Wednesday, December 29, 2010

Quarterback Rating

The NFL has a QB rating, a composite statistic that combines yards, pass attempts, completions, touchdowns, and interceptions. Unfortunately, it's kinda arbitrary. In an effort to fix that I present an estimated points added statistic, which includes all of the above.

The basis for EPA is that at any given point on the field a team has an average number of points they'll get. At their own 20, it's about 0, at their opponent's 20 it's around 4 (for first and 10). 15 yards adds about a point. A turnover at the line of scrimmage is then -4 points (so -3 for a 15 yard interception). Similar values can be obtained for the other achievements. Here's the components:
One yard: 1/15
Interception: -3
Touchdown: 3
Attempt: -2/5
Completion percentage-60 (average): completions/150
It doesn't make total sense at first, but the results do. Here they are:

Player EPA PPG Wins
Philip Rivers 160.54 10.7 4.01
Tom Brady 158.89 10.6 3.97
Aaron Rodgers 129.14 9.23 3.23
Drew Brees 104.64 6.98 2.62
Michael Vick 101.44 8.47 2.54
Peyton Manning 100.3 6.69 2.51
Matt Cassel 99.6 7.1 2.49
Joe Flacco 97.22 6.48 2.43
Matt Schaub 93.38 6.21 2.33
Josh Freeman 85.41 5.69 2.14
Ben Roethlisberger 79.82 7.24 2
Jay Cutler 78.63 5.62 1.97
Kyle Orton 74.99 5.77 1.87
Matt Ryan 71.58 4.77 1.79
Eli Manning 71.25 4.76 1.78
David Garrard 66.95 4.77 1.67
Carson Palmer 51.13 3.4 1.28
Jon Kitna 50.41 5.05 1.26
Ryan Fitzpatrick 43.86 3.38 1.1
Tony Romo 43.17 7.21 1.08
Jason Campbell 37.89 3.16 0.95
Donovan McNabb 30.22 2.33 0.76
Shaun Hill 24.14 2.42 0.6
Chad Henne 21.06 1.51 0.53
Alex Smith 20.9 2.09 0.52
Mark Sanchez 18.96 1.26 0.47
Sam Bradford 15.32 1.02 0.38
Kerry Collins 13.71 1.52 0.34
Matt Hasselbeck 7.29 0.52 0.18
Brett Favre 0.93 0.07 0.02
Derek Anderson -11.48 -0.96 -0.29
Jimmy Clausen -40.12 -3.35 -1

The best quarterbacks in the NFL are right at the top, as they should be. The PPG column accounts for some quarterbacks (Vick, Romo) not playing all their games. Most useful though is the wins column, which divides EPA by 40 (as shown earlier in the week) to get the expected wins added by a player over a replacement quarterback. For example, with his 4 wins added Tom Brady has taken the Patriots from the border of the playoffs to being the best team in football. Sounds like an MVP to me.

NFL Parity

Through 15 of the 16 games this season things have finally ironed out and the better team has started winning. It still seems though that the NFL has more parity that ever. The Chicago Bears already have a first round bye clinched with just 11 wins? The Vikings on their 3rd string QB can beat the Michael Vick led Eagles? These aren't normal in the NFL. Turns out, this year is surprisingly different.

In 2007 and 2008 the better team won 80% of the time in the NFL. It took a slight dip in 2009 down to 78%, but that may have been due to the last couple weeks when many of the top teams rested their starters. This year though variance says the better team wins only 74% of the time. That sort of drop is almost unheard of in professional sports, where the number usually changes at most 1% from the average. Is it the salary cap free year? Or maybe concussions taking the best players out of games? Could it be just chance? At the very least, it's a trend worth watching in the upcoming years.

Sunday, December 26, 2010

How many points for a win?

It's known among sabermetricians that if your baseball team can add 10 extra runs over a season you'll win another game (on average of course). This is useful because it's relatively easy to show that a player can add or remove runs from a team.
In basketball the corresponding number is 30 points (according to John Hollinger), which isn't quite as useful, but it's still not too hard to estimate the number of points a player adds.
I haven't found the number for football, so I decided to figure it out myself. Using linear regression on excel to relate point differential to wins I got the following data:
2009- 40 points
2008- 35.7 points
2007- 38.5 points

About 40 points in one season is a win? Sounds good to me. We'll show how useful this is later in the week.

