Thursday, December 04, 2014

Hosting the Broncos

Why do the Patriots host the Broncos 3 years in a row?

NFL Scheduling

Every once in a while, somebody will notice that a given NFL team will host another non-divisional team from the same conference three years in a row.  Today the Patriots are hosting the Broncos for the third year in a row.  That's so unfair!  Or so it would seem.  But it turns out that there are sound mathematical reasons that it works out this way. 

To explain the reasons, let's consider how the NFL schedule is generated.  The NFL has 32 teams, organized in two conferences, each of which has 4 divisions with 4 teams each.  And the season lasts 16 games long for each team.  This coincidence of numbers makes for a very elegant scheduling algorithm, which will disappear as soon as the NFL expands again.

Each team plays a mix of divisional games, intraconference games, and interconference games.  For starters, each team plays a home game and an away game against each of its three division rivals. 

The next consideration is the desire to have regular games against all the other teams in the league.  That's neatly arranged by having all of the teams in each division play all the other teams in each other division on a rotating basis.  For example, this season all of the teams in the AFC East play all of the teams in the NFC  North.  That rotation is on a four-year schedule, since there are four divisions in each conference.

In contrast, there is a three year rotation for interconference matchups.  This year, the AFC East plays the AFC West, while the AFC North plays the AFC South. Last year the AFC East played the AFC North.  Next year, they'll play the AFC South.  

So each team plays 6 games in the division, 4 games against all the teams of one other division in the same conference, and 4 games against all the teams in one division intra-conference.  The home-and-away matchups for division vs. division play alternates so no city will go too, too long without being able to see every other team.  That means every eighth season for interconference, every sixth season for intraconference.  These account for 14 of the 16 games played every season.

That leaves two slots to fill up the season.  The NFL fills the last two slots by having every team play one team from each of the other two divisions in the same conference, namely, the two teams that finish in the same respective place in the standings.  In recent years, the Patriots have finished in first place, and thus had to play the first place team from the other two divisions.

For many years, this led to the Patriots playing the Colts every season.  One season, when the Patriots finished in second, the Colts did the same thing, so they kept playing each other.  Now that Peyton Manning has moved to Denver, there is focus on that matchup.  And two years ago, back when Tim Tebow was their QB, the Broncos visited Foxboro to play the Pats.  Last year, they did the same thing.  

And a few weeks ago they hosted the Broncos again.

Why is that?  Well, let's look at how this can go.  The three other first place teams last season were the Broncos, the Bengals, and the Colts.  As I mentioned earlier, the Pats play all the teams of the AFC West this season.  That they host the Broncos is part of the divisional schedule.  Three years ago they went to Denver, and they'll go to Denver again three years from now.  And if they'd gone to Denver this year, they would have hosted Denver three years ago, so they still would have hosted Denver three years in a row.

Why does it happen?  It happens because the home-away switch has to interleave with the rotating division vs. division matchup.  Recall the list of the first-place teams: Patriots, Colts, Bengals, and Broncos.  Since the Patriots hosted the Bengals and visit Indy this season, the Broncos have to do the opposite, just to ensure all four teams have exactly 8 home games and exactly 8 road games.  This makes for a "cycle": Pats host Bengals, who host the Broncos, who host the Colts, who host the Pats.  A more compact notation  here would be (Pats, Bengals,  Broncos, Colts), where each team hosts the team after it.  Or, to use the geographic names, (East, North, West, South).  Last year was (East, West, North, South).   And the year before that was (East, West, South, North).  
If I keep East in the first slot, there are six ways to fill the other three slots.  And it turns out the NFL is on a 6-year rotating schedule in this respect.    Now if I keep East in the first slot, the third slot is in a regular rotation:

(East, *, South, *)
(East, *, North, *)
(East, *, West, *)
(East, *, South, *)
(East, *, North, *)
(East, *, West, *)

So, let's start with (East, West, South, North) and see what we're forced to do.  The next year we have (East, *, North, *).  If we want to avoid the (East, West, *, *) option, we have to use (East, South, North, West).  That gives us

(East, West, South, North)
(East, South, North, West)
and, if we want to again avoid a repeat
(East, North, West, South)
So far, so good, yes?  Well, at least as far as the East goes.  But notice that the South hosts the North two years in a row, the West hosts the South both times it is possible, and the North hosts the West two years in a row.

