Does Switching to Fast Paced Offense Mess Up Your Defense?

Does Switching to Fast Paced Offense Mess Up Your Defense?

Submitted by Yinka Double Dare on October 27th, 2016 at 11:26 AM

Texas blog Barking Carnival takes a look at the numbers and finds there is some relationship between switching to a fast-paced no huddle offense and a decline in your defensive efficiency numbers that year:…

(Note this isn't saying you can't have a good defense running HUNH, but that when you switch to it, you should expect a defensive decline that season)

OT: "It's Okay to Believe in the 'Hot Hand'"

OT: "It's Okay to Believe in the 'Hot Hand'"

Submitted by restive neb on August 26th, 2015 at 10:23 PM

A few months ago, there was some discussion about whether the "Hot Hand" was a real thing, or simply the expected result of chance over time.  A study in the 1980s ("The Cold Facts About the 'Hot Hand' in Basketball") suggested that believers in the hot hand were suffering from a "cogniitive illusion." 

In that mgoblog board discussion a few months ago, I mentioned that I had come across a study disputing that original study.  Unfortunately, I was unable to find it --  I had read it in a book that was given to me as a gift about a decade ago.  I had completely given up on finding the study.  However, I just moved into a new home last month, and while unpacking boxes this week, I came across the book!  It's titled "Anthology of Statistics in Sports", Edited by Albert, Bennett, and Cochran, and printed in 2005.  The specific study is titled "It's. Okay to Believe in the 'Hot Hand.'"  The authors' conclusion was that the original study was flawed, and that there was strong evidence that streak shooting was a real thing.

The data set included several games from the 1987-88 NBA season, and had several big name players included in the analysis.  One of those players, Vinnie Johnson of the Pistons, had a reputation as the ultimate streak shooter.  The authors looked to see if Vinnie really did accomplish low-probability streaks at higher frequency than other players, and the answer was a resounding "yes."  Fans were able to "make proper reputational attributions to those players who do the improbable and memorable more regularly than other players."

One of the more interesting results:  When looking at the probability to hit the next shot based on whether the previous shot(s) had been made or missed, Dennis Rodman's numbers really jumped out.  Probability after one make:  0.55.  After two makes:  0.78.  After 3 makes:  0.92.  Conclusion:  "success breeds success."  As he hits shots, his probability of a hit increases.  But then this:  Probability after one miss:  0.63.  After 2 misses:  0.69.   After 3 misses:  1.00.  Conclusioin:  For Rodman, "failure breeds success."  As he misses shots, his probability of a hit increases.  As with everything else concerning Rodman, that's just weird.  (Sample sizes diminished as the streaks continued, so this conclusion has to be taken with a grain of salt.)

OT - Why I Still Play Football, by John Urschel

OT - Why I Still Play Football, by John Urschel

Submitted by gwrock on March 21st, 2015 at 3:11 PM

Thought this was a good little read about why a particular NFL player continues to play football, potentially risking a promising career in mathematics.

Regarding balancing playing vs. brain injury risk:

Naturally, I believe that I have a certain insight into this dilemma, due to my non-athletic pursuits. In particular, I have a Bachelor’s and Master’s in mathematics, all with a 4.0, and numerous published papers in major mathematical journals. I am a mathematical researcher in my spare time, continuing to do research in the areas of numerical linear algebra, multigrid methods, spectral graph theory and machine learning. I’m also an avid chess player, and I have aspirations of eventually being a titled player one day.


Article on Chip Kelly and risk-averse football coaches

Article on Chip Kelly and risk-averse football coaches

Submitted by cheesheadwolverine on November 8th, 2012 at 11:06 AM

The Postgame (which is apparently a sports blog run by Yahoo) has a decent article on the non-sensical risk-aversion of football coaches especially in the NFL.  The article is somewhat marred by its single minded focus on Chip Kelly, but it's nice to see people finally realize some of the glaringly obvious stupidity in conventional football play calling.…

Mike Hart, The Decade’s Most Valuable Running Back

Mike Hart, The Decade’s Most Valuable Running Back

Submitted by The Mathlete on April 10th, 2012 at 10:47 AM

[Ed-Ace: Brian (knee) is day-to-day, though he did prepare some content that will be posted this afternoon. Post-Burke-return hoops stuff and a Spring Game primer will appear later this week. In the meantime, enjoy some Mike Hart.]