Wednesday, December 22, 2010

89 Games

Congratulations to the UConn Huskies women's team on their 89th win, eclipsing the Wooden/Walton UCLA teams from the early 70s. I'll admit, I was rooting against them. Not, as Geno would suggest, because of some hatred for women's athletics but because as a Stanford fan the UConn Huskies are the Lakers/Yankees/Patriots of the sport.

Some people have made a big deal about comparing the records of UCLA and UConn and their 88 and 89 game win streaks respectively. UConn's streak is great, but it's true though Women's basketball has less competitive balance right now than Men's basketball. How does it compare to the UCLA teams, and even streaks in other sports? I can answer that.

I'm going back the the Random Chance in Sports stuff here, and examining how often the better team wins in women's basketball. The chances then of the best team winning 89 straight are .844^89. In men's basketball (by the same method) the best team wins 80.8% of the time, and in the early 70s they won 80.1% of the time (those numbers are close enough to be the same thanks to errors). To have the same unlikelyhood as UCLA's streak, the UConn women would have to win 115 straight games. Here's a look at how other sports compare (UConn column is what it would take to match the Huskies, UCLA is to match the Bruins):

Uconn UCLA Longest
WCBB 89 115 89
MCBB 71 92 88
CFB 90 116 47
NBA 56 72 33
NFL 65 84 21
MLB 29 38 21
NHL 29 38 17

So the Huskies haven't yet matched what the UCLA men did, but their streak is far better than any other sports win streak. Maya Moore and company have played some incredible basketball, but Wooden's teams were amazing (7 straights NCAA championships!!). Now if you'll excuse me, I have to go make myself lunch in the kitchen.

Tuesday, December 21, 2010

A Comfortable Margin

I was watching a rerun of Winning Time on ESPN the other day, which was highlighted by Reggie Miller's 8 points in 9 seconds to beat the Knicks, all after Pacers owner Donnie Walsh had given up and retreated to his smoking room. The Knicks had been up by 6 with about 30 seconds left, was it reasonable for Walsh to leave? At what point in a game can you feel safe your team will win?

Just by observing basketball, a few years ago I had decided 6*(n)^.5 (where n is minutes left and n^.5 is the square root of n) was a good amount. If you were up by 6 or more with 1 minute left, 12 or more with 4 minutes left, 18 or more with 9 minutes left, etc. you'd be pretty safe.

Turns out the square root of n is pretty accurate. That's because the chance a team recovers a given amount of points depends on the standard deviation of the distribution of points. Standard deviation is the square root of variance, and variance can add. So the if the variance of 1 minute is V then for 2 minutes it's 2V, for 3 it's 3V, etc. So the variance is some constant k times n, and standard deviation is (kn)^.5, which is proportional to the safe margin.

Is the 6 constant accurate? Let's take a look at things on a per possession basis. The variance in one possession, based off of last year's numbers, is 1.22. In the final minute there are an average of 6 possessions total (more than the usual 4 or so), so the variance in the final minute is 7.3, and standard deviation is 2.7. Multiplying by 2.33 (so we're 99% sure, it's from z tables) we get 6.3, which is our final constant. 6.3!

Turns out 6*n^.5 was a pretty good guess, and accurate enough to use. It won't always work (it'll probably be a little less than 99% because one possession is not normally distributed), but it's a pretty good guide on when you should head back to your smoking room. Unless of course the other team has Reggie Miller.

