I have always been fascinated by the intersection of math and sports. Over the past several years, I have developed and refined a set of mathematical tools that I use to help me better understand the worlds of college football and basketball. With the 2025 college football looming, it is time to open up the analytical toolbox and see what we can learn.
Before we dive into the upcoming season for the Michigan
State Spartans and beyond, it will be helpful to review the results of the past
season.
General Lessons from the Past
During the summer college football fans and sports analysts
have limited information. However, there is no shortage of various predictions about
rankings, win totals, conference champions, and playoff participants. But how
accurate are these predictions, historically?
After studying this data for several years, the simple
answer is that on average, the experts do a good job, but there is also a
significant amount of variance. More quantitatively, I have developed these two
rules of thumb:
- The
preseason rankings are accurate to plus or minus 25 positions (one
standard deviation)
- The
preseason win total predictions (i.e. over/under lines) are accurate to
around 2.0 to 2.5 games, depending on the year.
This information is helpful when looking at the preseason
rankings and win predictions totals in July or August. Both data sets resemble
a bell curve (i.e. a Normal or Gaussian distribution). The math related to this
distribution tells us that approximately one-third of the teams will finish the
season more than 25 positions above (or below) the preseason ranking and more
than two games above (or below) of the preseason prediction.
But math also allows us to learn a bit more about the
contributing factors that result in this deviation. The difference in ranking
position is only semi-quantitative. But it is possible to dig deeper into the
deviation in win totals.
I have found that the difference in the number of wins
between the final tally and the preseason expected win total is due to three
factors: changes in the strength of each team's schedule, luck, and the
expert's ability to accurately predict the strength of each team.
These three factors do not contribute equally to the final
difference between prediction and reality. Here is another rule of thumb:
- Changes
in schedule difficulty contribute plus-or-minus half of a game (one
standard deviation)
- Luck
(good or bad) contributes about plus-or-minus one game.
- Differences
in the perceived strength of a team in the preseason contributes plus-or-minus
two games.
Some teams are luckier than others and some teams wind up playing an easier or hard schedule than expected. But the most significant impact on the accuracy of preseason predictions is simply that the experts do not have a firm grasp on how good or bad each team will be.
2024 Preseason Polls in Retrospect
Based on this context, Table 1 below shows the teams listed in the last year’s preseason top 25 (and beyond), based on the consensus of the preseason publications, my final power ranking, preseason expected win totals (based on my calculations last summer), and final record.
The table also includes the results of my calculation of the
impact of changes in ability, schedule, and luck on each team's final regular
season win total. These cells are color-coded depending on whether the impact
was positive (green) or negative (red).
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The table is sorted based on the preseason rankings, similar
to the information available to college football fans in this off season.
As an example, Michigan State started the 2024 season with a
consensus ranking of No. 66 My detailed mathematical analysis of the full
college football season and the Spartans' schedule resulted in a regular season
expected win total of 4.95.
Michigan State finished the season 5-7 which was essentially
exactly what was predicted. The Spartans finished ranked No. 70 in my final
power rankings, so the prognosticators correctly evaluated their true strength
in the preseason last year.
The right side of Table 1 reveals provides a little more
context. According to my calculations, Michigan State had a schedule in 2024
that was about a half game harder than expected (-0.46 to be exact). However,
the Spartans had a little over a half game of luck (+0.58). These two effects
cancelled out and resulted in the final win total matching the preseason
prediction.
Overachievers and underachievers
The data in Table 1 can be used to understand the results
from the 2024 season in more detail.
Eight of the top 10 preseason teams also ended the season in
the top 10, which is a bit better than usual. In 2023, only half of the
preseason top 10 ended up there. In 2024, only preseason No. 8 Michigan
(finished No. 25) and No. 10 Missouri (No. 33) underachieved significantly.
The rest of the 2024 preseason top 25 did not fare as well. Only
seven of those 15 teams ended the season in my top 25. A handful of those teams
finished the season with losing records: No. 11 Florida State (2-10), No. 12
Oklahoma (6-7), No. 17 Utah (5-7), No. 19 Oklahoma State (3-9), No. 23 Kansas
(5-7), and No. 24 Arizona (4-8).
A few teams in the lower end of the preseason top 25 did
overachieve. Notably, No. 15 Tennessee (10-3) made the playoffs, No. 21 USC (7-6)
ended the season ranked No. 12 in my power rankings, and No. 25 Iowa (8-5)
ended the season ranked No. 14.
