Why We Use Statistics, NFL Example Edition
We are now mostly through Week 10 of the NFL season, which means most teams have played nine games. Unless Kansas City manages to beat Pittsburgh by more than 36 points on Monday*—not, to be gracious about it, the Way to Bet—there will be four teams in the NFL that have give up between 10 and 20 points more than the have scored.
You would naturally assume that those teams would have losing records, either 4-5 or even, the closer you get to –20, 3-6. But certainly it depends on the distribution of your wins and losses. But, just for fun, let’s look at the four teams:
Team |
Wins |
Losses |
Point Differential |
Bengals |
4 |
5 |
-11 |
Dolphins |
4 |
5 |
-13 |
Colts |
6 |
3 |
-15 |
Cowboys |
4 |
5 |
-16 |
This, not to put too fine a point on it, is why we apply statistical analysis. A couple of blowouts (both New Jersey teams lost today by three touchdowns, though the Jets—Jersey/B, as Gregg Easterbrook’s sole viable contribution to popular culture named them—gave up extra points as well) may skew the record—if every other game is close. If I tell 100 people who know the rules of football but not the way the season has gone, “The Colts have given up 15 more points than they have scored through nine games,” chances are that 80-90 of them would guess the team was 4-5 or even 3-6. Some small number might guess 5-4, and an even smaller one will guess 6-3.
But then add information. For instance I say, “They lost their first game of the season by 20 points.” At this point, those will at least moderate math skills realize that the Colts are +5 over 8 games; 5-3 is not out of the question, though 4-4 remains the Way to Bet—by a much smaller margin.
Now I add, “Coming into this week, they had only won one game by more than three points.” Suddenly, that +5 looks strong; there is a shift of some set of the 4-5 people (who know the first week was a loss) to 5-4 (5-3 plus that loss).
The more information you get—“they were blown out by Jersey/B as well”—the more likely you are to guess that they might be 6-3. But the odds still don’t favor that. Indeed, the Dolphins have been blown out twice (-20, –34), but they have also won two blowouts (+22, +21). (The Bengals are 1-1 in blowouts; the Cowboys, like the Colts, are 1-2.)
So if we’re just looking at the raw data and the predictions of the people, we would see the Informed Voters hanging around 5-4 or even 6-3, the Paying Attention group splitting between 4-5 and 5-4, and some Randomly-Asked-Questions people guessing 3-6 or 4-5 (with a few clever enough to say 5-4 just because they know someone thought the question was interesting).
Any parallels to those complaining that Nate Silver was estimating percentages to four significant digits are left as an exercise to the reader.
*Or there is a blowout of epic proportion tonight between two teams that are both at least +100 through eight games.