Probability and belief

A few days ago, in Probability and the Problem of Life, I pointed out that there is no need to precisely calculate probabilities that we cannot possibly know in order to reach logical conclusions about them. Contra the opinions of the misguided math fetishists, logic is the foundation of math, not the other way around, and we can reach perfectly sound logical conclusions even if we are not able to make precise mathematical determinations or quantifiy all of the various factors involved.

Throughout the course of the discussion, it soon became abundantly clear that those who defend the theory of TENS on probability grounds do not actually believe their own position. Furthermore, it is relatively easy to demonstrate that although the very low probability events to which they appeal are mathematically possible, they are so highly improbable that no sane human being can credibly feign to take seriously, as evidenced by their own daily behavior with regards to other, much more likely events.

WRF3 asked me to identify the precise point at which mathematical possibility and belief part company; I said that for me it was somewhere between 1 in 4,165 and 1 in 17,347,225. The latter are the odds of being dealt four aces twice in succession from two properly shuffled card decks; I would not view that as credibly possible and continue to play poker with a machine that dealt out such hands. The absolute outer limit for even the most credible individual is probably 1 in 72,251,192,125, which would be three such unlikely hands.

But the reality is that for the average individual, the credibility ratio is much lower. Consider the recent statistical evidence of the New England Patriots having systematically cheated by deflating the football since the 2007 season:

While speculation exists that “Deflate Gate” was a one time occurrence, data I introduced last week indicated that the phenomena MAY have been an ongoing, long standing issue for the New England Patriots. Today, that possibility looks as clear as day.

Initially, looking at weather data, I noticed the Patriots performed extremely well in the rain, much more so than they were projected.  I followed that up by looking at the fumble data, which showed regardless of weather or site, the Patriots prevention of fumbles was nearly impossible.  Ironically, both studies saw the same exact starting point:  2007 was the first season where things really changed for the Patriots.  Something started in 2007 which is still on-going today.

I wanted to compare the New England Patriots fumble rate from 2000, when Bill Belichick first arrived in New England, to the rest of the NFL.  Clearly, one thing I found in my prior research was that dome teams fumble substantially less frequently, given they play at least 8+ games out of the elements each year.  To keep every team on a more level playing field, I eliminated dome teams from the analysis, grabbed only regular season games, and defined plays as pass attempts+rushes+times sacked.  The below results also look only at total fumbles, not just fumbles which are lost.  This brought us to the ability to capture touches per fumble.

To really confirm something was dramatically different in New England, starting in 2007 thru present, I compared the 2000-06 time period (when Bill Belichick was their head coach and they won all of their Super Bowls) to the 2007-2014 time period.  The beauty of data is the results speak for themselves:

The data is jaw dropping, and this visual perfectly depicts what happened.  From a more technical perspective, John Candido, a Data Scientist at ZestFinance who is a colleague of mine over at the NFLproject.com website and was also involved in the development of this research, comments:

Based on the assumption that plays per fumble follow a normal distribution, you’d expect to see, according to random fluctuation, the results that the Patriots have gotten since 2007 once in 5842 instances.

Which in layman’s terms means that this result only being a coincidence, is like winning a raffle where you have a 0.0001711874 probability to win. In other words, it’s very unlikely that results this abnormal are only due to the endogenous nature of the game.

Many of the arguments giving the Patriots the benefit of the doubt are evaporating.  While this data does not prove they deflated footballs starting in 2007, we know they were interested in obtaining that ability in 2006. (This is something I found out AFTER I performed the first two analyses, both of which independently found that something changed starting in 2007.)

I was skeptical when I first read the analyst’s theory, because he initially used fumbles lost rather than all fumbles; it is generally believed by football statisticians who have considered the question that fumble recoveries are random. And when fumbles rather than fumbles lost are utilized, the Patriots are considerably less of a radical outlier, although they are the only team that plays outdoors that fumbles as little as a dome team.

My first thought was that the anomaly was more a result of New England’s pass-happy offense than statistical evidence of ball deflation. However, a look at the passing statistics showed that New England was pass-happy as early as 2002, when they threw 601 passes, compared to 582 in 2014, and the fact that their plays per fumble from 07-14 increased so dramatically from 00-06 after the rule change that they requested does tend to confirm the analyst’s original suspicions.

 But my point is not to take a side in the latest New England scandal, only to observe that for the professional statistician, observation of a successful event against 1 in 5,842 odds is sufficient to indicate the results observed are probably not obtained naturally. And while this statistical evidence is not absolute proof (although it is interesting to see that the statistician’s odds are in the range I suggested should preclude belief), it is enough to indicate that the greater part of one’s efforts should be directed at discovering the precise nature and mechanism of the unnatural tampering indicated rather than on the unlikely natural explanation.

