Friday, June 24, 2011

Posts to Kobe, Tell Me How My Stats Taste may be a little slow this summer (and so is the audience, so it might not matter) but there is a reason behind it. My internship for the summer is with, and I've been busy doing projects with them. I've had a couple blog posts, but the big contribution so far has been working on the new Tennis Rankings and Wimbledon odds. They went up today, and I'm pretty proud. If you're looking for a fix from The Taste, here's where to go:

Sunday, June 19, 2011

Margo Dydek

A few weeks ago on May 27th former WNBA #1 overall draft pick Margo Dydek passed away from a heart attack. It was a tragic death for many reasons, including the fact that she was just 37 years old. Although her name may not be familiar to average sports fans Margo was one of the most unique basketball players of all time. She was picked first in 1998, and despite leading the league in blocks for many years never quite became a star. Although her stats don't set her apart, something else does: Margo was 7'2". 7'2" is extremely tall for a guy (an inch taller than Shaq), but astoundingly tall for women. If Margo were the same height as a male, how tall would she be?

For people of average height, a good rule of thumb is a +5 inch rule; add five inches to a women's height, and that's roughly how tall she'd be as a man. This would put Margo at 7'7", on par with the two tallest NBA players of all time, Manute Bol and Gheorghe Muresan. It turns out however that the standard deviation of female and male heights is not quite the same. According to a study from the early 90's, American men have an average height of 69.3 inches (5'9") and women average 64.1 inches (5'4") (Margo was actually Polish, but we'll ignore that for now). For men the standard deviation was 2.92 inches, but it was just 2.75 for women. This means that when you get to the upper ranges of height (tall basketball players) it becomes a +6 inch rule, making 7 foot tall men roughly equivalent to 6'6" women.

For Margo, the rule is even slightly higher. With a height of 8 sigma greater than the mean (statistically impossible basically) she outpaces even the tallest male NBA players. This chart shows how she compares to varying men.
Margo's equivalent height among men would've been an amazing 7'8.6". This height was likely less a blessing than a curse though, allowing her to play professional basketball but probably contributing to her health problems. RIP Margo Dydek, the tallest basketball player of all time.

Monday, June 13, 2011

Dallas Mavericks: NBA Champions

Congratulations to the Mavericks on their first ever NBA championship. They are one of the few teams that fully embrace the statistical side of basketball, and it paid off for them in the finals. They over came long odds to win it all, but somehow pulled it off with only 5 losses along the way. I'll be wearing the Dirk jersey for about a week straight in celebration. Well done Dallas.


Wednesday, June 8, 2011

2011 NBA Finals Odds-Update!

Through game 4, these are the likelihoods of the remaining outcomes:

Miami in 6: 31.5%
Miami in 7: 34.0%
Dallas in 6: 17.6%
Dallas in 7: 16.9%

It sure seems like the Mavericks have made quite a statement already taking two games from the presumptive favorites. The truth is though, 2-2 was the most likely outcome at this point in the series. Dallas's odds are better now, but not by much: Miami is still expected to win 65.5% of the time. Some significant work has been done, but the big game happens tomorrow as over half the series swings on game 5.


Dallas's comeback win last night brought the series back to 2-2, and is promising to make this an especially memorable finals. People have torn apart Lebron and Jason Terry's play, while praising Dirk and Dwyane Wade. Turns out though, sports reporters have missed the single best predictor in the series: whether or not I wear my old Mavericks jersey. I wore it for games 1 and 3, but not for 2 and 4. Clearly me not wearing the jersey corresponds exactly to Dallas winning. Is there something there? Or is this an example of me having to much time to think of wacky things now that finals are done?

Traditionally, statisticians use 5% as the probability cutoff for correlation. If there's less than a 5% chance something would happen randomly, they assume it's a non-random process. The chances that my fashion choices would correctly predict 4 games in a row is just 1/16, or about 6.3%. That's not statistically significant, but it's close. If my jersey gets one more game right however, the odds move to 3.1%, a level that actually is significant. I won't be wearing the jersey for game 5 (go Mavs!) so a Dallas win will be more than just an important finals game, it'll be validation for all who ever believed that their particular scrap of cloth influences their team's play.

*Okay, clearly my shirt doesn't influence the game. What's wrong with this analysis?
First, I set the null hypothesis halfway through. Flip a coin 5 times, then hypothesize those results happen, and your test will be significant. If I say my jersey is a predictor one way or another, it could predict a Dallas win or loss, so 6 games is the level of significance, not 5.

