skyking162

The big story from Week 1 of the NFL season was that most of the road teams won. Frankly, I wasn’t that shocked, as most of the road teams were obviously the better team. There was only one home team that was a significant favorites: New England. I remember that because I like to pick home favorites for my Survival League entry, and I had a damned hard time picking against my Bills right away.

This week is another tough week, because there are a lot of visiting teams who are again the favorites, but none a whole lot better than the home team. Thus, I’m declaring Week 3 Sky’s Official Upset Week. Yeah, you should be impressed.

These home teams will pull out the victory:
Minnesota upsets Chicago — The Vikings seem to have a decent defense, too, and I’m thinking the Bears are due for an offensive letdown.
Houston upsets Washington — David Carr is a much better quarterback than Mark Brunell. Get used to it. The defenses seem pretty equivalent. I’m going to assume that Samkon Gado gets the most carries for the Texans even though Ron Dayne’s starting. He will, right?
New York Jets upset Buffalo — Actually, I don’t think this one’ll happen, but I’ve got to stick to my thesis, right? That’s what a good writer does, right? They come up with a hook and stick with it no matter the consequences, right?
Cleveland upsets Baltimore — Sure, the Ravens have a great defense and sure, the Browns aren’t very good, but in games that are low scoring (that Baltimore offensive doesn’t scare anyone), anything can happen.
Denver upsets New England — This one doesn’t fit the home-team-as-underdog theme, but isn’t it about time that Jake Plummer plays well (he has been a good quarterback the past couple years, after all) and New England’s mediocre play bites them in the ass?
New Orleans upsets Atlanta — Drew Brees, Joe Horn, Deuce McCallister, Marques Colston, and Reggie Bush. If the Saints defense can stop the Falcons running game at all, they can rack up the points. Atlanta’s wins over Tampa Bay and Carolina aren’t looking so impressive as we would have assumed coming into the season, either.

These games don’t seem to have a favorite:
Cincinnati at Pittsburgh — Let’s go Bengals!
Carolina at Tampa Bay — Ugh.
Green Bay at Detroit — Ughlier.
Jacksonville at Indianapolis — Offensive shootout or defensive battle?
New York Giants at Seattle — 80% of the articles I’ve read are picking the Giants. Me, I’m going Seattle.
St. Louis at Arizona — Battle of the over-rateds.

I just can’t do it:
Philadelphia over San Francisco — The Eagles will be pissed about last week. There’s no way they don’t destroy the 49ers this week.

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Here are some observations and thoughts while watching the first round of games on opening weekend. A word of warning: as a football analyst, I’m a hack.

- The FOX pre-game show is awful. The low-light was a round of secret rapid-fire questions for the three “analysts”. The shtick was that the “analysts” couldn’t just spout off rehearsed answers. But while the questions covered exactly the topics you’d expect, nobody could string together a decent answer. Terry Bradshaw said he didn’t know which NFC East teams wouldn’t make the playoffs. Howie Long stole his Super Bowl pick from Jimmie Johnson’s notes. The only redeeming aspect was watching Joe Buck’s exasperation build over the three-minute segment. I think James Brown will be quite happy with his new digs.

- The highlight of the Bills’ season may have occurred on their first play of the season. That run defense is bad.

- Are teams catching on that running backs are subject to the whims of the offensive line? All these two running back systems say yes, they are.

- The Saints are my underdog pick of the year. Unless their O-line and defense are awful, you just can’t be that bad with Reggie Bush, Deuce McCallister, Drew Brees, Joe Horn, and Marques Colston are an excellent group of skill position players.

- The Patriots are making an early statement to earn Biggest Underacheiver of 2006. Their defense is making the Bills O-line look good and allowing the running backs to run sideways without punishment.

- Was Gary Kubiak the real brains of the Denver operation?

- Team defenses are ahead of the offenses so far.

- Maybe the Titans should have left Billy Volek as the starter.

- Call me cheesy, but I’m a big fan of all Peyton Manning’s commercials, including the new family ad that debuted on CBS today.

- I’d love to see histograms of running backs’ per-run yardage.

- I’d love to see team offensive and defensive leaders listed by yards per drive instead of per game. NBA analysts have caught on that tempo has a lot to do with points scored, why not the NFL?