Wednesday, December 15, 2010

Streaks in the NBA

Even without much press for the Bulls and their 7 straight wins there's been a lot of coverage of win streaks so far this season. How unusual is it that teams win 10 in a row? It's not as easy to calculate because assuming a 50% chance of winning makes streaks unlikely. It's easier to win 10 games in a row if you're the favorite than if you're even. What we're gonna use then is the number from Random Chance In Sports which say the better team wins 77% of the time in the NBA. From that we know even the best team in the league has only a 7% chance of winning it's previous 10 games. From other (rough) approximations we can learn there's roughly a 20% chance of any team in the league being on a 10 game winning streak. On average there should be one 6 game winning streak, and one that's longer (about 8 games), which is less than our current and recent win streak total. One possibly reason is the stratification of the Eastern Conference. The few really good teams can beat up on the really bad teams, leading to long winning and losing streaks (Celtics and Heat vs Cavs and Nets). We can also dig in deeper for certain teams:
Chicago Bulls: 7 wins
They've got Carlos Boozer back, and the team is working well. Unfortunately it'll be a while till we see everyone again with Noah's surgery.
New York Knicks: 8 wins (just lost)
It sure helps to have the easiest schedule in the league (average opponent: The Toronto Raptors). They've played will, but they're not gonna get out of the first round of the playoffs.
Miami Heat: 10 wins
They've won 10 straight because they've become Dwyane Wade's team. The offseason was full of "Lebron is #2" jokes, but it might actually be the truth. Wade has averaged 25.3 ppg in wins (27.3 on the streak), but just 18.7 in losses. Lebron has averaged 23.2 ppg in wins (24.9 on the streak) and 26 in losses. So they are gelling better, but it's because Dwyane is now the alpha dog.
Boston Celtics: 11 wins
11 straight wins happens normally if you have 4 hall of fame starters and the 5th is an MVP candidate. Especially with a little schedule break and some luck.


Monday, December 13, 2010

Bowl Predictions

Espn anchors were all putting their bowl predictions today, and while I like neither the bowl systems nor worthless games like Ohio vs Troy, I do like predictions so I'll join the fray. These predictions are a little different though, they're based off my original rating, so instead of a score they give a percent of winning. From most lopsided to least, here are this year's bowl predictions (in small print, I'm sorry, but that's the only way it fit):

Bowl Winner Pct Loser Pct
Fiesta Oklahoma 0.859 Connecticut 0.141
Las Vegas Boise St 0.834 Utah 0.166
Holiday Nebraska 0.802 Washington 0.198
Kraft Nevada 0.784 Boston College 0.216
New Mexico Brigham Young 0.775 UTEP 0.225
Capital One Alabama 0.759 Michigan St 0.241
Orange Stanford 0.746 Virginia Tech 0.254
Rose TCU 0.728 Wisconsin 0.272
Military Maryland 0.726 East Carolina 0.274
Hawai'i Hawai`i 0.691 Tulsa 0.309
Outback Florida 0.689 Penn State 0.311
BCS Champ Oregon 0.665 Auburn 0.335
Pinstripe Kansas St 0.655 Syracuse 0.345
Sugar Ohio State 0.654 Arkansas 0.346
TicketCity Texas Tech 0.652 Northwestern 0.348
BBVA Compass Pittsburgh 0.651 Kentucky 0.349
Meineke Clemson 0.627 South Florida 0.373
GoDaddy.Com Miami OH 0.625 Middle Tennessee St 0.375
St. Petersburg Louisville 0.622 Southern Miss 0.378
Insight Missouri 0.614 Iowa 0.386
Liberty Georgia 0.612 Central Florida 0.388
Independence Air Force 0.603 Georgia Tech 0.397
Gator Mississippi St 0.598 Michigan 0.402
Texas Illinois 0.597 Baylor 0.403
Humanitarian Northern Illinois 0.59 Fresno St 0.41
Armed Forces SMU 0.571 Army 0.429
Alamo Oklahoma St 0.555 Arizona 0.445
Little Ceasars Toledo 0.553 Florida Int'l 0.447
Champs Sports West Virginia 0.547 North Carolina St 0.453
Music City North Carolina 0.543 Tennessee 0.457
Cotton Texas A&M 0.539 LSU 0.461
Poinsettia San Diego St 0.528 Navy 0.472
Chick-fil-A Florida St 0.519 South Carolina 0.481
New Orleans Ohio U. 0.514 Troy 0.486
Sun Notre Dame 0.504 Miami FL 0.496

Some of these games are pretty set, but some (like the worthless Ohio vs Troy game) are pretty much tossups. Fortunately though, it's pretty easy to know what to expect. Adding the expected wins I should expect to get 22.53 games right. The standard deviation is 2.78 wins, so I can be pretty certain that I will get between 20 and 25 games right (inclusive). Only time will tell for sure.

P.S. I accept challengers. Keep track on your own and let me know.

Sunday, December 12, 2010

What Happened To The Iowa Hawkeyes?

A promising start suddenly turned into a 7-5 season with a challenging bowl game still ahead. How did that happen? What went wrong? How did a team that was supposed to improve play so much worse than last year? Here's the secret: they didn't. The Hawkeyes this year are just as good as they were last year.