Beyond the preseason Top 25, several teams had surprisingly
good seasons. Most notable was preseason No. 72 Indiana (11-2) who made the
playoffs and finished ranked No. 7 in my power rankings. No. 71 BYU (11-2, and
a final rank of No. 22), No. 77 Arizona State (11-3, No. 16), and No. 103 Army
(12-2, No. 30) also overachieved by four games or more.
Other notable overachievers in 2024 include preseason No. 31
Iowa State (11-3, No. 15), No. 35 South Carolina (9-4, No. 13), No. 50 Colorado
(9-4, No. 20), No. 52 Minnesota (8-5, No. 11).
Digging Deeper into the Data
Looking at records and raw rankings both before and after
the season will reveal the overachievers and underachievers. But the data on
the right side of Table 1 explains why the teams faired the way that they did.
Generally, the expected number of wins for even the top five
teams in the preseason are usually just above 10 wins out of 12 games. A team
needs a bit of positive luck to finish the regular season with 11 or 12 wins.
In any given year, the teams which finish the season in the
top 10 are both lucky and good. In 2024, Table 1 generally bears this out as
well, with a few interesting exceptions.
The two finalists in the inaugural 12-team college football
playoff, Ohio State and Notre Dame, both finished the regular season in the with
overall negative luck.
Neither team would have made the playoffs in previous years.
But both the on-field results and my post-season power rankings suggest that
the Buckeye and the Fighting Irish were the best two teams in the country and
succeeded despite a bit of bad luck in the regular season.
A closer look at the schedule and luck columns provides
additional information about a few teams in 2024. For example, preseason No. 8 Michigan
was almost a full two games worse than expected in ability. However, the Wolverines
also had a much tougher schedule than expected by over one game which
contributed to their underwhelming season.
A few other notable teams had close to or over a one full
game advantage in combination of schedule and luck. Missouri, Clemson,
Tennessee, Miami, and SMU all fall into this category. Farther down the rankings,
nine-win Duke also falls into this category.
Interestingly, none of those teams graded out more than half
a game better than expected in ability. Those five teams overachieved by winning
at least 10 games, but a large fraction of this improvement seems to have been
due to schedule and luck.
Another group of teams massively overachieved in the ability
category, but all had significant advantages in the schedule and luck categories
as well. Those teams include Iowa State, South Carolina, Colorado, Illinois,
BYU, Indiana, and Arizona State.
On the other side of the coin, there are a handful of teams
which ability wise appear to have been ranked properly in the preseason, but which
suffered due to a significant amount of negative impact from schedule and luck.
Mississippi, USC, Louisville, Kansas, Iowa, Virginia Tech, Nebraska, Minnesota, and Central Florida all fall into this category. All nine of those teams likely should have had better records than the history books will show.
Looking Ahead to 2025
With this information in mind, it may be possible to make
some initial predictions as to which teams might be overrated or underrated in
2025. Teams which benefited or suffered due to a significant amount of luck in
2024 may be more likely to regress to the mean in 2025.
When I performed a similar analysis last summer, I correctly
predicted better-than-expected seasons for Oregon, Notre Dame, and Penn State. I
also predicted worse than expected results from LSU, Utah, Clemson, Oklahoma State,
and North Carolina State.
In the 2025 preseason poll, my analysis suggests that there
are reasons to be skeptical about Georgia, Clemson, Oregon, LSU, Miami, and
Florida. All six of these teams generally appear in or close to the top 10 and
all benefited from a significant schedule advantage and/or luck last year.
Farther down the top 25 rankings, Oklahoma, Texas A&M,
SMU, and Texas Tech also sound similar alarm bells when I scrutinize the 2024
data.
As for teams to look out for which may exceed expectations, in
the Big Ten USC, Minnesota, Iowa, and Nebraska all fit the profile of teams
with over a game of bad luck in 2024. If that luck turns around in 2025, any of
those teams could play the role that the Indiana Hoosiers did last year.
In the SEC, Auburn and Mississippi are teams to watch out for.
In the ACC, Virginia Tech and Louisville are teams that could make a move. In
the Big 12, Central Florida is the team that I am most curious about while
Utah, Kansas, and Oklahoma State may bounce back to respectability in 2025 and underachieving badly in 2024.
With this introduction in place, it is time to turn our
focus to the Big Ten and specifically onto Michigan State. Next time we will
take a close look at the Spartans' schedule. Stay tuned.
Tweets
It is time to kickoff Dr. Green and White's (@PaulFanson)
annual math-driven college football preview series. In Part One, we take a look
back at the 2024 season to understand what the experts got right, what they got
wrong, and most importantly, why.
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