- Chad Pennington and Matt Hasselbeck have been extremely efficient so far.

- My AFC playoff teams: New England, Cincinnati, Indianapolis, Denver, Pittsburgh, Baltimore.

- My NFC playoff teams: Philadelphia, Detroit, St. Louis, Seattle, Arizona, NY Giants (Had to make up for the ho-hum AFC picks.)

- Early season fantasy MVP: Jeff Wilkins

- Kevin Faulk has the catch of the year so far. Wow.

- Tatum has the early rushing edge over Mike, although Shanahan gave Mike the first touchdown in the battle of the Bells.

- Fantasy football is awful compared to fantasy baseball. The head-to-head format has grown on me, even in baseball, as it’s a great alternative in leagues where keeping in touch with friends is more important than proving your baseball acumen. But fantasy football teams are ridiculously shallow — typically 10 teams drafting 8 positions each. Realizing that kickers and defenses don’t make a difference and tight ends are barely significant, that leaves five positions to draft. Add in the fact that the sub-top-three QBs are all the same, and it all boils down to who can find three stud RBs or WRs. How fun.

- I’d fix fantasy football by expanding the rosters: 12 teams, 2 QBs, 3 RBs, 3 WRs, 1 TE, 2 K, and 2 DEF. I’d also make the benches extremely deep, so that you have to spot the breakout candidates at the draft and not wait to pick up help off the waiver wire. I’d also shift some of the importance of TDs over to yardage, including points for receptions. Defenses also can earn points for yardage allowed.

- Baseball’s fake-to-third, throw-to-first pickoff move works about as often as football’s 4th down fake-the-hard-snap-count-and-call-timeout play.

- Can we stop now with the Larry Johnson 2000 yard predictions?

- Have I sufficiently overreacted to just one week’s worth of games?

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Yesterday was my first time out on the tennis court in 2006. Along with two blisters and a three-set sweep, I picked up some alarming insight into my tennis game. I have old player skills.

In baseball, “old player skills” refer to the abilities where older players hold a relative advantage over younger players. The most obvious old-player skill is patience. According to Tom Tango?s research, a player?s walk rate peaks at age 38, on average, whereas speed skills like stolen base percentage and contact skills like strikeout rate, peak at ages 24 and 27, respectively. Bill James was the first to discuss old-player skills in his 1987 Baseball Abstract

[A]s a players age, …
…power increases as a percentage of value, not in every case but in most. Thus, power is an old player?s skill.
…he will tend in most cases to draw more walks. Thus, drawing walks is an old player?s skill.
…his batting average will almost always decrease. Thus, hitting for average is a young player?s skill.
…he tends to drive in more runs and score fewer. Thus, runs scored are a young player?s skill, and RBI are an old player?s skill.

Bill James also points out that most major league players reach the majors at age 22 or later. But most superstars reach the majors before that age. With apologies to Luis Gonzalez, not many Hall of Famers suddenly pop into existence at age 30.

While speed is a young player’s skill, it’s also critical for maintaining a majorleague career. Speed allows a player to play critical defensive positions without being an offensive star. If a player’s hitting abilities start to errode and he can?t play the field either, he doesn’t bring anything to the team.

As has been beaten to death over the past ten years, walks are good. So it would seem that a young player with a high walk-rate would be a great combination. It is, unless those walks come as part of a larger package ? the dreaded old-player skill set. A 25 year-old that plays like a 35 year-old will get old quickly — think Ben Grieve. He joined the aging curve on the downslope and rode it into oblivion. On the other hand, players with the stereotypical prospect flaws ? striking out too much, walking too infrequently, hitting doubles instead of homeruns ? they have the upward slope of the typical aging curve to help them out.

Ok, so back to my tennis game — that’s what this whole article is about, remember? My tennis skills include footspeed, quick hands at the net, consistency, and strategy. Except for the speed, every good old tennis player I know possesses exactly those skills. They can?t beat you with power or a crazy serve, but they?ll out-smart you, out-rally you, and out-think you. Add to the mix the fact that I didn?t reach the pros by age 22 and I?m almost assured of never being a superstar. What will I do without my dream? Will my tennis skills wither and die by age 30? Or perhaps the silver lining in this story is my blazing speed. Will it allow me to age well and keep up my high level of play for twenty-five more years? I hope so. After all, I plan on winning an over-70 tennis tournament. Half that battle is just staying alive.