“The bottom line is, something happened in New England.  It happened just
before the 2007 season, and it completely changed this team.”

Which brings us back rather to my long-held position contra Mr. Sherlock Holmes: Once you have calculated the sufficiently improbable, you must reconsider your assumptions of the impossible.


Championship weekend

It looks like things are setting up rather nicely for the expected Patriots-Seahawks Super Bowl. The Packers have the best shot of any NFC team to knock off the Seahawks on paper, but seeing how limited Aaron Rodgers was against Dallas, I find it hard to figure out how the Green Bay offense is going to deal with the ferocious Seattle defense.

In the AFC, I’d be very surprised if New England didn’t simply bulldoze the Colts by handing off the ball 30+ times. What sets Bill Belichick above other clever NFL coaches is that he seldom overthinks his game strategy. He doesn’t assume that his opponent will be able to stop something simply because they are anticipating his attack, he forces them to prove that they are actually capable of doing so before bothering with any adjustments.

(This, by the way, is a very good lesson for any gamer to keep in mind. Never assume that anticipation is accomplishment, either on your part or the opponent’s.)

And, if the Colts do figure out a way to stop the New England running game, Belichick will promptly switch to the pass without hesitation.


Hail to the victors

Contra SEC loyalist Nate’s assertion, they’re chanting it now. B1G! B1G!

I’m not what you’d call a fan per se of THE Ohio State University, in fact, I think Michigan has better colors as well as the best uniforms and fight song in college football. But back in the day, when there were only two teams playing for the Big 10 title, I tended to favor Woody Hayes, Art Schlichter, and Archie Griffin over Bo Schembechler and the Maize-and-Blue. I have no idea why, but it still astonishes me that Griffin was not a star in the NFL. It didn’t surprise me that Rashan Salaam failed in the pros; all he ever did at Colorado was take a pitchout, beat an undersized cornerback around the corner, and run 80 yards for a touchdown. But Griffin was the real deal in college. Was he simply too slow? I have no idea.

Anyhow, with Harbaugh back at Michigan, Meyer leading a resurgent Ohio State, and both Penn State and Nebraska rebuilding their programs, it should be interesting to see if a rivalry between the SEC and the Big 10 develops. It’s enough to get this NFL fan paying a modicum of attention, anyhow.


Coaching craziness

Rex in with the Bills, Fox out with the Broncos, most open positions still unfilled… I wonder if Peyton Manning will retire as quarterback and take the OC position under Adam Gase as the Denver head coach?


Divisional playoffs, Day 2

The New England-Baltimore game was as good as the Seattle-Carolina game was bad. I turned the latter off after Seattle went up 7-0 as it was obvious that Carolina had no chance whatsoever. That pass from Edelman to Amendola was a fantastic call and executed almost flawlessly. John Harbaugh is a very good coach, but Belichick clearly outcoached him yesterday. The chess match was fun to watch; it was the exact opposite of watching a Denny Green-coached team in the playoffs.

Dallas-Green Bay should be a good game too, although I don’t think Green Bay will have too much trouble putting the Cowboys away on the frozen tundra unless Rodgers gets hurt. Dallas’s best option is to ride Demarco Murray hard.

The Denver-Indy game shouldn’t be as bad as Seattle-Carolina, but I can’t see the Colts hanging with the Broncos. The Broncos run better, pass better, have a better defense, and they’re playing at home.


NFL divisional round

Good game so far in Foxboro. Ravens started hot, but settled down, and Brady has been picking apart the Baltimore secondary with his slot receivers. But the Ravens are getting some solid hits on Brady and that could slow down New England in the second half.


Out-of-season shape

There are no two ways around it. I am getting old. I’m one of the two oldest guys on my veteran’s team and it’s not even close; the average age is more than ten years younger than me. In the weight room, I’m usually one of the three oldest guys there. And the gradual weight of age and injuries is accumulating to the point that there are days when there are more exercises that I can’t do at full weight than those that I can.

And yet, ironically, in some ways I’m in better shape than I’ve been for fifteen years. I started stretching regularly and I’m back up to 130 degrees on the leg machine, which isn’t as good as the 150 degrees it was when I could kick six-footers in the face, but it’s a lot better than the 90 degrees it was when I first broke it out again. I definitely recovered a modicum of my lost speed through increasing my stride length. I’m not only able to play complete games when necessary, but I’m also the only player that the captain feels able to take out and put back in again, knowing that I’ll still be at something close to full speed by the end of the game.

What I’ve done is back down on the heavier weight exercises, increase the lighter ones, and increase my running. I run at least one 5k per week, ideally one 40-minute session that covers between 5.5k and 6k, and if I can find the time, a second 20-minute session doing 2.5k to 3k. It’s the time that matters, not the distance; we play 40-minute halves and I’m trying to keep my body accustomed to that time frame.