2009 2010
Ranking 22 22
Point Diff 7.6 12.7
Exp Wins 8.97 9.37
Wins 11 7
Luck 2.03 -2.37

The Hawks have actually been more dominant this season increasing their point differential by over 5. They've played a slightly easier schedule though, so their ranking by my system is exactly the same, 22nd. The only difference is that they've gone from one of the luckiest teams in football to one of the unluckiest. Just look at their record in games decided by 5 or less: in 2009 they were 4-1, but in 2010 they've been 1-4. Just as I said before the season started luck doesn't transfer between years.
Some of you might point to a final loss at Minnesota as a sign that Iowa wasn't as good this year, losing by 3 in a game they one easily last year. Yes it was a horrible loss, but it's easy to forget how close the Hawks were to those types of losses last year against UNI (a win by 1) and Arkansas State (a win by 2).
I warned at the beginning of the season not to get too high on the Hawks, and I'll say the same now: don't get too low on them. They were unlucky this year but they'll be back strong again in 2011.

Friday, December 10, 2010

Pau Gasol vs Scottie Pippen

There are some silly people out there who've tried comparing Kobe Bryant and Michael Jordan. It's not a contest of course, MJ is the G.O.A.T. and Kobe hasn't ever been the best in the league. A more interesting contest is between their number 2s, Scottie Pippen to MJ and Pau Gasol to Kobe. It sounds absurd at first to compare Pau and Scottie, but Pau is one of the most under rated players in the game today and Scottie was over rated in his time.
First off, let's look at their place in my Top 5 ratings. Pau never shows up in the top 5 of any year. Pippen is the 4th best player in 93-94, but that was his best year and more importantly he was his teams star that year (MJ was playing baseball). Still, the edge here goes to Scottie.
Next, let's look at PER, a John Hollinger special. Specifically, let's look at their 3 best years as a #2.
Pau: 22.2 (08-09) 22.9 (09-10) 24.0 (07-08 and this year).
Scottie: 21.0 (95-96) 21.3 (96-97) 21.5 (91-92)
Admittedly, PER undervalues defense some, but the according to Hollinger's stats Pau is still better.
How about Win Shares? Here's each's three best years again.
Pau: 13.9 (08-09) 12.0 (05-06) 11.0 (09-10)
Scottie: 13.1 (96-97) 12.7 (91-92) 12.3 (95-96)
When he plays Pau is better, but thanks to his durability Scottie is more consistent. It's a pretty even draw.
One for Scottie, one for Pau, and one tie makes the two pretty even. Looks like it's a tie, which in a way makes sense. Kobe tried to match Mike with a great #2, a crazy guy (Artest for Rodman), a high level 6th man (Lamar Odom for Toni Kukoc), and of course Phil Jackson. All Kobe has to do now is win 72.

Sunday, December 5, 2010

College Football Top 25 12/5

There weren't many games this weekend, but the few that happened were big ones. Conference championships and rivalry games are often ripe with upsets, but not this weekend. Auburn impressed in their victory over South Carolina, but other than that things stayed roughly the same. Here's the Top 25:

Rank Team W L Rating
1 Stanford 11 1 636.37
2 Oregon 12 0 542.97
3 Boise St 11 1 525.48
4 TCU 12 0 461.33
5 Ohio State 11 1 395.29
6 Alabama 9 3 340.22
7 Auburn 13 0 274.84
8 Oklahoma 11 2 270.74
9 Missouri 10 2 236.33
10 Virginia Tech 11 2 216.21
11 Nebraska 10 3 212.35
12 Arkansas 10 2 209.14
13 Oklahoma St 10 2 206.51
14 Texas A&M 9 3 189.93
15 Florida St 9 4 183.7
16 Wisconsin 11 1 172.48
17 South Carolina 9 4 170.41
18 Arizona 7 5 165.38
19 LSU 10 2 162.8
20 Arizona St 6 6 150.12
21 Nevada 12 1 149.05
22 Iowa 7 5 148.86
23 Southern Cal 8 5 136.31
24 West Virginia 9 3 133.95
25 Florida 7 5 131.44

Auburn managed to jump a couple spots up to 7th in the rankings. Why are they only 7th still? Their multiple close games against teams early in the season still weigh them down, and point to a possible flaw in these rankings: teams are assumed to have the same level of talent throughout the season. Auburn on the other hand appears to have improved significantly as we got farther into the season (although I still don't think they're on the level of teams like Oregon and Stanford). We'll find out in the championship game between the Ducks and the Tigers, only a month away.