Second, correlation does not imply causation, so it's possible some non-random third party is influencing both. Maybe I put the jersey on only when Dallas is losing (subconsciously). Or maybe Dirk watches what clothes I wear and then plays accordingly just to mess with my head.
Finally, even if something happens only 3.1% of the time from random chance, a random distribution will still give that answer 3.1% of the time. If you have 32 octopi picking 5 games, one of them is probably going to pick all 5 right. Then you can name him Paul and get the whole world to watch him.
Nonetheless, even though it's not true, I still kind of believe in this stuff. The truth is, I won't be wearing the Nowitzki jersey for game 5 because I want Dallas to win. But I won't be placing bets on it.

Thursday, June 2, 2011

Ranking Shaq with the Centers

Only Shaquille O'Neal could steal attention from an exciting NBA finals as an over the hill 39 year old. His impact has been humongous not only on the court but off it too. Just look at the name at the top of the page (Kobe, Tell Me How My ? Tastes!). Watching him over the last 5 years it's easy to think of him just as an outsized personality, but he was maybe the most dominant basketball player of all-time. In the all time pinnacle of centers, where does the Big Aristotle rank? I created a cumulative index to try to find out. And then I changed things a little bit (I'll explain for each change).
My index was a combination of my work on the Top 5 each year, career win shares, MVP share, Basketball-reference's Hall of Fame odds (to include championships), and BBR's Elo player ratings. I altered things a little bit to help some defensive studs out, but pretty much stuck to the results.
There were two big names who maybe should be on the list. Arvydas Sabonis never got a chance to show the world what he could do in his prime, but some suspect he could've been the best center ever. Also, I left Tim Duncan out, even though he's really more a center (I'd probably put him right behind Shaq).

10. Dwight Howard (5 points in the index)
He proved himself the second best player in the NBA, and with it moved himself into the top 10, knocking Bill Walton (or Willis Reed) out. He and Ewing were the only centers under consideration who haven't won a championship, and everybody else besides Malone has won at least two. Howard's entering his prime, and his time will come.
9. George Mikan (7 points)
Mikan is without a doubt the hardest player to rank on this list. He played in a completely different era, and probably would play something like Aaron Gray if he were in the league now. At the same time, he was the NBA's first superstar, and the center piece of the leagues first dynasty.
8. Patrick Ewing (9 points)
He will always be known for failing to break through (or for his Snickers commercials) but he took the Knicks to the finals twice, and led a renaissance of New York basketball. It's just tough to go up against MJ in your prime.

7. Moses Malone (25 points)
Moses Malone is often a forgotten name among centers, quickly replaced by Olajuwon in Houston and never living on Dr. J's level in Philly. He peaked in a way that few players ever have. According to my top 5 calculations, Moses was the best player in the NBA in 1978-79, 81-82, and 82-83.
6. David Robinson (28 points)
Robinson was a physical specimen, and is being appreciated even more with advanced statistics. He consistently shows up at the top of Career PER or win shares lists, and can be seen by some methods as one of the best players of all time. He needed Duncan for playoff success though, and in his prime got it taken to him by the next man on this list.
5. Hakeem Olajuwon (24 points)
While his regular season stats aren't quite on par with Robinson or even Malone, taking both of the titles during MJ's break earned him a top 5 spot among greatest centers ever. He beat both Patrick Ewing and Shaq in those finals, and the way he dominated NBA MVP David Robinson forced me to give him a bump up this list.

4. Shaquille O'Neal (38 points)
Shaq was the best player in the NBA in the immediate post Jordan era, ruling over the league in 1999-00 in a way that few ever have. He could rule games physically, but also had great touch around the hoop. He never quite got all he could out of his basketball potential, but winning 4 rings and being an absolute force for 3 different teams still put him 4th on the list.
3. Bill Russell (37 points)
Russell helped integrate the sport, anchored the greatest dynasty in the history of athletics, and my be the best defensive basketball player ever. A player with 11 championships will never be seen again in any high level team sport.
2. Wilt Chamberlain (44 points)
He occasionally cared more about women or statistics than about winning, but he also once averaged 50 points and 27 rebounds per game, over an entire season. Nobody has had a game like that since him, and that what he used to average! Wilt the Stilt also managed to squeeze in a couple chips around Russell's hogging.
1. Kareem Abdul-Jabbar (46 points)
Kareem was the best player in the NBA for 7 total years, and was the best player in the league for 4 straight seasons from 1970-74, a streak matched only by Michael Jordan and now Lebron James (didn't see that one coming huh?). The NBA's all-time points leader is also the greatest center of all time. For now.