So, it's possible to schedule things so the East team doesn't have any repeat hosting, but doing so would force every other divisional matchup to be constant in terms of who's on the road and who's hosting.  You just cannot alternate a two-year rotation and a three-year rotation for everybody.  So what the league does is use all six possibilities.

(East, West, South, North)
(East, West, North, South)
(East, North, West, South)
and those three reversed
(East, North, South, West)
(East, South, North, West)
(East, South, West, North)

In other words, East@West, East@West, division vs. division, West@East, West@East, division vs. division.  And since the division vs. division matchups themselves alternate, either the third or sixth year is also going to be East@West, leaving us with three years in a row of East@West, followed by three years in a row of West@East.
[cross-posted at Pineapples in Alaska]





Saturday, June 21, 2014

surgical aftermath

I've been intending on writing an update for several weeks.  What's been the cause of the delay?  Mainly, I've been exhausted a lot.  Also, since I didn't really have leave to use, I've trying to work in spite of the exhaustion.

To organize my thoughts, I'll break the experience down into time periods

  1. Inpatient - Three days in the hospital, increasingly miserable because it was impossible to get a good night's sleep there.  
  2. At home, with brother in town for several days.  Finally sleeping and figuring out how to get the body working again.
  3. First week trying to work - pretty much impossible to do more than a few hours of work per day.  
  4. Second week - energy level still well below 100%.  Tried to do a small amount of running but just didn't have the energy.
  5. Third week - exercise time aside, energy levels pretty close to 100%.  

So I'm three and a half weeks out, feeling pretty tired for a Saturday.  Did 30 minutes on the elliptical machine last night, which felt fine.  

Back to the hospital.  Being in a hospital sucks.  More than I thought it would.  For starters, the bed just isn't comfortable.  Hospital beds bend and fold to help patients sit up, but they fold in the wrong place.  And when you're coming off abdominal surgery the last thing you want to be doing is a lot of sit-ups adjusting your body.  Also, the food was dreadful.  Being on a liquid-only diet sucks, but it turns out that their solid food is awful, too.  About the only thing they do well is administer pain-killers, but that's counter-balanced by the endless blood tests.

Going home was great.  Finally got some sleep, though the mobile feline heating unit made it a challenge to find a combination of blankets and comforters that would keep me warm without waking up in a sweat.  I gradually figured out the pain  issue - during the surgery the doctor pumped up my intestine with air to make it easier to see what was going on.  The gas was unpleasant.  Also, it felt like my entire abdominal wall clenched during the surgery and wasn't going to relax any time soon.  Things only started picking up when I switched from Percoset to Alleve.  Alleve is the best at relaxing muscles.  

The resected colon seems to be doing fine.  In retrospect, I'm wondering if this surgery was overkill, if it was disproportionate to the risk of whatever was left of the polyp.  (Which might well have been nothing.)  But I'm fine with the decision-making process, even though I suspect it will be viewed as wasteful in the future.

Friday, May 16, 2014

Losing a friend

Several months back, it may have been more than a year, I noticed that one of my Facebook friends, a guy I had met through playing Diplomacy, didn't seem to be participating in on-line discussions as often as he had.  I asked a friend we had in common what was going on, and I was informed that this person had cancer.

Well I just found out that the Duck has passed.  Really liked the guy, more so than most people.  The Duck was the kind of guy who was easy-going and naturally seemed to get along with everybody.  I didn't know him particularly well, but in another sense I did.  The nature of the Diplomacy-playing hobby is that you see people seldom, but when you do meet, the interactions are fairly intense.  The people involved are often very socially aware and we can make friends that last a long time.

Anyway, my own operation is coming up in less than two weeks.  I delayed it a week so I could go to a gaming convention.  I asked the scheduler if it there was an urgent need to schedule it ASAP and she said no.

In the aftermath of the positive colonoscopy, I've decided to also see a dermatologist to get him to look at all my freckles and moles.  Worried about melanomas now.  Am I becoming a hypochondriac?  I don't think so.  Having decided that I'm missing at least one anti-cancer allele, this puts me in a weird frame of mind.  I'll probably have to have regular colonoscopies for the rest of my life.