I'd also like to point out that Connecticut, which is in a BCS bowl, is ranked 59th. Maybe it's time to get rid of automatic qualifiers.

Ron Santo

On December 2nd Chicago Cubs great Ron Santo passed away at the age of 70. Possibly the greatest player ever not to be in the Hall of Fame, Santo played in 9 all-star games at 3rd base during the 60's and early 70's. Statistically, a quick look at shows that he matches up pretty evenly with the average hall of famer, and fairs even better in advanced statistics like Win Probability Added. As he showed in his broadcasting career though, Ronnie was never about just numbers, he was about love of the game, and love of the Chicago Cubs. And Cubs fans in return loved Ronnie:

And some great radio highlights of Ron Santo:

RIP Ron Santo 1940-2010

College Basketball Debut

Because I don't have enough to do already during finals week I have decided to debut my college basketball rankings for both Men's and Women's basketball. They are under the tabs up top like other rankings (there are more teams for the guys to accommodate the rankings compilations and trackers, thanks again going to the guys who run those). They'll probably be updated about every week or so throughout the season, along with some occasional commentary (especially for the women). Here's the top 10 for each:

For the guys:
Rank Team W L Rating SOS
1 Kansas 7 0 29.765 1.626
2 Ohio St 6 0 20.975 1.444
3 Duke 7 0 19.556 1.706
4 Pittsburgh 8 0 19.54 2.532
5 Arizona 6 1 16.082 1.192
6 Kentucky 5 1 15.818 2.749
7 Louisville 5 0 15.23 1.177
8 UNLV 7 0 13.996 1.487
9 Washington 4 2 13.517 1.755
10 Tennessee 6 0 11.647 2.752

The good news for Stan is that his Huskies, despite two early losses, are still on track to be a top level team. The good news for the Iowa Hawkeyes (and Jordan Stoermer) is that even before their victory over Idaho State tonight they still crack the top 100 at number 97.

For the girls:
Rank Team W L Rating SOS
1 Connecticut 7 0 53.917 2.746
2 Texas A&M 5 0 40.713 2.172
3 Baylor 8 1 37.951 1.788
4 North Carolina 8 0 27.79 0.868
5 Tennessee 7 1 25.83 2.768
6 Duke 8 0 25.593 3.234
7 West Virginia 7 0 21.915 1.878
8 Stanford 5 0 20.055 3.692
9 WI Green Bay 7 0 18.568 1.581
10 Ohio St 6 0 17.032 2.3

As expected from their early season troubles, the Stanford women are only in the eighth spot right now due to some early close games. UConn is still the team to beat, despite the loss of Tina Charles. Thanks to some great Kelly Kane impersonations over the last week though, the Cardinal should be ready for the upcoming stretch of four games against top 20 out of conference teams. One game of note, Stanford plays UConn on what would be the Huskies 88th straight win, equaling UCLA's record for most consecutive victories in college basketball.

Saturday, December 4, 2010

Games of December 4

Again, this may be a little late, but I had to beat Spence at racquetball this morning. I promise I haven't looked at scores yet (and again, it's all the math anyways). Here's hoping that either A)The predictions all go well this week or B) Auburn loses.

Washington 26 Washington St 23
It wasn't what Jake Locker and the Huskies were hoping for, but Stan should be proud to go out on a bowl qualifying note.

Auburn 32 South Carolina 28
Computers say this is going to be a close game. There's still hope for TCU.

Oklahoma 29 Nebraska 26
This game might decide who Stanford gets to play in their bowl game.

Oregon 38 Oregon St 23
Oregon St may be underperforming this year, but their still just not good enough to defeat the mighty Ducks.

Virginia Tech 25 Florida St 24
Despite being in the ACC this should be a great football game between two good teams.

Central Florida 28 SMU 16
This game already happened, and I was pretty close! Sorry Uncle Mark, maybe a better season will be coming around the mountain next year.