Tuesday, May 31, 2011

2011 NBA Finals

Although they lasted longer than expected, the young guns have been eliminated now leaving only two members of the (kinda) old guard standing: the Miami Heat and the Dallas Mavericks. This sort of performance was expected from the Heat (I predicted they would win 67 games. I was wrong, but after these playoffs it seems pretty reasonable). They Mavericks have come our of nowhere, even in the playoffs, starting off with less than a 5% chance of winning it all. Two of the games best scorers have taken over (with the help of some serious luck) and Lebron and Dirk will be on a collision course for not just their first ring, but their first Finals MVP also.

It turns out though, that the finals may not be the close battle you'd expect from two teams that dominated their respective brackets. Through out the regular season the Bulls were consistently better than the Mavs, and they only managed to last 5 games (although there were some pretty lucky Lebron J's to keep the Heat in games 4 and 5). The free throw discrepancy which was the story of the 2006 finals also is apparent between the Heat and the Mavericks regular season attempts. Even without Bennett Salvatore's help, the MiAmigos will likely get to the line more. Here's the breakdown of the occurrence rates of possible results:

Miami in 4: 9.9%
Miami in 5: 15.1%
Miami in 6: 23.0%
Miami in 7: 20.1%
Dallas in 4: 3.1%
Dallas in 5: 9.5%
Dallas in 6: 9.3%
Dallas in 7: 10.0%

Because of the 2-3-2 format things break down a little bit differently, and the home team is almost always most likely to win in 6 games. The overall odds of winning don't change though, the Heat should take the Larry O'Brien trophy 68.2% of the time. While as in any sport, there's enough chance involved to make all outcomes possible, but the most likely outcome is Miami in 6. A dynasty of the MiAmigos may be upon us.

Sunday, May 15, 2011

True Hoop 2011 Third Round

As the playoffs go on the picks necessarily get harder, and the odds get worse. The Bulls-Heat series is a prime example. Under the ratings currently posted, the Bulls win just over 50% of the time, and the most likely outcome is Miami in 6. In order to nail this pick down though, I started playing with the ratings a little bit. Turns out that for the NBA they are overly generous to teams that win low scoring contests (read: The Bulls), so I tweaked things a little bit. Now the power ratings match up a little closer to the points ratings (almost exactly for Bulls Heat it turns out) and favor the Heat to win the series 53.1% of the time. On the other side of things, no matter the results of Game 7 Dallas will be favored to win in 7 games (although by just .05% over 5 games against the Griz). So for round 3 I have:
Miami in 6
Dallas in 7
Neither of these look to catch me up much on the top half of TrueHoop guys, but if OkCity wins tomorrow I'll pass David Berri despite picking fewer winners than him (master of series length!). And this point, I'm rooting against myself anyways, GO BULLS!

Friday, May 13, 2011

2011 NBA Top 5

Last year at the end of the year I created an index to help figure out the NBA's top 5 players that year. It used the top 5 in Roland Rating, PER, Win Shares, Points Per Game, MVP voting, and the All NBA first team. This year I also added adjusted plus minus, although it's high variance can give some weird results. Here are this year's top 5 players, along with the points they have in the index:

Lebron James - 24
Dwight Howard - 22
Derrick Rose - 9
Kevin Durant - 9
Dwayne Wade - 8

There are a few things that stand out to me. First, Lebron James is once again the best player in the NBA, marking the fourth consecutive year by this index. It was a lot closer this year though as Dwight Howard stepped up his game to become the second best basketball player in the world. Next, the bottom became much more bunched together this year. Rose, Durant, Wade, Chris Paul and Kobe Bryant were all within two points of each other, which is pretty unusual. Finally, Kobe dropped out of the top 5 this year (and his post season performance supports that) marking for the first time a top 5 full of the leagues new stars. This is a generation that never really played in MJ's shadow, and is bringing the league back in the national spotlight. It's a fun group to watch.

