A few weeks ago, I dropped my annual math-based / statistical analysis of the upcoming 2018 college football season. In my analysis, I look at the numbers a couple of different ways including a probability-based win distribution and a game-by-game prediction based on a "reasonable" number of probable upsets. But, there has always been one calculation that has alluded me: the estimation of the probability that a given team will win their division and/or conference (including tie-breakers) and/or make the playoffs.
That is, until now.
For several years I have been able to calculate a "win distribution matrix" that gives the odds of any team winning anywhere from 0 to 12 regular season games. The challenge was that the values for each team were independent from each other. For example, I could tell you the odds that MSU would go 8-1 and that Ohio State would go 8-1, but it is much tougher to calculate in a systematic way the odds that MSU would beat OSU, MSU would lose another less critical game, and no other team would also finish 8-1 to cause a natsy tie-breaker. There are a total of 63 regular season Big Ten games, which means 9.2 x 10^18 combinations (2^63) of outcomes. Considering that the age of the Universe is estimated at about 4 x 10^17 seconds, a brute force calculation seemed... difficult. But, long story short, I figured out a way to simplify the calculation (using 120 MB of excel files).
So, I went back through my data from the preseason (based on power rankings derived from a consensus of preseason rankings) and calculated the odds that each team will win their respective division. Then, based on a projected point spread on a neutral field, I estimated the odds that each team would then win their conference title game.
As for the playoffs, there is actually a fairly straightforward way to estimate these odds, with a few key assumptions. If you look back at the teams that did or did not make the play-offs, there are a few extremely straight-forward trends:
Now, the major caveat here in the preseason is that the numbers that I derived assume that the preseason rankings are a correct indicator of how good teams actually are, which is just not true. Because of this, the numbers do have to be taken with a grain of salt, and there are not a lot of surprises (spoiler alert: Clemson and Alabama have great odds relative to the other 128 teams). But, this analysis does give us an unbiased way to looks at all 130 team systematically, which I believe is interesting.
Furthermore, I can also compare the probabilities that I calculate to the summer Vegas odds converted to probabilities. This is quite straightforward as (for example) odds of 3 to 2 works out to 40% (2/(3+2)). But, the raw Vegas probabilities are actually a little bit "juiced" because, essentially Vegas needs to make money. In any list of probabilities, the sum of all possible events should equal 100%. But, if you sum up the Vegas probabilities of all possible events (for example, the odds of each of the seven teams in the Big Ten East winning the division), you usually get ~110%. So, in order to make a fair comparison, I normalized the raw Vegas probabilities to 100%.
Perhaps more importantly in the long run, I can also run some "what if" analyses to see how sensitive a conference outcome might be to individual games. My new spreadsheet tool can also be easily updated throughout the season. So, I will be able to track, essentially in real time, the way these odds will change from week to week, based on updated power rankings and game results.
So, with my new calculation tool in hand, I wanted to take a quick spin back through each conference and see what the numbers say.
Big Ten
For each conference, I will present a data table showing the odds of each team to a) win their division (if there is one) b) win their conference championship game and c) make the playoff. I tabulated both the odds from my calculation and compared them to the odds derived from Vegas, specifically from Bovada. All columns that are labelled as something other than "Vegas" are using my calculation method. The table for the Big Ten is shown here:
That is, until now.
For several years I have been able to calculate a "win distribution matrix" that gives the odds of any team winning anywhere from 0 to 12 regular season games. The challenge was that the values for each team were independent from each other. For example, I could tell you the odds that MSU would go 8-1 and that Ohio State would go 8-1, but it is much tougher to calculate in a systematic way the odds that MSU would beat OSU, MSU would lose another less critical game, and no other team would also finish 8-1 to cause a natsy tie-breaker. There are a total of 63 regular season Big Ten games, which means 9.2 x 10^18 combinations (2^63) of outcomes. Considering that the age of the Universe is estimated at about 4 x 10^17 seconds, a brute force calculation seemed... difficult. But, long story short, I figured out a way to simplify the calculation (using 120 MB of excel files).
