Thursday, April 28, 2011

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 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.

Tuesday, April 26, 2011

Mavs over... Hornets?

Thinking about the second round this morning, I came to the conclusion that the Mavericks were in a pretty good place and could be able to take down the Lakers. This would be exciting of course, because nobody likes the Lakers. I eventually realized however that I don't have to count on Dallas, New Orleans could pull the feat off! If both the Mavs and Hornets win in the first round it would soon become objectively known as "the best thing ever" (you know this is objective, I would've said something about Bulls success if I made the decision). Suddenly, "the best thing ever" is within reach.
Well, kind of.
Dallas has upped their odds of winning from 73% at the beginning to 84.5% now. Meanwhile NO has raised it's chances from 19.5% to 25.3%. That means "the best thing ever" currently has a 21.4% chance of happening, up from 14.2% at the start of the playoffs.
Those odds are still pretty low, but it turns out that all of that swings tonight. If Chris Paul and co. drop the game tonight the odds of both victories occurring drop below what they were when the playoffs commenced. If the Hornets can pull off another upset though, the odds of TBTE will jump above 50%. The hopes of the world now rest on the shoulders of Aaron Gray (uh oh).


Wednesday, April 20, 2011

Picking Playoff Series Length

People who are good with numbers may have noticed that I picked an unreasonably large number of first round series' to be 5 games long. In fact, people who aren't good with numbers probably noticed it also because I picked 7 out of 8 to be the same length. It turns out however, that for a series with a clear favorite, that's the most likely out come. In fact, there are easy rules to follow.
*This all assumes that home teams win 60% of the time with equal skill. This also does not apply to the finals which have a different format (2-3-2).

When to...
Pick the home team in four
As I noted last year, sweeps are surprisingly unlikely. It's even more unlikely that a sweep is the most likely outcome, in fact there is no case where that could happen in this year's playoffs. Pick a sweep only when the home team is 3.67 or more times better than the away team, or has at least a 96.2% chance of winning.
Pick the home team in five
This is a much more common choice, especially with a lopsided first round series. Pick this when the home team is between 1.27 and 3.67 times better, or has between a 64.5% and 96.2% chance of winning.
Pick the home team in six
Never! The sixth game is on the road, so any team likely to win it probably would've already won in 5.
Pick the home team in seven
While rarer, when two teams are especially close the most likely outcome is often the home team in 7 games. Pick it when the home team is between .97 and 1.27 times better, or has between 51.2% and 64.5% odds of winning.

What?!? 51.2%? What if it's 51.0%, do you pick the home team in eight or something??
Turns out, that when the home team is slightly favored the most likely outcome is that the away team wins in 6 games, even though it's smarter to pick the other team to win. How do you compensate for this? It depends on what value is assigned to each. Using TrueHoop's 5 points for series winner and 2 points for correct number of games the boundary is set at .944 times better, or when the home team has a 50.1% chance of winning.

Pick the away team in seven
Don't do it! If they can win in seven, they're more likely to win in game 6 when they're at home.
Pick the away team in six
If you're going to pick the away team to win, unless for some super weird reason the away team is waaaaaaay better. Accordingly, pick the away team in six when it's 1.04 to 2.38 times better, or has between a 48.8% and 85.8% chance of winning.
Pick the away team in five
There's only a brief range where this is the right choice, but it still exists. If the away team is 2.38 to 2.83 times better, implying between 85.8% and 90.3% chance of winning, then pick the away team in five.
Pick the away team in four
If the away team is 2.83 or more times better, meaning they'll win at least 90.3% of the time, then pick them to sweep. This has probably never happened, and probably never will.

Summary (for lazy readers):
If you think the home team will win pick them in 5 games, unless if you think it's close than go with 7 games. If you think the away team will win, pick them in 6 games pretty much no matter what. Importantly, while it's often tempting it's never smart to pick the home team in 6 or the away team in seven. There will of course be sweeps this year, and home teams that win in six, but from a purely mathematical perspective, that's not a smart pick going in.

Saturday, April 16, 2011

True Hoop First Round

TrueHoop once again is running their true hoop challenge, and well I'm not officially a participant (someday...) I'm still going to put my predictions out there (which were done before today, just posted late):

Bulls over Pacers in 5
Magic over Hawks in 5
Celtics over Knicks in 5
Miami over 76ers in 5

Spurs over Grizzlies in 5
Nuggets over Thunder in 6
Mavs over Blazers in 5
Lakers over Hornets in 5

Yes it's bland, but that's what all the math says. None of the series' are close enough to be expected to go to 7 (although it's probably that at least one will), and only the Nuggets are set for an upset.

Also of note, my first three (okay, really two) articles outside of Kobe, Tell Me How My Stats Taste! The TeamRankings one has good math, and the ESPN one has good comments.

Thursday, April 14, 2011

NBA Playoff Analysis

So what trends stand out from the odds? There are a couple of interesting results, and they start right at the top with the Championship Odds.

Championship Odds
Chicago 0.274
Miami 0.228
San Antonio 0.13
LA Lakers 0.13
Orlando 0.062
Boston 0.051
Dallas 0.048
Denver 0.037
Oklahoma City 0.024
Memphis 0.009
Portland 0.003
New Orleans 0.003
Philadelphia 0.002
New York 0.001
Atlanta 0
Indiana 0

Only four teams end up having strong chances of taking the Crown this year, as Boston and Dallas have faded into the second tier lately, joining Orlando Denver and OKCity as fringe contenders.
The championship odds actually (Dad!) don't match up with the power ratings, where Miami is number one. Two things cause the discrepancy: The Bulls home court advantage and first round bye that is the Indiana Pacers. While the number one seed works out well for the Bulls, it has the opposite effect for the Spurs. San Antonio has a better power rating but because they have to face Memphis and then Denver (yeah, Denver) their schedule difficulty more than offsets home court advantage. One armed Manu Ginobili isn't going to help things either.

