March Self Locomotion Update

1000 miles is a really long way, folks.  March was our best month yet, but we still didn't manage a 1000 mile pace.  (Not that January and February were all that impressive of months to beat.)  The weather was warmer, particularly the week where we had multiple days in the 80s.  Since then we've had a little snow and have cooled back off into typical 40s and 50s.  With the warmer weather, we'll be able to get out more consistently, particularly Shannon and the girls on walks.  For me, I've still been playing a lot of basketball, which helps toward our goal, but not nearly as much as 2 hours of running would.  As the year goes on, I may be forced to cut back on basketball to boost some running numbers.  I've also been doing some major work on my running stride and form.  I'll write more about that another day, but the end result is that I've had to cut my distance way down when I run.  But, when your run is only 10 minutes long, it's a lot easier to squeeze into the day!

The numbers:
March total: 73.66mi
Total through 3/31/12: 173.43mi
March pace: 870mi/yr
Pace YTD: 698mi/yr
Current Deficit: 72.47mi


The usual graph:

This graph makes it hard to tell that March really was significantly better than February.  So rather than showing progress vs the goal, here's a graph of the gap between the two lines.

This makes it much easier to see what our progress has been like.  Our first mistake was to get a quick 20 miles behind before we really got started.  Sickness and cold through the second half of February had a big impact, but then you can see that we held our ground pretty well through March.  It's amazing how far "behind" we get from just a day or two of inactivity.

More sports math

With the final four starting any minute now, I'd better dash off an update on my new scoring system for basketball.  The topic was introduced, and I've given several updates since.

Most valuable games thus far:

NC State over Georgetown - 18pts (11/3, 2nd round)

Florida over Marquette - 16pts (7/3, 3rd round)

Lehigh over Duke - 14pts (15/2, 1st round)

Norfolk St. over Missouri - 14pts (15/2, 1st round)

Louisville over Michigan St - 13 pts (4/1, 3rd round)

Ohio St over Syracuse - 12pts (2/1, 4th round)

Kansas over UNC - 12pts (2/1, 4th round)

Ohio over Michigan - 10pts (13/4, 1st round)

Point values from possible outcomes:

Final Four:

   Louisville over Kentucky - 31pts (4/1, 5th round)

   All other results - 16pts

Championship game:

   Louisville win - 44pts (4/2, 6th round)

   Ohio St or Kansas over Kentucky - 38pts (2/1, 6th round)

   All other results - 32pts

We can see that despite adding the bonus points for upsets, the most valuable games are still those in the later rounds.  We have, however, greatly increased the reward for correctly picking upsets correctly.  The two 15/2 upsets in the first round this year were each about as valuable as correctly picking a 1 seed to win a final four game.  The championship game will still be the most valuable single game this year, as is probably should be.  My bracket only managed to get a single final four team this year (which is about average for me, sadly); it's easy to tell that some teams are pretty good, but not always easy to figure out which ones will win 4, 5 or 6 games in a row.  A perfect bracket up until now would be worth 247 points.

The other big question though is how this scoring system impacts bracket pools.  As my office pool used my new scoring system this year, they're my test sample.  15 brackets were filled out (I'm winning the non-paying division!).  For anonymity purposes, we'll call these people #1 through #15.  I'm also adding someone named "Chalk" which would be the result from picking every higher seeded team to win.

Person     Score     Traditional Score    Traditional Rank

1               112                 79                        3

2               108                 77                        5

3               108                 82                        1

4                98                  77                        5

5                93                  79                        4

6                88                  80                        2

7                77                  66                        8

8                73                  53                        11

9                70                  63                        9

10              70                   50                       12

Chalk         68                   68                        7

11              61                   37                       16

12              60                  54                        10

13              59                  50                        12

14              58                  50                        12

15              53                  45                        15

If the formatting isn't too terrible, we can see that changing the scoring system doesn't drastically change who did well and who didn't.  The max movement by any individual was 4 spots.  As 'Chalk' didn't pick up any bonus points, obviously he moved down, and it's nice to see that instead of being slightly above average (7th) we bumped this hypothetical individual down 4 spots.  As it turns out, the scoring system won't change who wins our competition, though it could have.

NCAA math: Round 1.25 update

Round 1 started off so boring.  Only 2 upsets on Thursday with just a 12/5 and an 11/6 upset.  Obviously that changed in a big way on Friday.  With Saturday games now half over, here's an update of the highest scoring games with my new scoring system:

Most Valuable Games:

Lehigh over Duke - 14pts (15/2, 1st round)

Norfolk St. over Missouri - 14pts (15/2, 1st round)

Ohio over Michigan - 10pts (13/4, 1st round)

Temple over USF - 8pts (12/5, 1st round)

VCU over Wichita St - 8pts (12/5, 1st round)

Colorado over UNLV - 6pts (11/6, 1st round)

NC St over SDSU - 6pts (11/6, 1st round)

98 points total were possible in the first round.  As #15 seeds were on a combined 4-104 streak, you probably didn't pick either of them, and therefore max out at 70 points, even if you got everything else, which represents about 70% of the possible points.  (Whereas with the traditional scoring, you'd only be out 2/32 points, or about 6%.)  So far 4 games are complete in the second round, with out an upset yet.  Perhaps a boring Saturday with mayhem on Sunday?