So, I went back through my data from the preseason (based on power rankings derived from a consensus of preseason rankings) and calculated the odds that each team will win their respective division. Then, based on a projected point spread on a neutral field, I estimated the odds that each team would then win their conference title game.
As for the playoffs, there is actually a fairly straightforward way to estimate these odds, with a few key assumptions. If you look back at the teams that did or did not make the play-offs, there are a few extremely straight-forward trends:
- No team outside of the Power 5 has made the playoffs.
- No team with more than 1 regular season loss has made the play-offs
- No team who has lost their conference championship has made the play-offs (even if they were undefeated prior)
- If a team finished with only 1 loss but did not win their division, they made the playoffs 2 out of the 3 times that has happened, with the exception of any Big 12 team that simply lost the tie-breaker. Only Ohio State in 2015 was shut out of the play-offs in this situation.
Now, the major caveat here in the preseason is that the numbers that I derived assume that the preseason rankings are a correct indicator of how good teams actually are, which is just not true. Because of this, the numbers do have to be taken with a grain of salt, and there are not a lot of surprises (spoiler alert: Clemson and Alabama have great odds relative to the other 128 teams). But, this analysis does give us an unbiased way to looks at all 130 team systematically, which I believe is interesting.
Furthermore, I can also compare the probabilities that I calculate to the summer Vegas odds converted to probabilities. This is quite straightforward as (for example) odds of 3 to 2 works out to 40% (2/(3+2)). But, the raw Vegas probabilities are actually a little bit "juiced" because, essentially Vegas needs to make money. In any list of probabilities, the sum of all possible events should equal 100%. But, if you sum up the Vegas probabilities of all possible events (for example, the odds of each of the seven teams in the Big Ten East winning the division), you usually get ~110%. So, in order to make a fair comparison, I normalized the raw Vegas probabilities to 100%.
Perhaps more importantly in the long run, I can also run some "what if" analyses to see how sensitive a conference outcome might be to individual games. My new spreadsheet tool can also be easily updated throughout the season. So, I will be able to track, essentially in real time, the way these odds will change from week to week, based on updated power rankings and game results.
So, with my new calculation tool in hand, I wanted to take a quick spin back through each conference and see what the numbers say.
Big Ten
For each conference, I will present a data table showing the odds of each team to a) win their division (if there is one) b) win their conference championship game and c) make the playoff. I tabulated both the odds from my calculation and compared them to the odds derived from Vegas, specifically from Bovada. All columns that are labelled as something other than "Vegas" are using my calculation method. The table for the Big Ten is shown here:
As I mentioned, there are not too many surprises here, but there are a few notable points. Based on their Top 10 preseason rankings, Ohio State and Wisconsin have the best odds to win their divisions. But, as expected, the race in the East is WAY tougher. Interestingly, my math tells a little different story than the adjusted Vegas lines. Specifically, OSU and Michigan both appear to be over-valued by Vegas by 5-6%, while MSU and Penn State's odds appear to be too low by 5-7%. In my preseason analysis, I projected Penn State to win the East, based on their schedule advantage. Similarly, my analysis (as well as common sense) would suggest Michigan should clearly have the worst odds of the "Big 4" of the Big 10 East due to their absolutely brutal schedule. My math took these things into account, while Vegas, oddly, does not seem to.
In the Big Ten West, my math and Vegas both agree within a few percentage points about Wisconsin's very good odds to return to Indy (~64%). However, Vegas seems to feel that the battle for second place will be way more heated than my calculations suggest, with 5 of the remaining teams having a 6-9% chance of making it to Indy. This is also quite surprising, as the preseason magazines are in virtual agreement that Iowa (23%) and Northwestern (11%) are the clear 2nd and 3rd best teams with the rest of the pack hanging well behind.