Last Week: 3-4 (Dad was 5-2)
This Season: 40-22

Sunday, November 28, 2010

College Football Top 25 11/28

Boise State lost their first game of the season, throwing the rankings for a loop (we're not gonna talk about Iowa). On the other end though, Stanford dominated a good Oregon State team. What's the payoff? Take a look.

Rank Team W L Rating SOS
1 Stanford 11 1 661.75 80.31
2 Oregon 11 0 568.29 57.06
3 Boise St 10 1 549.55 36.42
4 TCU 12 0 481.89 26.21
5 Ohio State 11 1 418.07 39.43
6 Alabama 9 3 344.51 55.54
7 Oklahoma 10 2 281.27 74.29
8 Missouri 10 2 245.19 53.65
9 Auburn 12 0 221.93 61.89
10 Nebraska 10 2 221.1 46.44
11 South Carolina 9 3 213.89 63.61
12 Arkansas 10 2 213.52 55.75
13 Oklahoma St 10 2 210.48 50.59
14 Virginia Tech 10 2 210.14 42.9
15 Texas A&M 9 3 199.78 72.04
16 Florida St 9 3 199.09 53.78
17 Wisconsin 11 1 181.14 34.47
18 Arizona 7 4 174.44 72.56
19 LSU 10 2 163.74 59.33
20 Iowa 7 5 157.77 44.34
21 Arizona St 5 6 154.18 77.87
22 Nevada 11 1 150.54 26.7
23 Southern Cal 7 5 139.44 104.72
24 West Virginia 8 3 137.5 35.3
25 Florida 7 5 135.75 67.95

That's right, Stanford is now the best team in the nation. After a couple of dominating wins against pretty good teams the Cardinal have established themselves at the top of the rankings. There's a lot of excitement about being #4 in the BCS, but Stanford may be sold short by that. Should a team ranked that high, well higher than Auburn, get a shot at the championship game? To look at that we have to take a look at the no MoV rankings, which aren't for predicting, but instead evaluate what a team has accomplished.

Rank Team W L Rating SOS
1 Auburn 12 0 27.65 6.91
2 Oregon 11 0 25.63 6.4
3 Oklahoma 10 2 25.24 10.01
4 Stanford 11 1 23.96 7.54
5 Missouri 10 2 23.37 9.27
6 TCU 12 0 22.46 5.61
7 Texas A&M 9 3 21.03 10.51
8 Oklahoma St 10 2 20.05 7.95
9 LSU 10 2 19.49 7.73
10 Arkansas 10 2 19.09 7.57

Stanford now sits at 4 (sounds familiar), but the number 1 and 2 are Auburn and Oregon, just like the BCS. Maybe there'll be some upsets next week, but if not the nation's best college football team will have proved it all too late.

Friday, November 26, 2010

BCS Week- If We Had Playoffs

What would the playoffs look like if my proposal was in place today?
Because all 4 undefeated teams are in the BCS top 6, the 6 teams selected for the playoffs are just the BCS's top 6, in order.
4-Boise State

Oregon and Auburn would get first round byes, then TCU would play Stanford and Boise State LSU in the first round. Here are the odds of each team making it to various rounds:
Into Semis Into Finals Champion
Oregon 1 0.514 0.29
Auburn 1 0.295 0.085
TCU 0.503 0.355 0.174
Boise St 0.784 0.431 0.263
LSU 0.216 0.054 0.017
Stanford 0.497 0.349 0.17

Oregon would be the favorite thanks to the bye, with Boise St. right behind them. TCU and Stanford are fairly equal, and Auburn would have an outside shot. LSU would just enjoy getting to the playoffs.
This post wraps up BCS week, and it's time to move on and figure out how Auburn keeps winning. Plus, it's time for some basketball. Anyways, I hope everybody has enjoyed a full week of posts.

Games of November 26th/27th

It's still the end of BCS Week, and the middle of Thanksgiving weekend, but it's time to predict the games that are happening this weekend. Seeing as I'm home in Iowa, I'm also including my dad's predictions (in italics).

Iowa 33 Minnesota 14
Iowa 29 Minnesota 9
The Hawkeyes should finally be able to safely win a game.

Stanford 37 Oregon St 21
Stanford 44 Oregon St 17
There won't be any home fans because we're all on turkey break, but the Cardinal will still take care of business.

Alabama 32 Auburn 25
Alabama 21 Auburn 17
This is the game I've been looking forward to for a month. The game where Boise St. makes it to the championship.