Despite the running, I’m at 192 these days, and I’m topping out my curls with 5-rep sets using the 60-pound dumbbells. I think I need to get down to 185 to really get ripped, but that’s not too bad considering all the holiday feasting of the last six weeks.

Three lifting days, two running days, and seven stretching days per week seems to be doing the trick. There is no fooling Father Time, but at least one can hope to mitigate some of his more deleterious effects.

Last season ended pretty well, as I got our only goal in the last game and ended up on five in seven fall games. I’d likely have had a second goal if the ball hadn’t abruptly stopped in a mud patch in the area when I was breaking on goal again.  But I’d really like to make it to the ten-goal mark in a half-season, so I’m training hard in order to try and make that possible. At the very least, I’d like to be sure I end up in double-digits for the full season as it’s already clear that playing a spoiler role is the most we can do.

We’ve actually played very well against the better teams, garnering ties against two of the top three teams, but we’ve also been playing down to the level of the lesser teams and failing to put them away. I’d like to win one more championship before I stop playing for good, but it won’t happen this year.


Finally, a good game

The difference between watching games between two teams who should be in the playoffs – Dallas and Detroit – and teams who shouldn’t be – pretty much the other six teams – was glaringly apparent yesterday. I think the playoffs worked best when there were three divisions and one wild card team; just as there are more teams than there are NFL-caliber quarterbacks, there are more teams in the playoffs than there are playoff-caliber teams.

But as long as there are four divisions (which works well for other reasons), it would be better if there was only one wild card team and one first-round bye. I have no regard for the “best teams” argument, because the only “best teams” that matter are already guaranteed entry. If you’re only the third-best team in your four-team division, you shouldn’t be in the playoffs. If you’re only the third-best of the non-division winners, you shouldn’t be in the playoffs.

The Eagles, who lost to the Seahawks, Cowboys, and Redskins before beating the Giants to close out the season, weren’t going to do anything that Carolina won’t do, which is to say lose to the Seahawks next weekend.

As for last night’s game, it was good to see Tony Romo finally get the playoff monkey off his back. The controversial call shouldn’t have been made in the first place, because a) it was offensive pass interference when Pettigrew grabbed Hitchens’s facemask, b) the contact was minimal, and most importantly, c) it was a completely uncatchable ball. Stafford literally hit Hitchens in the back right in the numbers; there was absolutely no way the receiver had any sort of play on the ball. Furtheremore, there is no “face-guarding” rule in the NFL, or, for that matter, in NCAA football; it is only deemed pass interference in high school football, specifically National Federation of State High School Associations rule 7-5-10: “Any player hinders an opponent’s vision without making an
attempt to catch, intercept or bat the ball, even though no contact was
made.”

When the officials call pass interference on a player who hasn’t turned around, they do so because he has crashed into a receiver who is coming back for a high ball, to distinguish them from defenders who crash into a receiver when they themselves are going for a high ball. That was not the case in the play being discussed, for the obvious reason that Stafford threw the ball into the Dallas linebacker’s back. Recall the NFL’s pass interference rules: Actions that do not constitute pass interference include but are not limited to: (c) Contact that would normally be considered pass interference, but the pass is clearly uncatchable by the involved players.

ESPN’s Todd Archer asked Pete Morelli (who is admittedly not a very good ref: see the NFC Championship Game 2009) about the call turned non-call:

Todd Archer: Can you talk about the decision to overturn the call and why you overturned the call?
Pete Morelli: The back judge threw his flag for defensive pass
interference. We got other information from another official from a
different angle that thought the contact was minimal and didn’t warrant
pass interference. He thought it was face-guarding.
Archer: Which official?
Morelli: The head linesman.
Archer: What did you see?
Morelli: It’s not my responsibility. I’m a hundred miles away.
Archer: Face-guarding is not a foul?
Morelli: Face-guarding is not a foul. It is a penalty in college but not in professional football.
Archer: What is the process you go through after you announce the call? Should you have waited before you announced the call?
Morelli: Probably, yes. The information came and then the officials got
together a little bit later, after it was given to me, the first
information. It would have probably been smoother if we got together.

He did the right thing. It’s better to get it right and look like a fool or a fix than allow a bad call to stand when he knows better. As for the decision not to flag Dez Bryant for coming onto the field without his helmet in protest of the call, I think it was a correct no-call. We want to see the refs let minor things go in the playoffs (that’s why Suh was permitted to play when his suspension would never have been overturned in the regular season), and no one wants to see a playoff game settled by an off-the-field foul by an excited player in an overheated moment that harmed no one. I wish more NFL games this year had been refereed in the style Dallas-Detroit was; I simply do not understand those fans who seem to enjoy a blizzard of yellow flags and seeing every third play called back.

