Statistics are often used to help us make important decisions. For example, many industries use Six Sigma to make decisions that improve the quality of their processes. But can we use statistics to show that sometimes what we think are informed decisions are really no different than a coin flip? In this article I'll attempt to do just that.
It's no secret that betting on NFL games is popular. Those casinos in Vegas didn't build themselves! But are there people that can correctly pick NFL games consistently? If there are, they certainly would enter the SuperContest.
The SuperContest is a competition run by the Las Vegas Hilton. Contestants pay a $1,500 entry fee prior to the start of the NFL regular season and then pick 5 games each week against the point spread. The SuperContest pays out the top 20 contestants. Because of the large entry fee, only bettors that truly know their stuff enter. These aren't your average Joes! And because they only have to pick 5 games each week, they can select the games they feel the most confident about.
The best thing about the SuperContest is that all of the results are online! I obtained the number of correct picks for each of the 508 contestants that have made selections every week. I did this after 9 weeks of the NFL season, so each contestant has made 45 picks. Now all I need is 508 different people to call a coin flip 45 times.
Hmmmmm, that could be hard to do. Luckily, I can use Minitab Statistical Software to simulate the data for me! I simply go to Calc > Random Data > Binomial.
I generated 508 rows of data so there is one row for each person. There are 45 trials, because we want to simulate 45 coin flips. And the event probability is 0.5, because the probability of correctly calling a coin flip is 50%.
Now I have a column of data that represents the number of coin flips each of 508 different people would be able to correctly predict out of 45 attempts. I also have a column of data for the number of times each contestant in the SuperContest picked the correct team in 45 NFL games. I'll use a histogram to compare the two.
NOTE: When picking NFL spreads, sometimes the game ends in a push, which pretty much means the bet is a "tie." Obviously there are no ties when you call a coin flip. But I needed to count the ties somehow so every contestant had the same number of trials (45). To do this I divided the number of ties in half and added it to the contestants win total. Having more than 2 or 3 ties was rare, so it didn't affect the numbers much. Here are the results.
On second thought, why don't you compare the histograms first. Which one is the random data I created with Minitab, and which one is the data from the Super Contest? Take your time...........I'll wait.
Have you figured it out yet?
Pretty tough, isn't it?
Ok, that's probably enough. The first histogram is the random data, and the second histogram is from the SuperContest. But look at how similar they are! We can use Minitab's Descriptive Statistics to break down the numbers even further.
Again, the two groups are very similar. If you call a coin flip 45 times, on average you would expect to get it right 22.5 times. The mean of both groups is just about 22.5! And look at the maximum. The current leader of the Super Contest has correctly picked 32 NFL games. So you would think that he knows what he's doing! But the random data also had a "person" correctly call 32 coin flips. The real explanation is the sample size. With 508 people, somebody is going to get lucky and get a lot of calls correct. But when we look at all the data, we see that just as many people are getting unlucky, which is why the mean is still close to 22.5.
And now I'll drive the point home with an embarrassing personal story. As a way to get my fiancé, Fay, more interested in football, I've created a competition. Each week we pick the spreads from every NFL game and keep track of who does better. I don't consider myself an expert, but I watch a lot of football and know quite a bit about it. Fay picks teams based on location and colors. And if she can't decide after that, she asks what the spread is. That's right, most of the time she selects teams without even knowing the spread! And how have we done so far this year?
Kevin: 45 games correctly picked out of 109. I pick correctly 41.3% of the time.
In other words, if Fay had placed $110 on every game she picked this season, she'd be up $1,030. If I had placed $110 on every game I picked this season, I'd be down $2,540.
I was about to go cry myself to sleep, but then I decided to compare her percentage to the SuperContest. Out of the 508 contestants, she has a higher percentage than 361 of them! Fay is beating 71% of the people in the SuperContest! And she's picked 64 more games! So I really shouldn't feel ashamed. After all, she doesn't know more about football than me, she's just getting luckier calling a coin flip..........right?