced the closest guess would win the meat and presumably not go hungry for a long time. Galton believed that, for the most part, people were stupid and he could prove this by showing how far off their guesses were. Somewhat ironically, while nobody guessed the weight, Galton found that the average of all 800 guesses was only a few pounds off the 1,198-pound weight of the ox.
We now call what Galton had found the Wisdom of the Crowd, and while it only applies to certain topics, we are better off taking opinions from as many people as possible, rather than just asking one person, even if that one person is an expert. Regis Philbin said when somebody on Who Wants to Be a Millionaire? asked the audience, it was extremely rare that the majority would give the wrong answer. So even while most people in the audience will give the correct answer, we would much rather have the option to ask the whole audience than to ask one random person in the audience.
Predicting the NFL
With this in mind, let’s look at the accuracy of betting lines and their ability of correctly predict the outcome of NFL games. Point spreads exist because they make betting on single games tougher. However, if we are predicting the winner straight up, we can use the point spread as a helpful tool (we’ll get to picking against the spread in a bit).
Remember that the guy setting the line is not making a personal prediction on the game. He wants to choose a number that will evenly divide bettors (which is how he earns his money). He can allow the market to guide him and readjust the line if the bets become too one-sided. The crowd will ultimately dictate the line.
From 2009-2013, the favorite was victorious in 857 of 1269 picked games, which is a 67.5% success rate (even games were not included). Things fluctuated over the years with the success ranging from a low of 64.4% correct in 2012 to a high of 71.3% the following year.
Compare this to the best picker on ESPN’s Pigskin Pick ‘Em Game in 2013, who predicted the winner in 75% of the games. In other words, he picked just ten more games of the 256 correctly than the spread did. The technique of the winning picker is unknown, but going with the odds on every game means putting in virtually no work. Copy and pasting selections would have tied for the 47th overall rank on ESPN, which is still in the 99.9th percentile.
On the other side of the spectrum, in 2012 the favorite picked 163 games, or 64%, accurately. The top picker on ESPN correctly choose the winner in 188 or 73% of games. But even in a down-year, the line still beat over 500,000 guessers.
Using a crowd to pick a game can change depending on which crowd you go with. Ask a bunch of fifth graders and you will not get the same results as bettors who are putting money on a game. The line differed from the majority’s pick on ESPN in 60 games in 2012 and 2013. The line favorite in those games won 37 to ESPN’s 23. This is too small of a sample to draw any conclusions from, but one possible reason being that ESPN’s users are more likely to make risky picks without money on the line.
Degree of Certainty
While every game has two teams, not all are equally difficult to predict. Favorites in games with a point spread of less than three won just 52% of the time, while teams favored by 11 or 11.5 points won 90% of the time. As the spread increases, we find that the chance that team will win the game steadily increases as well.
Picking Against the Spread
Picking a winner is one thing, but Galton’s hunch about people being dumb (we’re talking about beer drinking football fans here, not rocket scientists) must fall apart when they come up against the spread, right? Not exactly.
Picking against the spread is tougher: The guy who won Pigskin Pick ‘Em against the spread last year picked 159 games right compared to the straight winner who got 191. Still the masses guide the betting line, which will shift over the week. ESPN sets their lines on Tuesday, but you don’t have to make your pick until game time, which allows a few more days for the crowd to work their magic. And unlike ESPN, virtually all betting sites do adjust their lines as the week goes on.
If the line increases from Tuesday to Sunday (I usually take the average line from multiple sources, thus increasing the crowd size), even if it’s not by much, it would be wise to bet the team will cover. On the other hand, if an injury leads to a decrease in the crowd’s confidence and a shrinking spread, we would be wise to go with the underdog. It is not complicated (nor is taking advantage of “soft lines” new strategy), but it has been right 52 out of 90 times this season, which is better than 94% of about 100,000 entries on ESPN. If you don’t think a day or two will make much difference, note that it has only worked 44 times on Yahoo! where lines are set on Thursday.
How do the Experts Stack Up?
The remarkable thing about the Wisdom of the Crowd is not that the crowd is better than any given analyst, but that the crowd even comes close. When we step back and consider what exactly the crowd is—in Pigskin Pick ‘Em it is anyone with internet access, in Vegas lines it’s anyone with a few bucks—we would probably think most employees of sports networks would be much better than such a motley crew.
PunditTracker.com looked at predictions made by 13 analysts from ESPN and Sports Illustrated from 2009 to 2012, and found that only two, Jim Trotter and Kevin Seifert, were better than the Vegas odds. In a separate 2012 study, they found that on average 23 analysts from ESPN, CBS, and Yahoo (a mini-crowd of analysts) picked the right winner in two more games (165 to 163) than the odds. Recently they looked at 24 analysts from ESPN, CBS, and Yahoo and found that none of them have picked better than Vegas from 2012 through the first five weeks of the 2014 season. As a group they’re 4% worse on average.