Meh.  Will miss Duck at DixieCon.



Sunday, May 04, 2014

Best of Bond, Part V

The Timothy Dalton Years

And the series moves forward at its glacial pace.  Today we consider the two contributions by Timothy Dalton.  Personally, I enjoyed both The Living Daylights and Licence to Kill, but neither did particularly well at the box office.


The Dalton films moved away from the increasingly comic (and increasingly ludicrous) themes of the later Moore films, and tried to bring back a more serious tone, as had characterized the earlier Connery offerings. They succeeded to some extent, but moviegoers didn't respond to Dalton's darker tone.

Let's recall the criteria in this series of evaluations again:

  • Bond – who the actor is, how good he is, and what he brings to the role
  • the Villain- Mr. Big, Scaramanga, etc.  I judge the films on how compelling the villain is.
  • the Bond Women – some films have few, some have many, but I’m pretty sure all have at least one. The quality ranges from Denise Richards’s absurd nuclear physicist to, of course, Mrs. Bond herself, not to mention Pussy Galore
  • the Good Guys – M, Q, Moneypenny, Felix Leiter in his many incarnations and other sidekicks
  • the Henchmen on the other side like Jaws, Oddjob, and Nick-Nack.
  • the gadgets – not just judging how neat the gadgets are, but whether they were unwisely allowed to take over the film (as often happened with the later Roger Moore filims)
  • whatever else I happen to think of

And now we move to

The Living Daylings


Thursday, April 17, 2014

bounce in my step

Good News

So the pathology report is back.

Two small polyps: Fragments of tubular adenoma. Negative for high-grade dysplasia or malignancy.

Large polyp ("mass"): Tubular adenoma with small foci of superficial high-grade dysplasia. No high-grade dysplasia is seen t the cauterized margin in the plane of sectioning, but it is not possible to fully evaluate all of the margins.

Translation:

Wednesday, April 16, 2014

shit just got serious

Will I owe my life to President Obama and John Roberts?

Since roughly my 40th birthday, I've been feeling an increasing pressure to get a colonoscopy.  My family has a history with colon cancer on both sides.  My father had a polyp removed about 12 years ago, and on my mother's side, her mother and an aunt or two all ended up with colon cancer.  It actually took out my Nana, the first family death I dealt with at the age of 11.

So when Obamacare was implemented, I made it a priority to finally get a colonoscopy.  I thought it would be a wise precaution, given the family history.  But even though the family has a history, we don't have a history of early onset cancer.  So I was pretty much assuming I'd get a clean bill of health.  And when I met the GI specialist, he said that there was a 20% chance of finding something.

Well, we hit that 20%.  And three times, to boot.  Two polyps: one 9 mm and the other 5 mm in size.  Both were removed. Also, and most worrisome, there was a 25 mm "mass".  And, worse, the doctor didn't think that he got all of it when he removed it "piecemeal".  

So that's going on.

Monday, March 24, 2014

Health care costs are weird

So I recently had my first physical in a few years.  I'm a bit unfamiliar with how this works, since it's been a while.

No cost to me for the physical - I thought it might be $20, but I'm fine with that.  But it's free.

Today I got an invoice for the lab tests on blood and urine samples.  Now this gets weird.

11 different tests were done, with costs for each ranging from $33.27 to $234.30.  But CareFirst says that the "allowed costs" for these tests range from $0.62 to $8.20.  Apparently LabCorp would charge $234.30 if I did not have the clout of Blue Cross Blue Shield on my side?

LabCorp wanted to charge $1,135.85 for the tests.  CareFirst is paying them $43.53.  I pay nothing (other than my premiums.)

This whole thing baffles me.  What's up with the rest of the $1100+ of the bill?  Is this just some kind of game that everybody plays?  My insurance pays for 3.8% of the bill, and the lab writes off 96.2% of the bill?

This is a bizarre system, to say the least.

Should get to the Bill Murray reviews soon.  The Bond series is in limbo until I can find a way to re-watch the Dalton films, but they're not on cable much, and not to be found in the library system.  Bodes poorly - they are apparently the least popular.