In honor of Michigan’s all-time leading rusher’s birthday yesterday, a look at one of the unique careers in college football.

Since the 2011 season completed, I have been re-loading 9 seasons worth of games (6,063 to be exact) to update my database to include 2011’s new feature of Win Percent Added. In doing so, something immediately popped out at me. No running back added more wins to their team than Mike Hart did for Michigan.

Sometimes when you are looking at advanced stats you are surprised by how counter-intuitive results can be and sometimes you are surprised how well the data fits the existing narrative. Mike was the back who wouldn’t go down, always got the extra yard, killed the clock and never fumbled. Those are all the things that factor highly in Win Percent Added, especially the 4th quarter capabilities. Burning the clock in the fourth quarter is a key requirement of a successful running back. Especially a Michigan running back. No one did it better than Mike.

For his career, Mike Hart was responsible for 4.4 Wins running the ball. Reggie Bush edges him out if you count receiving WPA, as well, but those are tainted wins. It’s not just longevity and playing time that pushed him to the top. His per game average of 0.11 is fifth, behind two players with only a single season in the database and two more with two seasons at non-BCS level schools.

Freshman Season

At this point, writing about Mike Hart is a daunting task. What is left to write that hasn’t been written? He joined the team in the 2004 class as a 3 star recruit. He nearly set the national high school rushing record but wasn’t even the highest ranked running back in Michigan’s class. He would have been the fifth highest rated running back in Miami’s (YTM’s) recruiting class. He saw his first quality action in his second game of his career against Notre Dame in the second week of the season. By week three he was over 100 yards and posting a +5 EV+ and a crucial .36 WPA as Michigan held on for a 24-21 win over San Diego St.

Hart would go on to string together three straight 200 yards games in Big Ten play, including a 0.26 WPA in the Braylon Edwards game. His EV+ was always strong for a running back but where his EV+ was strong, his WPA was Herculean. Mike Hart made all the plays to win the game but none of them to lose them. By the end of the 2004 season true freshman Mike Hart had gone from anonymous three star to posting a per game WPA of 0.15, still my best recorded number in the Big Ten.

Sophomore Season

Injuries killed a large portion of the 2005 season. Kevin Grady, Max Martin, Antonio Bass and Jerome Jackson all took carries but none could come close to the production from Mike Hart. Kevin Grady was the only one to surpass a +1 EV+ in his absence, and that was mostly unnecessary against Indiana. Jerome Jackson did have a solid 0.14 WPA on 11 carries in an overtime win against Iowa, but that was limit of the success when Hart was out. In five full games of action Hart averaged 0.23 WPA which if replicated across an entire season would have given him the second highest (Reggie Bush, 2005) WPA average in a season for any running back since 2003.

It’s hard to think about what could have been with a healthy Mike Hart. Three carries in a seven point loss to Notre Dame, a DNP in a three point loss to Wisconsin eight ineffective carries in a four point loss to Ohio. There’s a very real chance he swings those three games and Michigan shares a Big Ten title with Penn State and spends its holiday taking on Florida State in the Orange Bowl rather than getting screwed over by the refs in the Alamo Bowl.

Junior Season

With fewer games coming down to key fourth quarter possessions in 2006, Michigan didn’t need the fourth quarter machine Mike Hart. He finished the season with a profile almost exactly like Chris Perry’s 2003 season. With not much in the way of close games, he didn’t have any massive, WPA pushing games like he had in his first two years, but 10 of 13 games would finish at .07 or better. For the year Hart ended at .09 WPA/game, his third top 20 Big Ten WPA year in as many tries. John Clay is the only player to have even 2 top 20 finishes.

