NFL Draft Pick Value

It's nice to change things up from the NBA playoffs every once in a while, so here's a project that I did over a year ago. It was actually going to develop into my final project for Math of Sports before I got started on the rankings system. This probably would've given much less material to blog about, but that doesn't diminish it's usefulness over the next few days. Below is my chart for average NFL draft pick value.

As a little background, something like this has been bouncing around among NFL teams for years, and they almost all follow the chart. It can produce some shocking results (is the number 1 pick really worth five number 30s?) but trades over the past few years show it's been followed to a T. My graph was supposed to be an improved version of the chart.

To set up my graph I used Career Approximate Value from ProFootballReference.com. It's a rough way to get all players on a statistically equal footing for judging their career quality. While it's not perfect, its definitely good enough to get a rough number for value, great players have up over 100 while crap players can have CarAV in the single digits. I took the data for the top 60 draft picks in the 1970s, and the top 30 in the 1980s (people who's career had finished. Also, I typed this all in because I didn't think of copy paste. Dumb.). After doing some moving averages, I decided the best fit was an exponential, which is also fitted on the graph.

As you can see, things drop off fairly slowly. The "half-life" (physics!) is about 38 draft picks, meaning that one pick is worth about two picks from a little over a round later. The draft chart actually follows this pretty well from the mid-4th to mid-7th rounds, but overestimates the value of high picks at other times. The exponential fit may slightly underestimate the value for the top few picks, but just by a little bit. It's clear though that the number one pick should probably be worth 2 number 30s, not 5.

Also amusing to note is the bizarre curse of pick 7. Over the 20 years of data here it's averaged being worth that of a pick 20 spots lower. Adrian Peterson and Champ Bailey have probably reversed that recently, but it's still maybe worth a though for the 49ers and their new coach Harbaugh.

On the whole, this graph shows us that the draft chart used by NFL teams significantly overvalues top picks. So if you're team trades some picks to move up in the draft this weekend you should be worried about the deal you're getting. If they play it smart and move down however, it means somebody might be reading Kobe, Tell Me How My Stats Taste.

p.s. The third ESPN article went up a couple days ago. It may turn into a playoff long gig. Fingers crossed.

How often does the best team win?

A couple months ago I asked how often the best team wins the world series. It turned out to be a surprisingly low percentage, and with the wacky final four I started asking the same questions about college basketball. Using the random chance in sports method to determine how often the best team won I calculated the probability of the best team being champion. Naturally it extrapolated itself to all sports:

NBA: 81%

This is by far the highest, and also the most wrong. Single teams don't distance themselves as often in the NBA, and some research I did in high school suggests that better teams win 60% of finals games, not 80%. Adjusting for that in the last two rounds puts the odds at around 48%.

College Football: 57%

People rag on the BCS, but I showed during BCS week that small playoffs are often better at selecting champions. Again, adjusting for using only the top teams and not the general random chance lowers the odds to 47%, which is still pretty high.

NFL: 55%

Even though this is the pro sport where the best team wins most often, single elimination hurts it. Byes help though (these odds assume the best team gets a bye). Assuming that the best team only wins .7 of the time (better for the playoffs) lowers the odds to 42%

You may be laughing now because I've corrected the random chance odds for each sport so far. It's much more accurate for the remaining sports though, either because top teams distance themselves farther (MLB and NHL) or because there is a full range of opponents in tourney play (MCBB and WCBB).

Women's College Basketball: 36%

We're probably a little thrown off because of UConn's recent success, but actually with 6 rounds of play even the women's tourney is ripe with upsets.

MLB: 33%

Series' are a necessity in a sport where even the worst teams win almost 40% of their games. The first round should probably become a best of 7 to help that out (it'd boost odds about 5%).

Men's College Basketball: 28%

We've seen this on full display in the tournament, as the clear best three (Ohio St, Kansas, Duke) have all fallen to lesser opponents. 6 rounds is fun though, so it's worth diluting it, but a 7th in the future would be a stretch.

NHL: 28%

This may seem weird with many former dynasties like the Canadiens, but in reality the modern day NHL is as full of parity as baseball, and with an extra round the best team's chances are the worst of any major U.S. sport.

The Suuuuuper Bowl

Tomorrow is Super Bowl Sunday, a once a year American special. The matchup between Green Bay and Pittsburgh manages to combine two of the best three teams in football (New England just didn't show up against the Jets). In fact, the Packers and the Steelers have been at the top since the very beginning of the season. After week 3 I ran the rankings for the first time. Number 1 was Pittsburgh, number 3 was Green Bay. Both teams were among the four that spent time on top throughout the season.