I haven't really had time to calculate lots of different brackets and look at the results.  The weather has been too nice to sit at the computer all day.  (I only sat in front of it for half the day!)

Bracket Math: Day 1

I've got limited amounts of free time that aren't taken up by Starcraft, but here's a quick update.

 

First off, I'll point out that Shannon got 15 of the 16 games right on the first day.  I think I got 10.  But more importantly, what is the impact of the new scoring system?  Well, the system rewards upsets, and for a while, I was afraid there wasn't going to be a single upset in the first day of games.  VCU managed to hold off Wichita State for the first 12/5 upset, and then Colorado beat UNLV (11/6 upset) in the last game of the night.

 

Most Valuable Games:

VCU over Wichita St - 8pts (12/5, 1st round)

Colorado over UNLV - 6pts (11/6, 1st round)

All other 1st round games - 1 pt ea (14 games, 14 points)

 

Total points thus far: 28.

 

Early on, we can start to see the large effect that the bonus points for upsets has.  If you picked every better seed to win yesterday, you'd have gotten 14/16 games right for 14 points.  If you picked every lower seed to win, you'd also have 14 points.  Both would have been somewhat foolish predictions (100% upsets being much more foolish) and would have yielded equally.

 

My concern, however, is this: either foolish method would have been better than me.  I got 10 games right, but neither of the upsets.  Now, me losing in bracket challenges to foolish people is a long-standing tradition, so that isn't a problem in and of itself.  But consider instead someone who recognizes that there is about 1 5/12 upset each year in the tournament.  Rather than trying to predict which 1 or 2 12-seeds will pull it off this year (like I did), why not just pick them all?  If you get 1 right, you get 8 points.  2 gets you 16.  And if you are wrong on them all, you only miss out on 4 points.  As I've mentioned, I think more analysis is warranted, but for now, my gut says that the upset bonuses are too high.

 

A mitigating thought: I think that bracket "goodness" ought to mirror the excitement of the tournament itself.  There are two primary components that make the tournament interesting, even if your team isn't involved.  One is good basketball and crowning a champion and all that, but the other is the early upsets.  (You know, those Cinderellas that the TV announcers can't stop speculating about.)  Picking VCU to win probably wasn't 8 times more difficult than picking Wichita State.  (Kenpom gave VCU a 22.8% chance.)  But VCU winning might be 8 times more exciting than a world with no upsets.  Sports nerd-dom is good and all, but the excitement is what gets so many people (even Shannon) involved.

 

p.s. I think with my new scoring system, the maximum possible points in a tournament would be 863.  (Unless, of course, you can find a higher arrangement.)  I haven't checked all the possibilities, as that can't be done by brute force with any computer I have access to.  (Or any computer at all, at least not without using logic to make some very significant reductions in the number of calculations that need to be made. (Which is probably possible, but I haven't done it.  My method was one of some superficial logic and trusting my mathematical gut.))  Total points possible in last years bracket was 410, for comparison.

It's about 30 degrees (F) hotter than usual at my house.  How's the weather where you are?

Sport Nerd Challenge

The time has come for NCAA basketball tournament brackets.  People across the country are devoting untold hours researching and discussing basketball this week.  Hundreds of millions of dollars will exchange hands.  But I have a nerdier question that simply who will win basketball games.  I want to know what the best way is to determine who wins the brackets.

 

Now, "best" is a subjective term here.  So my idea here is that a non-zero number of you will submit a scoring system for dealing with bracket picks, along with an argument as to why that scoring system for brackets is superior to all others.  Some definition of what your overall purpose is may be necessary in your justification.  I present below a few common scoring systems, along with a brief discussion of some pros and cons.

 

Note: For all discussion here, the "first four" games are ignored and the 32 Thursday/Friday games are considered Round 1.  (This is not a requirement for your comments, but simply what I'll be doing.)

 

System #1: 2^(Rd#-1)

This is the most common scoring system.  Each game within a round is worth the same number of points, and each round is worth the same total number of points (32).  This system is simple, easy to implement, and widely accepted.  But if the best argument for something is simply that doing it differently is hard, that's not very convincing.  In general, games in the later rounds do need to be worth more than games in the earlier rounds; at the time of picking, we don't even know who will be in the championship game, let alone who will win, so picking the winner is fairly difficult.  However, this system awards the same number of points for getting the winner correct as for getting all 32 games correct in the first round.  Which is harder?  I suspect that any given year a non-trivial percentage of brackets get the winner right, perhaps varying from 5-20%.  However, how many get the entire first round correct?  Out of the millions of brackets entered on ESPN.com, only a very small handful.  So, what is more deserving of 32 points last year, picking UConn to win it all, or picking Butler, VCU, Gonzaga, Richmond, Florida State, Morehead St and Marquette to win, while at the same time not picking Princeton, Michigan St, Memphis or Missouri to win?  The tougher task should be rewarded accordingly.