Senior Season

For the second time in his career, injuries would derail an outstanding Mike Hart season. After surviving The Horror and somehow managing a strong WPA in the follow-up beating by Oregon, Hart was on track for a season to along side his junior year. An ankle injury in mid-season cost him a couple games of action and a couple more of effectiveness. 2007 would be his lowest rated season but still crack the Big Ten top 50. He would finish the year with enough quality carries to become Michigan’s all-time leading rusher and set the then non-existent WPA record.


When I talk to people about how much more valuable quarterbacks are than running backs they usually point to running out the clock in the fourth as the unquantifiable equalizer between the two. When I first developed the Win Percent Added I was anxious to see how true it was. If you properly value the ability for a running back to keep the clock running and close out a game, what happens to the value relationship between quarterback and running back. After I crunched the numbers I found that the fourth quarter benefit was largely overstated. Until I looked at Mike Hart. There are very few running backs whose value is truly magnified by the little things like the narrative claims.

Mike Hart is the narrative.


Mike Hart, Seasons

Season G EV+ WPA Yards/Gm Att/Gm
2004 11 2 0.15 130 24
2005 8 0 0.14 84 18
2006 13 2 0.09 120 23
2007 9 (0) 0.06 129 25

Mike Hart, Games

Year Week Vs EV+ WPA Rush EV+ Rush Att Yards
2004 2 Notre Dame (0) (0.02) (0) 6 20
2004 3 San Diego St 5 0.36 5 25 121
2004 4 Iowa (2) - (2) 23 98
2004 5 Indiana (2) 0.05 (2) 18 79
2004 6 Minnesota (4) (0.13) (4) 35 158
2004 7 Illinois 4 0.38 4 39 231
2004 8 Purdue 5 0.33 5 31 207
2004 9 Michigan St 3 0.26 3 33 224
2004 11 Northwestern 9 0.26 9 23 151
2004 12 Ohio St 2 0.05 2 15 59
2004 20 Texas 1 0.14 1 21 82
2005 1 N Illinois 5 0.17 5 19 117
2005 2 Notre Dame (1) (0.02) (1) 3 4
2005 5 Michigan St (1) 0.46 (1) 36 220
2005 6 Minnesota (1) 0.06 (1) 27 111
2005 7 Penn St 4 0.34 4 23 114
2005 8 Iowa 0 0.01 0 5 18
2005 12 Ohio St (2) (0.06) (2) 8 14
2005 20 Nebraska (2) 0.14 (2) 19 74
2006 1 Vanderbilt 1 0.15 1 31 146
2006 2 C Michigan 9 0.17 9 17 116
2006 3 Notre Dame (5) - (5) 17 124
2006 4 Wisconsin 1 0.03 1 23 91
2006 5 Minnesota 2 0.13 2 30 194
2006 6 Michigan St 3 0.08 3 17 122
2006 7 Penn St 3 0.12 3 26 112
2006 8 Iowa 1 0.10 1 31 126
2006 9 Northwestern (0) 0.07 (0) 20 95
2006 10 Ball St 1 0.12 1 25 154
2006 11 Indiana 4 0.15 4 17 92
2006 12 Ohio St 5 0.09 5 23 142
2006 20 USC (3) (0.09) (3) 17 47
2007 2 Oregon 3 0.09 3 21 127
2007 3 Notre Dame 5 0.11 5 26 187
2007 4 Penn St (2) 0.06 (2) 44 153
2007 5 Northwestern (5) (0.07) (5) 30 106
2007 6 E Michigan 7 0.30 7 21 215
2007 7 Purdue 3 0.11 3 21 102
2007 10 Michigan St (1) 0.03 (1) 15 99
2007 12 Ohio St (2) (0.06) (2) 18 44
2007 20 Florida (8) (0.05) (8) 32 128


Ivy League Academic Index

Ivy League Academic Index

Submitted by Swayze Howell Sheen on December 25th, 2011 at 1:50 PM

Neat article about the "academic index", used by the Ivy League schools to ensure some kind of fairness across schools. The basic idea is simple: compute a formula based on GPA and SAT scores, and ensure each school has about the same average across their athletes.