Oklahoma St 34 Oklahoma 33
Oklahoma 36 Oklahoma St 30
These two Big 12 juggernauts are battling for the state and conference title. With a good win, Ok St could thrust itself into the BCS spot light.

Arkansas 30 LSU 25
Arkansas 28 LSU 24
I don't like picking two SEC teams, but this is another great game that will likely have an upset.

Wisconsin 34 Northwestern 16
Wisconsin 42 Northwestern 21
In a way this is the 7th game this week because I was busy picking so many close ones. It probably won't be close, but maybe Northwestern can pull an Iowa on them.

East Carolina 38 SMU 36
SMU 38 East Carolina 28
Replacing the Georgetown game, this one is for my uncle Mark. SMU, his alma mater will have a shootout today at East Carolina.

Last Week: 5-1 (A return to normalcy)
This Season: 37-18

Thursday, November 25, 2010

BCS Week- Playoff Proposal

So I've criticized the BCS, talked about the computers, and even done some research on playoff systems. If we're gonna get rid of the BCS though, we need a solid system to replace it. Here is what I think would be the best playoff system:

A Six Team Playoff
This is good in that it often selects the best team (yesterday's post). It also is small enough that other bowl games could exist around it, with it's five games being the same the BCS currently has. Most importantly though, it maintains the importance of every game in college football. Even the best team in the nation can't afford to lose a game and drop it's bye.

All Undefeateds Get In
If a team wins all of it's games, they've done all they can. All undefeated teams deserve a shot at the national championship. This doesn't disrupt the six team part normally, the most undefeated teams ever before was five. If there are more than seven undefeated teams though, the playoffs should be expanded.

A BCS Style Ranking Fills In The Rest
The BCS isn't perfect, but it's pretty good. Swapping out the computers will help make it better too. Usually there will be few undefeated teams, so the top 6 teams in the nation should get it, as determined by the BCS. The ranking system should also select the top two teams to get byes. There will be argument over this, but unlike the BCS angered teams will have a chance to put their money where their mouth is.

No Automatic Conferences
All teams are FBS teams already, all of them deserve to be treated equally at this point. Sorry SEC, I know you're whining. You're not one of the two best this year anyways.

That's it. It's not an overly complex system, it's basically just the NFL conference playoffs. Fingers crossed that someone from the BCS reads this and agrees. Unfortunately though, it looks like we might be stuck for the time being.

Wednesday, November 24, 2010

BCS Week- Which type of playoff is the best?

One of the goals of a playoff should be to reward the best team. This is why 1 seeds get to play 8 seeds, and why higher ranked reams get byes. Is there a way to maximize the chance the best team wins? With a couple reasonable approximations, I think there is.

Approximation 1: I'm going to assume the best teams wins at a constant percentage (X) of the time. This is not true, it depends on the strength of various teams, but it's a serviceable estimate.
Approximation 2: To do this I need to know where the "best team" is in the BCS standings. I'm going to assume that the likelihood drops off geometrically with each spot. So if the 1st team has a .5 chance of being the best, the second will have .25, the third will have .125, the fourth will have .0625. Of course, this has to be adjusted so that the sum equals 1, so the first team's chance is 1-R where R is the rate of drop off. Here's another example: 1st= .333, 2nd is .222, 3rd is .148, etc.

The chance that the best team wins in an N team is easy to calculate (using normal playoff systems and giving byes to the best teams). But instead of putting in tables with too much numbers like I normally do, I've broken out the markers and done a graph. If you can do this with software please let me know, it'd clearly be way better.
For the mathematically inclined there's a whole family of interesting curves that serve as many of the boundaries, all with the formula R=(1/X-1)^(1/odd).