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I threw down this challenge a few days ago: How many different ways could you fill out a 64-team NCAA bracket?

I can think of three different approaches to solving the problem, all obviously leading to the same answer. Many people would argue that it’s really the same solution looked at three different ways. I wouldn’t disagree, but having taught high school math for 2+ years, I can almost guarantee that 1/3 of a class of seniors would understand each one of these methods the first time through, but not the other two.

Approach 1: Work Forwards
Starting with the first round, there are 32 games where you must choose one of two teams. The total number of ways to make this decision is 2×2x2×2…x2 32 times — or 2^32. For each of those distinct situations, you then need to pick the 16 second round winners. There are 2^16 ways to do this. So far, there are 2^32 * 2^16 possible brackets. Bringing the third round (with eight games) into play, there are 2^32 * 2^16 * 2^8 unique brackets. Going all the way through the final game (one game, one decision) the total number of unique brackets is 2^32 * 2^16 * 2^8 * 2^4 * 2^2 * 2^1 = 2^63.

Approach 2: Work Backwards
Starting with the winner of the tournament, there are 64 options. For the runner-up, there are 32 options, because the runner-up must come from the opposite side of the bracket as the winner. For the two final-four teams that don’t make the final, there are 16 options each (these two teams must come from a different quarter (regional) of the draw than the team they lose to in the final four. So far, the total number of possible brackets is 64*32*16*16. Next, for each of the four teams that loses in the elite eight, there are 8 options, yielding a total of 64*32*16*16*8*8*8*8. Including the teams that get to, but lose in the sweet sixteen and the round of thirty-two yields a final answer of 64*32*16^2*8*^4*^8*2^16. Writing each number as a power of two yields, not surprisingly, 2^63.

Approach 3: Go Right at It
There are a total of 63 games in the NCAA tournament, as every team except the winner must lose exactly once. As such, there are 63 blanks to fill in for a bracket. For each blank, you must pick one of the two teams in the game immediately feeding into that blank. If there are two choices for each of the 63 blanks, the total number of combinations is 2×2x2x…x2 63 times, or 2^63. Didn’t see that coming, did you?

A Story About Gauss

There’s a “famous” story about Karl Frederich Gaus during his school days. His teacher asked the class to add up all the numbers between 1 and 100, thinking it was a good way to waste time (see, educational systems have always been bad.) Gauss figured out the sum almost immediately, claiming to have found a formula for adding up the numbers 1 through N, no matter what N is. The formula is N(N+1)/2 and yields 5,050 in the 1-100 example.

Why do I bring up this story? Because there are three different ways of interpreting that formula.

Interpretation One: Write all the number down on a long slip of paper and fold it in half. Each number pairs up with another number: 1/100, 2/99, 3/98, … , 50/51. Each pair adds up to 101 and there are 50 pairs. 101 x 50 = 5,050. This corresponds to the formula 100/2*101.

Interpretation Two: Take the average of all the numbers. Of course, this could require we add them all up, but it’s pretty obvious that the middle is 50.5. Then multiply by how many numbers there are: 50.5 x 100 = 5,050. This corresponds to the formula 101/2*100.

Interpretation Three: Write down the sequence once, and then a second time in reverse underneath. Each pair of values adds up to 101 and there are 100 pairs. But since we wrote the sequence twice, we have to divide by 2: 101*100/2 = 5,050.

The first explanation is what Gauss is rumored to have discovered. But either of the second two explanations is much better at explaining why the formula works for a sequence with an odd number of terms, where the midle number doesn’t pair up with another number.

Hat Tips…

… To HED for proposing the question (and answer).
… To alll math geeks out there just for being you.

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Given a 64-team NCAA field (it’s more traditional and the 65th team is pretty much irrelevant), how many unique ways can a bracket be filled out? (Yes, legally, you can’t pick a champion that you had losing in the first round. Come on, this isn’t a trick question.)

Answer coming at a later date, with three different approaches.

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