More here:…

Should the Big Ten, SEC, etc., be forced to do something like this too? (it certainly would be interesting to know the AIs of various schools)

Never Punt with Denard?: Fourth Down Strategy Revisited

Never Punt with Denard?: Fourth Down Strategy Revisited

Submitted by The Mathlete on September 21st, 2010 at 10:02 AM

[Ed.: Bump. This makes sense to me: Michigan should mostly dump special teams once it gets across midfield.]

As Brian highlighted in the UMass round-up, maybe forgoing the punt altogether might not be such a bad decision. He noted my earlier look at the the topic and I wanted to pull it back and revisit and refine some of the work.

I looked at the years 2004-2009 and only looked at the top 20 rated offenses for each year. This study assumes that Michigan’s offense this year will be at a top 20 caliber and provides a broad enough definition of greatness that there is a good sample size. I did not distinguish what type of offense (Texas Tech Air Raid vs Georgia Tech triple option vs spread and shred) was used to get into the top 20. I will detail more assumptions as they are applicable along the way. In place of fourth down conversion percentages I used third down conversion percentage since the data pool is much larger and covers a wider variety of opponent levels. Since the thought process on a third down and fourth downs are roughly the same in most all (for now, anyway) situations, it seems reasonable to use the third down numbers.

Time for a you know what…


Assumptions: Top 20 offense, average defense, average punt game, average field goal kicker.

Based on these assumptions, except for long yardage, the punter should grab a seat once the offense crosses midfield. On your own side of the field the decision still makes sense starting around the 30 for shorter yardage situations and becomes more viable for longer yardage as you cross further down the field. Field goals become practical with 4+ yards to gain and only from about the 5-25 yard lines.

There are two big advantages a potent offense has that make 4th down tries more logical. The first is that they have more to gain by success. With a limited number of drives in a given game, why give them away for free? The second is that they are more likely to make them. Good offenses are more likely to be in better position on fourth down and more likely to make it.  Here is a chart of great offenses fourth down conversions compared with all offenses. The right hand column was the one used for the above chart.

To Go All Teams Great Off
1 72% 74%
2 57% 60%
3 51% 54%
4 47% 50%
5 42% 45%
6 38% 41%
7 35% 37%
8 32% 34%
9 30% 32%
10 27% 30%

It’s not a huge advantage on any one given down, but Top 20 offenses convert the same opportunities about 2-3 percentage points more often than the average offense. Note: the rate of conversion for great offenses was much higher in the original analysis and is part of the reason the chart isn’t quite as go for it as the original.

But we don’t have an average <blank>

<blank> = Kicker

Let’s start with the kicking game, which is currently 5 points below average on the season and rated third worst in the country after the first three weeks.


Assumptions: Top 20 offense, average defense, average punt game, below average field goal kicker (FG make odds are reduced by 25% everywhere on the field).

The decisions near midfield obviously aren’t changed but now attempting a field goal on 4th and 5-9 from inside the 25 is no longer the most valuable option.

<blank> = Punter

I know it hasn’t been the most Zoltanic of starts for Will Hagerup, but at this point if he can hold onto the snap, there is no point in adjusting him to below average, even if he isn’t an advantage at this point.

<blank> = Defense

This is the one that seems a bit counterintuitive and Brian and I disagree on. I say that the strength or weakness of your defense is irrelevant to your offensive decision on whether or not try a fourth down conversion. My belief that it is irrelevant is based on this chart.