So the more often the better team wins (farther right) and the less accurate BCS rankings are
(farther down) the more teams the optimal playoff has. Interestingly, at no point is the traditional playoff structure (powers of 2 like 2, 4, 8, etc.) the most efficient. Odd ones like 3, 5, and 6 swipe up large areas on the graph. What's important though are which values college football has for constants.
Using the Massey Ratings number 1 as the true "best" team, the drop off constant is .667. Using my ratings to find the true "best" team the best match is a constant of .429, and an average of the two gives a constant of .579 (yeah, that's not the arithmetic average, but it works).
Based off the calculations earlier in the week the better team wins about .85 of the time. That seems high though for a tournament with all the best teams in the nation. You could use my ratings to find a ratio between teams like Boise St and Auburn, and then you'd often get winning percentages around .7 or .75 (this year it's a little lower, the top teams are kinda bunched).
Using .85 and .579 as constants the most effective playoff system is a 6 team playoff.
Using .7 and .579 as constants the most effective playoff system is a 3 team playoff.
In general, 3, 5, and 6 team playoffs are the most effective for college football (hint for the BCS- NOT A 2 TEAM PLAYOFF). 3 and 6 are probably better than 5 because of the wide range of constants they cover. Which one of those two should be the playoff system in college football is a question for tomorrow.

Tuesday, November 23, 2010

BCS Week- BCS Computers

As part of it's rankings the BCS includes 6 computer rankings (all without margin of victory). Here's a breakdown of all 6, with some thoughts on they're accuracy. For those of you looking for dirt on the BCS, look at the last 3.

Sagarin Elo Ratings
Jeff Sagarin is THE big name in sports rankings systems, and without including him the BCS would be making a serious mistake. His Elo system is not his primary ranking, but it is the one that fits BCS requirements (the other is predictive). The Elo system is based off the rankings used by chess players, which has worked well over the years, but he doesn't give details.

Peter Wolfe's Ratings
Peter Wolfe is another big name, and he also has some very good rankings. His are probably the most mathematically sound, he uses the Bradley-Terry method to find the ratings that maximize the probability that the results of the real world happened. It's a great basis, but the one problem is that under that method all undefeated teams should have infinitely high ratings. Since this doesn't happen he presumably includes some limiting factor, but it's likely sort of arbitrary, reducing the mathematical rigorousness.

Ken Massey Ratings
Ken Massey doesn't give many details on his BCS ranking system, but it gives good results and his other ratings are documented as being mathematically solid. I'm guessing actually that his ratings are similar to mine, but I'm not sure. Even if they stunk though he'd deserve to be included for all his contributions to the rating community.

Anderson Hester Ratings
There is very little description for these ratings, but from what there is I see two problems.
1. They only include opponents record and opponents opponents record. This does not look deep enough into strength of schedule, and over rewards teams in weaker conferences (all conferences will have roughly .500 for both records, regardless of strength).
2. They include a conference rating as part of strength of schedule. Should New Mexico's losses reflect negatively on playing TCU? I don't think so.
Fortunately for the AH ratings the two flaws kind of cancel each other out. There are still better ways to rank teams though.

Colley Matrix Ratings
The Colley Matrix Ratings are great because they are mathematically sound and he even gives details on how the ratings work. They are not so good though, because they don't rank teams very well. He uses FBS games (and FCS vs FBS games in a weird way) only, but I've programmed his system and here's how the top 10 looks with all 730 teams:
1. Auburn
2. LSU
3. TCU
4. North Central
5. Boise St
6. Oregon
7. Stanford
8. St Thomas
9. Missouri
10. Wesley
Not only is LSU now ahead of TCU, but there are suddenly teams from other divisions like D3 St. Thomas up there. Does North Central deserve to be there? No, and this flaw severely limits the Colley Matrix method.

Richard Billingsly Rankings
Billingsly's rankings are by his own admission the least mathematically complex of the BCS rankings. They were also created through a process of his own tinkering. While it's neat that he was able to just mess with the games until it works, that involves way too much personal bias to be a part of deciding the national championship. The other, more glaring problem is that he uses the previous year's final rankings as part of his formula. While it's true that teams don't change too much between years, each season should be completely separate if you're evaluating the national champion of that year. He admits that the preseason rankings have an effect on undefeated teams. In week 8 of the BCS this year Missouri averaged 6th in the computer polls and was in the top 10 in all but Billingsley's, where they were unranked because they didn't play well last season. A system like that definitely should not be a part of the BCS.

So 3 systems (Anderson/Hester, Colley, Billingsly) should not be included in the BCS, who replaces them? Here are three of my favorites:
Pugh Ratings- These have great math behind them, and the work too.
Doktor Entropy Ratings-These are commonly cited as a good set of rankings, although they'd have to be adjusted to join the BCS.
Random Walker Rankings-Randomly ranking monkeys is a cool premise, with some neat theory behind it.