Weeks 3-6: Pittsburgh

Weeks 7-9: Tennessee

Weeks 10-13: Green Bay

Weeks 14-17: New England

Okay, I don't understand Tennessee either (some mid season turmoil really threw them off), but the other three numbers ones showcased the power of predictive systems.

Points line for the game gives the following prediction:

Green Bay 22 Pittsburgh 21

The expected total points is 42.76, and the expected differential is 1.43. By the rankings system the Packers have a 52.4 percent chance of winning, but with a little twist we can also calculate the chance of victory. Calculating the game score standard deviation (and adding in uncertainty on each team's value) then averaging the two we get the expected standard error for the super bowl is 11.50 points. Importantly, it's much larger than the expected differential. A z score of .124 means the Packers should win 54.9% of the time. Interestingly, with a line of 3 for the Packers, that means there's a 55.5% chance that the Steelers cover (umm, still not endorsing gambling no matter how good the Prediction Tracker thinks I'd be). Actually though, even with the 1.43 number there's a high degree of uncertainty because each team's rating has an error of about 2.5. On the whole what it all means is that we have two of the absolute best teams in football, and picking the winner might as well be a coin flip. It's gonna be a good game.

Today's NFL games

My predictions were in late to The Prediction Tracker due to computer troubles, but for those interested here are my predictions:

Green Bay 24 Chicago 20

As unfortunate as it is, the Packers are a better team. Actual predicted line is 4.35.

Pittsburgh 25 New York 19

After taking down a couple of AFC powers, the Jets will likely finally go down to the Steelers this week. Actual predicted line is 6.00.

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.

New NFL and NBA rankings

Each week I have a chance to go over the college football rankings, but I haven't had a chance recently to look at the professionals. What's up in the NBA and NFL (besides me being embarrassed by the Detroit Lions)?

Here's four trends to look at going ahead:

1. The NFC West sucks.

Anybody who follows football already knew this, but having 24th ranked St. Louis as their best team is almost unbelievable. Ishan stands a chance at winning his bet that the 49ers make the playoffs (made when they were 0-5) but I think the winner is goint to be the Rams. That's right Masta' P, your St. Louis Rams will beat Seattle on January second for their 7th win of the season, clinching the division by tiebreaker over the Seahawks.

2. The Bears aren't just lucky.

Yeah, the Bears have won some close games this season. They've lost some too though, and updating the rankings through today they'd project to have 6.23 wins at this point, not too far from the 7 they actually have. They have a touch finishing schedule (average opponent rating of 1.67, right in between the Colts and Patriots) but with the parity in the NFL this year they are still predicted to have 2.73 wins. A 10-6 Chicago Bears team? That could make the playoffs.

3. The Heat will "get better".

Yeah, they're 7-4, but they're atop the power rankings and should be 9-2 (9.09 wins exactly). As the season goes on those mistakes will iron out, and I project them to finish at 67-15 at their current pace. They'll probably regress to the mean some, but the MiAmigos are still a very good team, probably the best in the NBA.

4. The Hornets are for real.

Chris Paul's return (not "CP3" a terrible excuse for a nickname) and the new focus on defense are a big deal. They boast the best record in the NBA at 9-1, and THEY'VE PLAYED THE TOUGHEST SCHEDULE. Once the easier teams roll in, they'll kick even more butt. At this rate, they'll finish the season 70-12! Don't expect that, but do expect them to stick around as a legitimate dark horse contender.

Random Chance in Sports

This post is a followup to Random Chance in the NFL which highlighted the lowered competition in the NFL this year. It showed that the best teams win 62% of the time this year, far less than previous years. How often the better team won in previous years and in other sports were still left unknown though. Until now. Here, using the same methodology focusing on variance, here are the data on the last three full seasons in the four major american sports:

	2008	2009	2010
MLB	0.59	0.6	0.59
NBA	0.77	0.77	0.75
NHL	0.56	0.61	0.61
NFL	0.8	0.8	0.78

On average the better team wins 60% of the time in MLB, 77% in the NBA, 60% in the NHL, and 79% in the NFL. But how about this year? How often does the best team win in the NFL this year? It's gotten better since the last look, so far this year in the NFL the better team wins 70% of the time. While this is still an unprecedented increase in parity, it is also slowly getting closer to the norm we'd expect, thanks largely to big losers like the Bills and Panthers. So while this NFL season may have some crazy outcomes, it's still less random than sports like Hockey.

This article originally ran with a bug in the program used to calculate variance. While the effect on previous season results was minimal, it messed with the current season results a lot. The NFL is not actually just random chance this year, although going with just home field advantage would still be pretty good.

The Detroit Lions?

Am I really trying to tell you that the Detroit Lions are the 8th best team in football, even though they're 2-6? I am, and I'll tell you why.