Great defense obviously give up fewer points than bad defenses but the key point is that the difference between a great defense and a bad defense is consistent up and down the field. Giving the opponent a first down at midfield isn’t a guarantee of a touchdown even with a bad defense and isn’t a guarantee that pinning an opponent deep against a great defense will keep the other team off the board. In fact, the gap between the two is about .25 points per first and 10 all the way from the 1 to the 90. If this is true, then the ability of the defense is irrelevant to the offense’s decision to go for it. For that to be the case, there would have to be evidence that the difference between a good defense and a bad defense changes at different points on the field.

So what does all this mean

If Michigan can maintain their feverish offensive pace this year and fail to find an adequate kicker, I think their decision set in all but late game score specific situations should look something like this:


As I noted previously, if you buy into this mentality, it opens up another opportunity, changing your early down play calling. If your four down strategy has changed, so should your down by down playcalling. It may become more viable to risk a wasted down with deep ball knowing that you have an extra, or it might just make sense to keep the ball short in the air and on the ground knowing that over four plays instead of three the likelihood of getting the yardages greatly increases so play to have the shortest possible fourth down attempt if you don’t convert before that.

Big Ten Home Field Advantages

Big Ten Home Field Advantages

Submitted by Brhino on June 18th, 2010 at 4:06 PM

Apparently the Big Ten Network's website is running a poll to determine which Big Ten team has the "best home-field advantage".  Popularity contests do not good data sets make, so I figured I'd apply a lot of counting and a little math and see what I came up with.

The rules:

  1. For each Big Ten team, I tallied up their total wins over the last 11* years, and seperately tallied how many of those wins came at home.
  2. I ignored nonconference games.  Those will naturally boost home winning percentages as you invite the baby seals to get clubbed at your house, and play home-and-homes against teams that might actually beat you.
  3. I wanted to compare how well a team did at home compared to how well it did on average, rather than just totalling home wins and saying "golly, Ohio State must have the best home field advantage because they won at home a lot".  Well, unfortunately, they won on the road a lot too, so it doesn't tell you much.
  4. Of course, the inverse of saying a team has a "Strong home field advantage" would be to say that same team "Sucks on the road".  I'm looking at you, Indiana.

*I had planned to look at the last 10 years, but made my spreadsheet a big too large and went on my merry way entering in data.  I was all done by the time I realised my mistake and I saw no reason to discard the 1999 season just because it was one more than I had planned to look at.

The Results:

First, and just for the record, here's your overall Big Ten winning percentages for the last 11 years:

Rank TEAM WINNING % Home Wins Home Wins Rank
1. Ohio State 76.14 35 1.
2. Michigan 67.05 32 2.
3. Wisconsin 57.95 28 T4.
4. Penn State 56.82 28 T4.
5. Iowa 55.68 30 3.
6. Purdue 51.14 27 6.
7. Northwestern 44.32 22 8.
8. Michigan State 43.18 23 7.
9. Minnesota 39.77 20 9.
10. Illinois 34.09 16 T10.
11. Indiana 23.86 16 T10.

Yeah, I know.  I don't like it any more than you.  Anyhow, as you can see, there's not a lot of difference between a team's overall rank and its rank in terms of raw number of home wins.  A bad team is a bad team at home or on the road, and ditto for a good team.

Surely there must be something to the fearsome reputations to such locations as Beaver Stadium and the Horseshoe though, right?

At first, I tried expressing home field advantage as the percentage increase of home winning percentage over total winning percentage.  However, I found that this simply weighted the home success of bad teams much higher.  Instead, I totaled the number of wins each team had at home, subtracted the number of wins each team had on the road, and averaged over 11 years to yield a number I'm calling the Expected Increase in Wins at Home (EIWH).  In other words, every year each team plays 4 Big Ten home games and 4 Big Ten road games.  How many more wins, on average, does a given team expect to claim at home than it will on the road?  The results are as follows:

Indiana 1.00
Iowa 1.00
Purdue 0.82
Michigan State 0.73
Penn State 0.55
Michigan 0.45
Minnesota 0.45
Northwestern 0.45
Wisconsin 0.45
Ohio State 0.27
Illinois 0.18

The results have some suprises.  Iowa, a slightly-above-average team overall, earns an average of one more win at home than it does on the road, as does celler-dwelling Indiana.  Indiana has only won five Big Ten road games in the past 11 years.  Iowa has a reputation as a tough place to play, especially at night, but the Indiana results are inexplicable. 