Part of this discrepancy is due to a clear shortcoming of my calculation method. As I mention above, I am making the assumption that the preseason rankings are a correct assessment of the relative strength of each team. In reality, we know that this is not true. The Vegas odds do seem to consider this factor, as no team has odds longer than Rutgers at 300 to 1. Now, if Rutgers really is only the 86th best team in the country, then their odds of winning the Big Ten East really would be roughly the 1 in 3 million that I calculated. But, if nothing else, this would be a terribly risky line for Vegas to put out, as some sort of miracle run by the Scarlet Knights could bankrupt the whole town. And, there is some possibility that Rutgers is simply better than we think. For now, I do not have a way to bake this uncertainly into my calculations, and as such, my calculated odds plummet for teams that are projected to finish in the bottom part of their division / conference.
That said, Vegas seems strangely optimistic about the chances of Nebraska, Minnesota, and Purdue, while Iowa looks seriously undervalued. In my preseason analysis, I picked Iowa to upset Wisconsin and make a surprise trip to Indy. I still really like that pick, and furthermore, my "what if" calculations quantify my speculation from my preview that the Wisconsin at Iowa game on September 22nd is, by far, the biggest game in the Big Ten West all year. My numbers suggest that a Badger win would bump Wisconsin's odds to win the West up to 83%, while a loss would drop the Badgers odds to 27% and elevate Iowa's odds to over 60%. That is an enormous swing for a single contest. In contrast, the result of any of the six conference games between OSU, MSU, PSU, and UofM only appear to move the odds of the winning or losing team by 15-20 percentage points.
As for the odds to win the Big Ten Championship Game, at first glance it is surprising that my calculation actually gives Wisconsin much better odds than Ohio State (34% to 24%). But, a little more thought reveals the reason why. The reason is that Wisconsin simply has an easier road to get to Indy in the first place and the first step in winning the BTCG is simply to win your Division. It is unclear why Vegas does not seem to consider this, as they have the odds for OSU and Wisconsin as the mirror images of my calculation (23% to 35%). In addition, the over-valuation of Michigan and Nebraska, and the under-valuation of PSU, MSU, and Iowa clearly carry over in the Vegas odds for the BTCG.
Finally, as for the odds to make the College Football Playoffs, both my calculation and Vegas agree that Ohio State has the best odds at around 30-35%. In general, my calculated Playoff odds relative to the BTCG odds have shifted in a few odd ways. MSU, PSU, and OSU's odds actually are better than their odds to win the Big Ten Title. I believe that this speaks to all three team's fairly light non-conference and Big Ten West cross-over schedule, as well as the fact that an 11-1 team that losses a division tie-breaker still has a great chance to reach the playoffs. Conversely, my calculated odds for both Wisconsin and Michigan to make the Playoffs dropped relative to their odds to win the BTCG, likely due to their more difficult schedules (which increases the odds of losing 2 games in the regular season, which history shows is a no-go for the playoffs). As for Vegas all I can say is the idea that Michigan's odds would somehow jump up from 13% to win the BTCG to 17% to make the playoffs is flat out hilarious, based on their schedule. This has "sucker bet" written all over it. Finally, my math suggests that MSU, Iowa, Wisconsin, and Penn State all have a better chance for the playoffs than Vegas thinks.
ACC
In the ACC, my calculation in regards to Clemson match the Vegas odds very well across the board for all three phases of the season (division, conference, and playoffs) although my math suggests Clemson is very slightly over-valued. In the Division races, similar to the Big Ten, Vegas sees both races as a bit more open. In particular, my math suggest that Florida State and Louisville are both under-valued in the Atlantic Division, while Duke and GA Tech are both over-valued in the Coastal Division, which is depressing the odds for the two favorites: Miami and VA Tech. In my preseason analysis, I picked VA Tech to win the Coastal Division after a minor upset of Miami, and my "what if" calculation confirms the importance of this November 17th match-up. If Miami wins that game, I project an 88% chance that they win the Division, while a VA Tech win translates to a 69% chance for the Hokies.
On the Atlantic side, my "what if" analysis strengthens another warning that I issued in my preseason analysis and that is: what out for Louisville. While their odds to win the Division are still under 10%, if they were to somehow upset Clemson on November 3rd, I project that the Cardinal would actually become the favorite to win the Division by a margin of 38% to 33% for Clemson and 23% for FSU.
