THE HOT TEAM THEORY IN FOOTBALL
Pigskinrevolution.com
In our visits with NFL teams, we were on multiple occasions told by coaches
that their playcalling decisions were influenced by how their team was
performing on that particular day. If the offense wasn't moving the ball
they would be less likely to go for a 1st down facing 4th and short than
if they were performing well. The implication is that past performance
on a short timescale -- less than a game -- was a good predictor of future
performance -- the remainder of that game.
We can put this theory to the test. One can easily find the scoring by
quarter for each team for each game of a regular season. We created a
dataset of pairs on numbers (points scored in the first quarter, points
scored in the last three quarters) for all of the 2005 regular seaon games.
For example, in week ten Baltimore visited Jacksonville. The score at the
end of the 1st quarter was 3-0 in favor of Baltimore. The final score was
30-3 in favor of Jacksonville. So this game led to two datapairs in our
study (3,0) and (0,30). The (3,0) pair is from Baltimore who scored 3
points in the first quarter and were shut out the rest of the game. (0,30)
corresponds to Jacksonville's scoring: no points in the first quarter
but 30 points in the last three quarters. 256 regular season games gave
512 datapairs.
We performed a Pearson Correlation comparison to see if there was any
relationship between the points a team scores in the first quarter and
the points they then score the remainder of the game. If there were an
exact positive correlation (that is, the more points you score in the
first quarter means the more points you will score during the remainder
of the game) then the result of the Pearson Correlation would be a number
very close to 1. If on the other hand, there is no relation between the
points a team scores in the first quarter and how many they score in the
remainder of the game, the correlation will be close to zero. (There is
another extreme, that scoring a lot of points in the first quarter means
the team won't score much during the rest of the game. In that case the
correlation result would be negative, as low as -1 in the extreme.)
Often the result is intermediate and the correlation can be categorized
as weak, moderate, or strong.
The result for the 2005 season was a Pearson Correlation of 0.047, very
close to zero. To test the significance of this, we did a quick study
generating a series of 512 pairs of random numbers and seeing how often
the Pearson Correlation was at least as far from zero as 0.047. In 100 such
trials, the correlation was at least 0.047 from zero 32 times. Thus we
conclude that the correlation between points scored in the first quarter
to points scored the remainder of the game for the 2005 regular season,
0.047, is statistically consistent with 0 and there is no evidence of
a relationship between these two quantities. It follows that the claim
that a coach can deduce during a game how his team will perform based
upon the team's early performance in that particular game is in serious
doubt.
One more study from the 2005 season is worth noting for its contrasting
result. We also compared the number of points scored in the first quarter to the final score (i.e.
to the points scored in all four quarters). Here the Pearson Correlation
was 0.49. This is considered a weak to moderate correlation and a positive
result. Not surprisingly, if you give a team a head start on points (i.e.
lots of points scored in the 1st quarter) they are likely to end the game
with a significant number of points, just by scoring an average number of
points in the last three quarters.
Some may have noticed a parallel here with a study performed in 1985 by
psychologists Gilovich, Vallone, and Tversky, published in the journal
COGNITIVE PSYCHOLOGY. Looking at the shooting of NBA players, they concluded
that shooting streaks were consistent with randomness and the idea that the
"hot" player should take the shot was a myth.
So what does this have to do with ZEUS? Although ZEUS does account for a
teams' seasonal performance, it only looks at the score DIFFERENCE in
determining the optimal playcall. Whether a team leads 7-0 or 49-42 is
not a factor in the proper choice of plays.