On the other end of the spectrum, Illinois has only earned 16 of its 30 victories at home, which makes for an interesting contrast with Indiana in spite of the two school's proximity at the bottom of the overall standings.  Strangest of all, the feared Horseshoe in Columbus grants a very modest advantage to the hated Buckeyes.   They have less of a home field advantage than such teams as Northwestern (a school which, from my personal experience, barely fills half its stadium with home fans) and Minnesota (who played in the sterile Metrodome for all of the period of this study).   

What's the message here?  It seems that the level of hype attached to particular stadiums has little relation to the advantage those stadiums grant to the team playing there.

Reasons for ND hopelessness: trends in average win percentages

Reasons for ND hopelessness: trends in average win percentages

Submitted by michelin on November 9th, 2009 at 8:00 PM
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Much has been made of the recent UM record.    However, whenf statisticians seek a more reliable measure of a team’s quality and the direction of a program, they look at the bigger picture by (1) comparing that season record with records from other schools and (2) considering not a single year, but groups of years (called a moving average).

(1)     I looked at the records of the two most recent coaches among our rivals.  I found that ND had a 3 win season, OSU had a four win season;  and MSU had three four-win seasons.  Some of these occurred during coaching transitions, like UM’s.   But others had no such excuse.…

(2)    As in prior threads (see footnote*),  I now report the  analysis of the records of the ND coaches,  based on the victories averaged over each of 4 successive seasons.** 

Results: Under Lou Holz, the trend was positive overall (with an increase of .125 victories per year).  Yet, much as occurred during LC’s initial years, the gains were all early, and were followed by a gradual decline.  For all the subsequent coaches at ND, the trends  were  consistently negative (a decrease in average victories of   -.25 per season for Davies, -.25 per season for Willingham, -.10 per season for Weiss. However, the trends appear downward at a uniform rate, starting at Holtz’s peak.


1. The ND program is progressively deteriorating. 

2. One wonders if the many coaching changes contributed to this.  I have given mixed shades to the transition years, in which one coach has at least 2 years of the other one’s players.  From this, one wonders whether Willingham would have continued the upward trend if he was kept and could play his recruits during what were the first two years of Weiss’ tenure. 

3. Since ND faces massive losses next year, including the OL, RB and probably Clausen and Tate, in addition, with a completely inexperienced backup QB who will be unable to practice and coming off ACL surgery next August, one must seriously wonder when—no, whether—the ND program will get back on track.


If UM uses ND as an example of what might happen to a program, the questions for UM now is whether it will follow the pattern of Holtz, who began with a decline in average wins—similar to what is likely for RR (although Holtz did not have the big immediate dropoff in average wins from his predecessor, since that average was already quite low). The promising thing is that, unlike ND, UM has more, not less, starters coming back for the next two years.  Clearly, it’s way too early to tell—as Brian has intimated today—but I can't help worrying that we might end up like ND if we keep getting rid of coaches before they can build their program. 


* In two previous threads titled “Reasons for Hope” (for UM), and “reasons for MSU hopelessness.”  Another interesting and pertinent link from another poster is:

**Note that it’s not a simple average.  At the beginning of a coach's tenure, his record is shown as an average that includes the prior coach's average--which may be either better or worse than the current record.  As, such the first two years of each coach’s tenure are shown as mixed colors, as they reflect the recruits of the previous coach as well as the performance of the current coach.  (just ask yourself, if Bo were alive and took over the coaching job of the perennial celler-dweller Northwestern team in the 60's, would he be responsible for the first few years?)