First, they have a positive point differential from barely losing most games, but winning large in their two wins. They've scored 15 points more than their opponents, only two less than the 5-3 Eagles.

Second, they've played one of the hardest schedules in the entire NFL, with only 1 of their 8 opponents having a record below .500 (the Minnesota Vikings). In fact, with an average opponent strength of 1.32 (about the New Orleans Saints) they have played the hardest schedule in the NFL.

Still, with their rating and schedule the Lions should have 4.4 wins. They're easy to see too: one bad call against the Bears, Ndamukong Suh making an extra point against the Jets, and maybe punching in one of the final red zone trips against Green Bay. With 8 game left though, expect the Lions to "suddenly improve" because they'll get better luck eventually.

Random Chance in the NFL

Normally over the course of an NFL season power rankings regress towards the mean and extreme ratings get closer to 1. This season however, the best and worse ratings are already closer to 1 than last season's final ratings, and we haven't had any undefeated teams for a couple of weeks. Has NFL parity really increased?

One way to judge parity might be to look at the percentage of time the better team wins. With no parity, the best team in a given game would win 100% of the time, being far better than it's opponent. But with perfect parity the better team would win only 50% of the time, and NFL game would be random chance. It's obvious that chance plays some role because otherwise the Rams would never win a game, but how much of a role it plays can be uncertain. To look at that, I'm going to look at what percentage of the time the best team in a game wins.

The key to my search was to look at variance in win numbers across the NFL. If all teams won 50% of the time, then winning percentages would be clustered around .500, giving a small variance. On the other hand, if the best team always one there would be undefeated and winless teams along with other extreme records, leading to a high variance.

Through 5 weeks in the NFL, variance per team was 1.24 wins per game. That matches up with the better team winning 62% of the time. To confirm, I looked back at the previous games to see how often the higher ranked team won. Turns out, the higher ranked team won 63% of the time, so it's pretty clear that in the NFL this year the better team wins somewhere around 62% of the time.

For comparison, I also looked at the last three years by variance. In 2009 the better team won 78% of the time, and in both 2008 and 2007 the better team won 80% of the time. If the Chiefs and Bears hadn't already made it clear, statistics show that this year parity and random chance have reigned over the NFL, so much so that picking winners is basically a crapshoot. At least that explains why my rankings systems can't pick NFL games. Also, it may give the Bears a chance at the playoffs. I kinda like this random chance thing.

NFL Rankings 9-28-10

Three weeks into the NFL season I am debuting my NFL rankings. It's all posted under the page links at the top, but for the lazy here are the top 10.

	Team	W	L	Rating	SOS
1	Pittsburgh	3	0	8.402	2.352
2	Atlanta	2	1	4.653	1.687
3	Green Bay	2	1	3.524	1.393
4	Tennessee	2	1	3.427	1.109
5	Chicago	3	0	2.969	1.658
6	Philadelphia	2	1	2.108	0.931
7	NY Jets	2	1	2.067	1.101
8	Kansas City	3	0	1.456	0.539
9	Indianapolis	2	1	1.454	0.587
10	New Orleans	2	1	1.356	1.122

What stands out about these rankings? First, they do a good job of noting that even though teams like Chicago and Kansas City are undefeated, they're not necessarily among the three best teams in the league.

Among the teams themselves there are a couple trends of note. First, the torch appears to be passing, as former great teams like the Colts and the Patriots (almost exactly average now) give way to new top tier teams such as the Falcons and the Packers. Manning and Brady are giving way to Ryan and Rodgers. While it's early, that may be a trend worth following.

It's also astounding to note the parity among NFL teams. Flipping a coin you'd expect 4 teams to be undefeated, but there's only three right now. There's also very few teams that have yet to win a game. Pittsburgh is significantly better than the average team right now, but other teams might just be lucky to be up there. Either way, don't expect too many teams to run away with their division this year.

Masta' P's Rams

On request, I've taken a look at the St. Louis Rams hopes for the 2010 season. Taking the NFL team ratings from last year (St. Louis was last, of course), I calculated the expected wins for St. Louis this year. It's rough because it doesn't account for any roster changes, but honestly Sammy Bradford won't add much yet. Turns out, the Rams can expect about 3 wins next year (3.05) even without any improvement. They benefit from what should be an easy schedule, and actually a mathematical curiosity. Using strength of schedule only the Rams would expect 2.75 wins. However, they're so much worse than the best teams that they have basically no chance of winning whether it's against the best team in the league, or the 10th best. When they play the best teams though, it increases their strength of schedule (decreasing estimated wins) without actually having a real effect on their likely number of wins. So Masta' P, there's a little on your Rams.