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.

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.

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.

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.

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.

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.