 

System #2: Rd#

The next most common and simple system is increase the value of each game by one point in each round.  Rather than increase geometrically (1, 2, 4, 8, 16, 32), they increase arithmetically (1, 2, 3, 4, 5, 6) which serves to over-emphasize the opening rounds.  Again, I think the important question is to ask which is harder: guessing the champion, or getting an additional 6 games right in the opening round?  A further downside to this scoring technique is that is allows some people to build large advantages early on, which become almost insurmountable later; the contest isn't too exciting if the championship game isn't enough to bring you back significantly.  System #1 has the opposite problem, of course, where there is almost no lead that is safe: the final 2 victories of by the champion are worth 25% of the total points available, which generally corresponds to well over 1/3 of any individual score.  It doesn't seem right that such a huge percentage of your points hinge on the final 2 games in a 63 game tournament.

 

System #3a: Seeds

System #3b: Difference in Seeds

The idea behind these systems are to award risks by offering bounties for picking upsets.  A point value of a victory by a given team is equal to that team's seed, i.e. a 12/5 upset is worth 12 points.  (Or, in system 3b, it would be worth 7 points.)  Victories by favored (or evenly seeded) teams are worth a single point.  These systems risk over-valuing upsets to the point that bracket pickers are encouraged to simply pick every upset.  Statistically, a few will hit, and if the bonus is big enough, it doesn't matter that you missed on the majority of them.  A scoring system shouldn't favor mindless picking of lower seeded teams any more than it should favor mindless pick of higher seeded teams.

 

So where does that leave us?  Its time to start combining the best aspects of the various systems.  Pay attention here, because the math gets slightly trickier.

 

System #4: 2^(Rd#-1)+(Seeding Difference)*Rd#

This is just system #1 with an added bonus for getting upsets, which scales through the rounds.  Picking 11-seeded VCU to win in the first round last year would have required guts (and luck) so we want to reward that with more than a single wimpy point.  So you get 1 point, plus the difference between their seed (11) and their opponents seed (6), for a total of 6 points.  But to pick them to win a second game?  Even less likely.  So, their victory over the 3 seed was worth 2^(2-1)+(11-3)*2 = 2+16 = 18 points.  But here is where the quirk of this method kicks in.  In VCUs next game, they played 10th-seeded Florida State (having just knocked off the 2-seed (ND)).  VCU was (by seed) basically a coin flip to win the game, so that victory was worth only 2^(3-1)+(11-10)*3 = 4 + 3 = 7 points.  Perhaps the craziest thing about a system like this is that going into the tournament, it is impossible to know how many total points there are going to be, and that victories in different rounds can be worth very different amounts.  The most valuable win last year would have been VCU's next game where they beat 1-seed Kansas for a 48 point victory.  (That's 2^(4-1)+(11-1)*4 = 8 + 40 = 48 points, if you didn't want to work that out in your head.)  The final game, as it wasn't an upset, was worth 32 points, which tied with Butler's upset of Florida.  The next most valuable games were 3 2nd round upsets at 18 each.  This system certainly gets hard to track in your head, because so many different things can happen, and opponents affect point values.  A weakness is that the 8/9 games become fairly mindless.  9-seeds actually have a slight advantage historically, and a victory over a 9 seed is worth 2 points, whereas the 8 seed winning is only worth 1.  You really should just pick all the 9s.  However, this is only going to net a few points, which probably won't be too consequential.  (A perfect bracket in last year's tournament would have been worth 410 points, though, if Butler had won the final, it would have been worth 30 more points than the UConn win.)

 

So, what have I missed?  What crazy idea do you like?  (And yes, I know the tournament starts in earnest in about 36 hours.)

Self Locomotion Update

Though it was a day longer, February has ended anyway.  Here's the update in our family quest to propel ourselves forward 5,280,000 feet this year.

General Update:  The first half of the month went really well.  We were on a 1000 mile annual pace for the first two weeks, aided by lots of walking around Chicago.  Shannon and I each did about 4 miles each of the two days we were there.  Remember, walking to a museum counts, because it would have been reasonable to take a car, bus, train or cab there if we had wanted to.  Walking inside a museum doesn't count.  The second half of the month we got busy, basketball got cancelled (remember 1 hour of basketball = 1 mile in my world), and then I got sick.  So, we fell right back off to essentially the same pace as we had in January.

Numbers:
February total: 47.92mi
Total through 2/29/12: 99.77mi
February pace: 605mi/yr
Pace YTD: 609mi/yr
Current Deficit: 64.2mi