As we saw earlier though, the top finishers in Pigskin Pick ‘Em are often as good or better than the experts, so clearly somebody has figured out how to outsmart the masses, right? This really comes down to how many games you are picking. Somebody will win Pigskin Pick ‘Em with a high total, but unless they can perform at such a high level for multiple years, it’s possible they were just lucky. I could accurately pick every game over the whole season with a coin-flips, but that should not make you want to ask me for advice on who to pick (more likely you’d beat me up and steal my lucky coin). Lots of people have perfect weeks, but most cannot maintain that level for more than one week, let alone 17.
Remember when I said that ESPN and Vegas differed on who would win 60 games over the past two years and Vegas has been right in 62% of those? This in no way guarantees that Vegas will be more accurate every season. In fact, ESPN got 13 of the 22 games right in 2012, but Vegas got 28 of 38 right in 2013. So in a dispute who are you better of going with? Obviously we don’t know who is more accurate this season until it is too late.
So Far in 2014
Through the first six weeks of the 2014 NFL season, the line has picked the right team to win in 60 of 90 games, which is right about where it should be based on the last few seasons. The majority has correctly chosen 61 games in Pigskin Pick ‘Em.
The contest has hundreds of thousands of entries coming from people of all walks of life, with all sorts of levels of knowledge about any given football game. Given the choice between them and someone who covers football for a living, you may be tempted to listen to the later. What we find in the numbers though is that the crowds (on ESPN) are actually as good or better than all 13 of ESPN’s NFL experts, all seven of CBS‘s, both of Yahoo!’s, and all four of Fox Sports’ (and their projection software).
The crowd may not help you win your office pool, but surprisingly its track record has shown that if you put aside your ego and stick with the majority every time, you will finish ahead of almost everyone in the crowd individually.
Author Note: I don’t gamble or claim to know anything about it. The preceding is not intended to help you win money, and I’m not sure it even can.
Like most single, American men in their mid-20s I spend my Friday nights watching Slavoj Žižek videos. These are only enhanced more by watching them with YouTube’s caption feature, which automatically translates language into words.
The accuracy of the captions is not very good, but when combined with Žižek’s near-impossible Slovenian accent, they are beauty. Here he is talking about movies:
Then that hurt.
Shocked God a chink Egypt pretentions Craig.
Dreams a document that he owned,
A making coffee.
Let ‘em around a movie,
How close we rebuked rich right.
You let him bat about, ok.
Good visual problems making coffee,
Or some freshman she said amish, I think.
Bitch, I like got the Italian because I’m totally theoretically crap.
Gotta go I think it’s much better than the movie.
A few days ago, we found that that the relationship between wins and salary among MLB teams in 2014 was not that strong. Today we’re going to see if that was a fluke or the norm.
Graphs get bigger with one click!
Because the average team salary has increased by about $40 million over the past decade (and $80 million over the last two), we can’t compare wins to money spent straight up. To address this I have created Salary+, making the league-average salary for each season is 100. If you’re familiar with stats like OPS+ and ERA- you probably get it, skip the next paragraph. If not:
Like salary, most stats change over time. The average hitter in 2000 had a .345 OBP, but the average hitter in 1968 had a .299 OBP. In order to better compare players from those years, we take the player’s OBP, divide it by the league average for that season, and multiply it by 100. So if your OBP+ is 100 you were an average hitter for that year. If you’re above 100 you were above average, if you are below 100, below average. That goes for any stat you see a + after. Conversely we have ERA- because the lower the better, so an ERA- of 100 is average, but 60 is awesome.
Salary+ keeps things proportional, so the R-squared value is the same for each season whether you use the actual dollar value or the Salary+ value. In 2014, the R-squared for salary compared to wins was 0.087, which is not all that strong of a relationship. If we expand our pool back to 1988 (that’s all USA Today had in its database), that gives us 724 team seasons and an R-squared of 0.163. So this season was below average, but clearly there is more to a winning team than spending a lot of money. I left out the 1994 and 1995 as they were shortened due to the lockout.
I wanted to see how much the relationship fluctuated from season-to-season, so I found the R-squared of each season and plotted them out. In the early 1990s there was virtually no relationship, but it rose sharply toward the end of the decade.
Part of that I would credit to the increasing range of salaries, which doubled from 1992, when the R-squared was at its lowest, to 1999, when it was at its peak. This would seem to lend credence to the thinking that the Yankees (who won the AL from 1998- 2001) bought their way to the top. Since 1988 the Yanks’ R-squared for salary and wins has been stronger than the League-average at .295.
Over the past decade though, the relationship between salary and wins has again been on the decline. Teams with smaller budgets have been able to compete by minimizing their cost per win. Oakland has managed to average 88 wins on an average Salary+ of 66 since hiring Billy Beane. Still, in 2014, five playoff teams in 2014 came from the League’s top third, three from the middle, and two from the bottom. Spending money helps, but it does not guarantee anything: Four of the five highest salaries did not make the playoffs in 2014.
While we’re at it, here are a few more graphs using Salary+. Everyone knows the Yankees like to spend a lot of money, but I never realized it was this much.
And in the interest of symmetry, here are the lowest spenders.