If this were an NCAA bracket we'd be looking for a couple teams to go on runs. Some of that is lost with multiple games series, but there are still 3 teams that could go a couple rounds past expected:
Memphis has looked strong throughout the year, and appear to be powering forward even without Rudy Gay. Marc Gasol and Zach Randolph are ready to wreck havoc on old guys like Tim Duncan. There's actually a 10.5% chance that the Grizz win not only one but two rounds to make the conference finals.
Orlando hasn't seemed to fully gel this year despite big hopes following their fall trades. Don't sleep on them though, they've quietly snuck up to 5th in the power ratings and have a lot to prove this postseason. The Magic have a 12.6% chance of returning to the finals after a one year hiatus.
Denver has exploded since the Melo trade, but it might not be for the reasons you think. They've actually been planted in the top 10 since this year's first power ratings, but were one of the NBA's unluckiest teams before Carmelo left. Since then they've played only slightly better, most of the improvement has come from some bounces that finally went their way.

Finally, while some first round series' are little more than speed bumps there are a couple that could send lower seeds into the second round. Last year the rankings were 8 for 8 in the first round, and while I'm not expecting that this year (about 6.3 for 8 is expected) I'm just saying...
Here are the top three first round upset candidates:
1. Denver over Oklahoma City (52.2%) This one is statistically a coin flip, but I'm going out on a limb and saying the Mountain West will soon be going Goo-goo for Gallo (Cray-Cray for Nene?). Anybody know how to get a phrase copyrighted?
2. Memphis over San Antonio (27.6%) Once again, these are very good odds for an eight seed. Still not great odds for winning though.
3. Portland over Dallas (27.0%) These odds are almost surprisingly low considering all the positive pub the TrailBlazers have been getting. I'm not sold on them though, they've played better since Gerald Wallace joined but not that much better. It just happens that Dallas isn't great either.

On the whole the 2011 NBA playoffs bring a deep pool of talent, especially out West, and a slew of potential title candidates. The Bulls(!!!) are the definite favorites, and the Lakers have surprisingly low odds of winning, but nothing's set in stone except the seeding right now. With a jacked up intensity, slowed down pace, and shortened benches anything could happen. Let the games begin.

NBA Playoff Odds!

It's back, the NBA playoffs! Who's going to win? This year The Taste is more equipped to answer that question thanks to the new bracket builder, which for the playoffs has been altered to include series play and home court advantage. Odds to get through each round are below, with analysis following in a later post.

Rd 1 Rd 2 Rd 3 Rd 4
Chicago 0.955 0.673 0.405 0.274
Indiana 0.045 0.006 0 0
Orlando 0.874 0.31 0.126 0.062
Atlanta 0.126 0.012 0.001 0
Boston 0.812 0.294 0.11 0.051
New York 0.188 0.027 0.003 0.001
Miami 0.869 0.64 0.346 0.228
Philadelphia 0.131 0.04 0.007 0.002
San Antonio 0.724 0.467 0.286 0.13
Memphis 0.276 0.105 0.038 0.009
Oklahoma City 0.478 0.191 0.08 0.024
Denver 0.522 0.236 0.111 0.037
Dallas 0.73 0.318 0.146 0.048
Portland 0.27 0.069 0.017 0.003
LA Lakers 0.805 0.549 0.307 0.13
New Orleans 0.195 0.064 0.016 0.003

Monday, April 4, 2011

Men's and Women's Championship Game Odds

The women's tournament has turned the way of the men's, and now we have two unexpected final pairings. The games will still happen though, so here are projected scores and winning percentages:

Connecticut 78 Butler 72
UConn wins this game 69% of the time. Kemba Walker for belated player of the year?

Texas A&M 82 Notre Dame 78
Texas A&M wins 63% of the time. Playing the nation's hardest schedule will likely pay off for an Aggies team that spent a large chunk of the season #1 in the power rankings.

With these two games we will put a cap on an excellent college basketball season that has clearly showed why they play the games.

Sunday, April 3, 2011

Are the Spurs tanking on purpose?

Okay, almost certainly not it'd be kinda dumb. But here's an interesting thought. As of a few days ago the number 1 seed in the west had to play a dangerous Memphis team, followed by either the super hot Nuggets or Kendrick Perkins Thunder. The two seed though got New Orleans w/o David West or maybe the Trail Blazers just hanging on, followed by a struggling Mavericks team. Is that enough to over come home court in the third round? The playoff odds (now adapted for the NBA, with home court!) give us a good look:
With Spurs #1, Lakers #2
Spurs are champs 15.1%
Lakers are champs 14.7%
With Lakers #1, Spurs #2
Spurs are champs 15.6%
Lakers are champs 13.4%

So with last Wednesday's standings it actually is beneficial for the Spurs to lose. On the whole though, it's risky because right now the Hornets have dropped into eighth, and the clear goal is to avoid the Grizzlies.
Another possible winner here is the Bulls, who would go from 28.0% to 28.8% if they get home court advantage over the Spurs in the finals. For a team that was given little shot earlier in the year, the Bulls have really come on strong over the last month. Maybe there is an advantage to playing all the way through the season.