If the Lions fans want to blame anyone, they should blame Jim Caldwell for failing to go for it on 4th-and-1. The football gods obviously did not like that, as they promptly punished the Lions with a 10-yard shanked punt. Caldwell played to avoid losing throughout the second half; switching to a four-man rush and abandoning the blitz took the pressure off Romo, who made Detroit pay for it.

And besides, those petty flags would have caused us to miss the redemption of Dallas’s rookie defensive end, whose utter stupidity in not falling down to seal the game once he’d recovered the fumble was made up for by creating and recovering another fumble to win the game. In the end, with two minutes left and two timeouts, Stafford only managed to produce two fumbles. Game over. The better team won.


NFL Playoffs: Wildcard round

I felt rather sorry for the Cardinals. I have no doubt they would have won with even a journeyman starter, but it’s a little tough to generate offense with a 4th-stringer. As for the Steelers, it’s obviously time for Polamalu to retire. I don’t know why the media is always down on Flacco; he may not be Manning, Brady, or Rodgers, but you can obviously win a Super Bowl with him.

The Bengals are similarly overmatched. They’re playing hard, but I can’t see them coming back against the Colts. The only game I’m even all that interested in is Detroit-Dallas. I can’t help but notice that no one is clamoring for an expanded playoffs considering how bad the first-round matchups have been this year.

As for the Super Bowl, New England beating Seattle as the last hurrah of Brady and Belichick is my prediction.


I miss the bowls

When I was a kid, New Years Day meant hearing my mother, who grew up in Pasadena, watching the Rose Parade. I’d watch the four bowl games, the Sugar Bowl, the Cotton Bowl, the Rose Bowl, and finally, the Orange Bowl.

And sure, it wasn’t always possible to know who the “national champion” was, but nobody really cared all that much, what was important was that the Big Ten won the Rose Bowl, that Oklahoma didn’t win the Orange Bowl, and that the games featuring the sort of matchups you hadn’t seen before were either a) good games or b) ridiculous blowouts. I don’t even know why I hated Oklahoma, Arkansas, Alabama, Florida, Michigan, and Notre Dame, or why I liked Baylor, Texas, Ohio State, Pitt, Florida State, and USC. But I had a favorite in every major conference

For me, things started to fall apart with the Bowl Coalition in 1992. The Big 10 and Pac-10 wisely held out for three years, but everything went south, literally, with the Bowl Alliance and the creation of a national championship played at the Fiesta Bowl on January 2nd.

Now, I no longer even watch college football on New Years Day. I don’t know who is playing in the bowls, and I don’t care. Are people any happier or more interested in college football now that the “national championship” is the de facto SEC championship? It appears I’m not the only one who is less interested in the unambiguous national championship system.

  • “The average attendance for bowl games has declined each of the past six
    seasons, down to 49,116 last season, the lowest mark since 1978-79, when
    there were 15 bowls, according to the NCAA bowl record book.”
  • “The Michigan State/Stanford Rose Bowl earned the top audience of the BCS
    slate, with a 10.2 U.S. rating and 18.6 million viewers on ESPN New
    Year’s Day — up 9% in ratings and viewership from Stanford/Wisconsin
    last year (9.4, 17.0M), and flat and up 6%, respectively, from
    TCU/Wisconsin in 2011 (10.2, 17.6M). Despite the increase, the game tied
    the second-lowest rating ever for the Rose Bowl.
  • The UCF/Baylor Fiesta Bowl drew a 6.6 U.S. rating and 11.2 million
    viewers Tuesday night, down 11% in ratings and 9% in viewership from
    Oregon/Kansas State last year (7.4, 12.3M), and down 21% and 18%,
    respectively, from Oklahoma State/Stanford in 2011 (8.4, 13.6M). The
    game earned the second-lowest rating and viewership for the Fiesta Bowl
    in the BCS era, ahead of only Oklahoma/Connecticut in 2010 (6.2, 10.8M). Overall, the Orange and Fiesta Bowls rank among the ten lowest rated BCS bowls of all time. 
  • In 2014, the BCS Championship game drew in 25.5 million viewers, and that was just the ninth-watched BCS title in history.

Here is what appears to be the root of the problem: “They (ESPN) need live content, even mediocre live content,” Maestas
told USA TODAY Sports. “Even 400,000 viewers in a sad bowl with 25,000
people in the stands is getting better (viewership) than 100 channels
out there.”

But what’s good for ESPN isn’t necessarily good for the game of college football. Quite the opposite, it appears. At least the NFL, for all its lunatic lurching about in its attempt to grow its female audience, is in control of its own destiny. This may explain why I won’t be watching a single bowl game today, but will not miss a single playoff game this weekend.