As for the ACC Title game, Clemson and Miami's odds look spot on, but my calculation is more optimistic for VA Tech and FSU than Vegas is. Interestingly, the Vegas odds for Miami to make the playoffs look strangely low (as do VA Tech's) while FSU's odds seem a bit inflated.
Big 12
In general, the Big 12 is kind of annoying. All the other conferences have a divisions and championship games and I could use the same mathematical framework on each of them. Not so for the Big 12. It was fairly straightforward to work out the probabilities for a team to get the #1 seed (the 1st column above), but the #2 seed was a bit tricky and I essentially estimated it based on a normalization of a given team's odds to finish first. I then worked out the odds for each team to win the Big 12 Championship (the 2nd column above).
When I compared these odds to the adjusted Vegas odds, the results were similar. In line with the other conferences, my odds for the bottom half of the conference drop much faster than Vegas, which means my calculations say that teams like West Virginia and Iowa State are over-valued by Vegas. The other team that seems to be over-valued, both for winning the conference title and especially for the playoffs, is Texas. My preseason analysis pick, TCU appears to be severely under-valued for the conference title, but my odds for the Horned Frogs to make the playoffs differ by less than a percentage point than the Vegas odds. At the end of the day, both my numbers and Vegas like Oklahoma to win the Big 12, but oddly my calculation suggests Oklahoma is under-valued by Vegas, especially when it comes to making the Playoffs.
As for the "what if" sensitivity analysis, for the Big 12 is basically just suggests that the games involving Oklahoma, TCU, and/or Texas are all pretty important, which is not a surprise.
Pac 12
In my preseason analysis of the Pac 12, I predicted a chaotic finish where Oregon and Utah would win the North and South, but a look at my calculated odds gives me a little pause. In the North, my math suggests Washington is the prohibitive favorite, and the Vegas odds basically agree. The main difference otherwise is that some of the probability that my math gives to the Huskies is distributed to the bottom of the conference by Vegas.
In the South, my calculations diverge from Vegas's a bit more, as my calculations are much more positive for USC and Arizona than are the Vegas odds, while Vegas gives surprisingly good odds to UCLA, as well as both ASU and Colorado. As for the Pac 12 Championship Game, my odds match those of Vegas quite closely for the top half of the conference with the exception of USC, who Vegas seems to be under-valuing. As for the Playoffs, Vegas seems to be under-valuing the Washington and Oregon, but not USC or Stanford.
As for the "what if" sensitivity analysis, the Stanford at Washington game on November 3rd looks to have the biggest impact in the North, as it could drive Stanford's odds to almost 60% or Washington's to almost 80%. Down south, the USC-Arizona game on September 29th appears to by the biggest swing game, as USC's odds to win the South could go up to 79% with a win or down to 29% with a loss.
SEC
As for the SEC, there is a strong correlation between my results of those of Vegas, again, with a few noteworthy exceptions. In the race for SEC East, my math consistently give the top three teams (Georgia, South Carolina, and Florida about a 5% better shot at winning the Division. However, I think that this is likely due to a siphoning of probability from the top of the division to the bottom. Out West, my math suggests Bama might be slightly over-valued, while Auburn and especially Mississippi State appear undervalued.
In my preseason analysis, I picked Alabama to rip through the West and South Carolina to score an early upset over Georgia to claim the East. My "what if" analysis agrees in part, but it looks more to me like both Division races are essentially a 3-team race. In the East, If UGA beats either USC or Florida, their odds rise to the 70-75% range, but if they lose either game, their odds falls way down to around 25%. Similarly, out West, the math worked out almost identically when Alabama plays Mississippi State and Auburn. Bama just happens to drop both of those teams at home, while Georgia faces both on the road.
