The past two years, a group of friends and I have tried predicting college and NFL games each week. Here’s what our picks looked like for Week 1 of the college season. The bolded team was the winner of that game.
NFL Week 1:
I compiled the week by week results into tables:
The “Combined” pick is the team the majority of us picked. For instance, the first three combined picks for the college picks above are Oregon State, Michigan, Ohio State. In the college picks, we had four people, so when two people picked one team, and two people picked the other, the combined pick was undecided. In those cases, I gave 0.5 to the combined win column and 0.5 to the combined loss column. The NFL picks had five people, so there wasn’t a need to do that.
For college, the combined pick would have finished 4th out of 5, 6.5 games behind the leader. However, for the NFL, it beat the top individual by 4 games. I think this is because there was a 5th person to swing the group decision when there were two people on each side. In contrast, the college pick used a 50/50 split. The group was more accurate when more people contributed. I would expect a slight increase in accuracy with a 6th person because in a 3 on one side, 2 on the other situation, the 6th person could tie it up, indicating the group wasn’t so sure about the game. Instead of a decisive yes, maybe the group would be accurate in going 50/50 on it.
In 2015, the combined pick finished 1 game out of first in the college picks and 3 behind in the NFL picks, good for second place in both. The college and NFL picks that year both had five participants. 2015 College with five people was 72.2% accurate. 2016 College with four people was 64.8% accurate. On the other hand, the NFL picks had five people both years and the accuracy was 62.2% and 64.4% respectively. With this small sample size, there was a significant difference from five to four people. Staying at five people resulted in close to the same correctness.
The other pick that bears explaining is “538” for the NFL. These were the picks from FiveThirtyEight. In 2015, it beat our best individual by 8 games. In 2016, it tied the combined pick at 64.4% accuracy. 538 was better than any of us individually, but together, we matched its accuracy.
Now for some graphs. This gives us a good look at the race throughout the season.
Daniel started out strong. In the middle, it was a fight between Daniel and Josh, and then it came down to Josh and I in the last couple of weeks.
I got off to a big lead but by Week 9, Daniel had caught me and he led the rest of the way.
The college average for everybody for the whole season was 66%. The toughest week was the bowl season.
The NFL season average was 60%, meaning NFL games were somewhat harder to predict correctly.
I calculated our agreement on games with a weighted average of our picks. That is for college since we had four people. The range is 50%, which would be 2/4 agreeing, to 100%, which is 4/4 agreeing. The NFL agreement is The range is 60%, which would be 3/5 agreeing, to 100%, which is 5/5 agreeing.
When 4/4 people pick a team, that’s a pretty confident pick. Are we more likely to be right on those than when 3/4 pick a team? In College 2015, this is what happened:
College 2016 featured a steeper drop off:
NFL 2015:
NFL 2016:
There are two interesting things about NFL 2016. One, we hardly did better with all five agreeing than we did with a complete split. I don’t know why that is. Two, the total percent correct as calculated from the big tables at the start is lower than any of the subgroups. How can this be?
When we look at that graph, we think the total should be between 63% and 67%. This is an equation to represent how we intuitively think of it in three major parts: 5/5 agree, 4/5 agree, and 3/5 agree. Each of those has two minor parts: the majority wins, and the majority loses.
Each of the three main terms counts equally because is in each one. The second minor terms are eliminated since .
There are three possibilities for each game: 5/5, 4/5, or 3/5 people agree. Each one has a different probability of occurring. 5/5 agree: 43.5%, 4/5 agree 27.0%, 3/5 agree: 29.6%. Then, there is the probability that the majority pick is actually right. For 5/5 this is 66% as seen in the first column of the graph. What we don’t think of is that while the 5/5 situation gives everyone a win, the 4/5 and 3/5 situations do not. They only have 80% and 60% of the effect. If the majority is right, then 5/5, 4/5, or 3/5 people get a win. On the other hand, if the majority pick is wrong, then (1-5/5) = 0/5, (1-4/5) = 1/5, or (1-3/5) = 2/5 people get a win.
This is very close to the 60.07% value for total percent right.
Doing the same thing for the college picks gives 65.68% compared to the actual value of 65.59%.