Regarding the SEC Championship and Playoff hunt, my math shows Alabama with a modest advantage over Georgia in both categories by 5-10 percentage points, while in contrast, Vegas pegs Alabama's odds as almost 30 points higher than UGA. Strange. It is also a bit odd that my math gives Auburn a slightly better chance that Vegas does to win the SEC Title, but Vegas also gives the Tigers a 4% better chance to make the Playoffs. Other than that, my math suggests that Mississippi State and South Carolina are a bit under-valued in the Title and Playoff races, while Florida, Texas A&M, and LSU are all a bit over-valued by Vegas.
What about Notre Dame?
Good question. Well, since they don't have either a division or a conference, there is flat out less math to worry about. The adjusted Vegas odds for the Irish to make the playoffs are only 13.33%, while I have their odds of going 11-1 or better to be at 13.99%, so we are in agreement. I also saw somewhere online that ESPN calculated ND's odds to make the playoffs at over 40%. Yeah... no. Just no.
Mountain West
For the Group of Five teams, there is less data available, and from here on out, I will only make a few simple comments based on my numbers and the Vegas spread for the conference title. In the Mountain West, the message is simple: Boise State is way better than everyone, and Fresno State and San Diego State will battle it out for the West. The Bronco's odds to win the MWest title is higher than any other Group of Five team, which is why many experts are penciling them into the Fiesta Bowl already.
AAC
In the AAC, UCF and Memphis both seem to have clear edges in their divisions, with UCF being favored to repeat as champs. However, Vegas sees only an 11-percentage point gap between the two teams, while my math suggests the gap should be ~24%. Furthermore, the Vegas odds for Houston and Navy both seem a bit inflated.
MAC
In MACtion, my calculations show Ohio running away with the East, while Toledo and Northern Illinois are in a virtual dead heat for the West. As for the MAC Championship, all three teams are in the running, with Toledo have a 5-6% edge. Interesting, for whatever reason Vegas's predictions deviate from my own more than any other conference. Vegas actually pegs Ohio as the team to beat, and among other things, likes Western Michigan's shot at the Title way more than I would have guess based on my data set.
C-USA
And finally, there is Conference USA. In general Florida Atlantic is the projected team to beat, with Marshall a bit behind. The Vegas odds more or less track with my results, with the normal pattern of the teams near the bottom of the league having a bit higher odds that I would project, based on my calculations.
(P.S. Sorry Sunbelt, I still didn't run any number for you guys.)
Wanna Bet?
OK, what I am about to type here is perhaps not just a bad idea, it is perhaps a terrible one, but... here goes. In my various forays into the math of sports, I often run across the question, "can I use this data in Vegas?" In the 10+ years I have been tinkering with these number, I have not found any reliable method. But... as I have shown above many times, my calculations highlight several team that are either over-valued or under-valued by Vegas. Considering my calculations are built on the foundation of a consensus of preseason rankings and a mathematically consistent framework, this seems like as good an area as any. So, as a final thought, I went through any picked out 10 possible bets that all have reasonably good odds of happening (at least 14%) and all have a good calculated return on investment (ROI) which I define as my odds multiplied by the money line minus the odds of losing times the bet. I assume a $100 bet for each contest. Those Top 10 Bets are shown here:
So, for a hypothetical $1000 bet, the return would expected to be over $600. Now, of course any actual combination would be different than this, but I would only need to get 2-3 of those bets correct to break even, and that is exactly what my probabilities would suggest. I will personally NOT be betting with this information, as I do not actually gamble, but I will be certainly be checking back with this prediction at the end of the year.
PLEASE DON'T USE THIS INFORMATION TO ACTUALLY BET. NO REALLY, DON'T DO IT. This is the first year I have even tried this methodology. You have been warned. Also, I believe that I am using the lines as they came out in June or July. The current lines may have already moved.
As a final note, I would be remiss if I did not also mention that, yes, MSU making the Playoffs is one of my highlighted best, with an ROI of 48.4%. I don't fell good about this necessarily, but I basically felt like I needed to include based just on the math. But, as my brother-in-law once said, "Never bet on MSU, for or against, in any sport, for any reason." I think that is still pretty good advice.
As always, enjoy!
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