Thursday, May 5, 2011

One Year (plus)

I missed it by four days, but May 1st was the one year anniversary of Kobe, Tell Me How My Stats Taste (at the time it was Shaq's Big Brickhouse). While there were a couple of breaks throughout the year, the posts have been coming at a surprisingly regular frequency and I think the quality of work now far surpasses what I would've imagined when I started. I'm not going to recap the work (that was done well in the 100th Post) but I am going to provide something that I could not have a year ago: mid series odds.
Bulls vs Hawks
Current Standings: tied 1-1
Favorite's odds: Bulls win 86.9%
*Impact of game 3: .226
The Bulls were dealt a shocking blow in game 1, but they're enough better it should just be a bump in the road.
Heat vs Celtics
Current Standings: Miami leads 2-0
Favorite's odds: Heat win 88.3%
Impact of game 3: .171
Unless something drastic happens (Delonte West & Lebron's mom part 2?) the Heat are gonna be in the eastern conference finals.
Thunder vs Grizzlies
Current Standings: tied 1-1
Favorite's odds: Thunder win 51.3%
Impact of game 3: .383
The Grizz's game 1 win makes the series pretty even odds going forwards. Game 3 will decide a lot.
Lakers vs Mavericks
Current Standings: Dallas leads 2-0
Favorite's odds: Mavs win 78.3%
Impact of game 3: .298
One dynasty fell in round one. The Lakers need to win game 3 in Dallas to keep a second one alive.

*Impact measures how much of a series swings on a given game. Every game 7 has an impact of 1, because the winner wins the series. It's a teams odds of taking the series with a win minus their odds with a loss. A bigger number means more importance.

Monday, May 2, 2011

Andre Ethier vs. Raul Ibanez

There are two spectacular hitting streaks going on in baseball right now. One has Andre Ethier playing strong with hits in 27 straight games. The other has Raul Ibanez going 0 for his last 34 at bats. PTI just asked which one is more impressive, and with a little help from probability I aim to answer that here.

This season the league-wide MLB batting average is .250. That's interestingly considerably below the usual league total which got as high as .269 in 2006. However since we're looking at which is more impressive (less likely) in the MLB this year, I think .250 is a good number to use.
For Ibanez, it's simple to just take .750^34 to get his odds. The chances of going 0 for 34 over any given set of 34 at bats is just 5.65*10^-5, a very small number. On the other had, with well over 5000 at bats in any given year, there are many chances, so it should happen every 3 or 4 years.
For Ethier we have to make some assumptions about his at-bats per game. He has 111 at bats over his 29 games this season (slightly less than 4 per game). While average doesn't work perfectly because it's especially hard to get a hit with just 2 or 3 at bats, some games he may have been taken out only because he already had a hit. The two cancel out, so we'll go with 111/29 at bats per game. He then has about a 2/3 chance of getting a hit in any given game, and a 1.82*10^-5 chance over any 27 game stretch. Even without compensating for few chances, that's less probable than Ibanez's streak. Overall, Ethier 27 game hit streak is less likely for an average player, and therefor more impressive.

Sunday, May 1, 2011

NBA Second Round Odds and Analysis 2011

The first round of the NBA playoffs has ended (and the second round actually started, oh well), so here are my odds for the remaining teams going forwards:

Rd 2 Rd 3 Rd 4
Chicago 0.932 0.541 0.379
Atlanta 0.068 0.006 0.001
Boston 0.302 0.103 0.052
Miami 0.698 0.35 0.246
Memphis 0.409 0.131 0.029
Oklahoma City 0.591 0.222 0.06
Dallas 0.366 0.214 0.064
LA Lakers 0.634 0.433 0.17

Many teams have drastically increased their odds at the championship, but the effect is due more to the Spurs loss (my second most likely upset last round!) than to overcoming any hurdles so far. Here are the current Championship odds:

Championship Odds
Chicago 0.379
Miami 0.246
LA Lakers 0.17
Dallas 0.064
Oklahoma City 0.06
Boston 0.052
Memphis 0.029
Atlanta 0.001

Chicago has emerged as even more of a favorite than before, and they can thank Atlanta for that. While all signs indicated that Dwight Howard and Orlando would meet the Bulls in the second round, Atlanta pulled a shocking upset by tricking the Magic into not making any of their threes. Threes were never a specialty for the Bulls though, and they should easily take care of the Hawks (who in reality kinda stink) on their way to the conference finals. Because they have such an easy schedule, along with their #2 power rating, the Bulls have emerged as a true favorite.
The Lakers have also upped their odds, both through dispatching a decent first round foe, and by gaining home court advantage in the West. A Bulls Lakers finals may be in the horizon.
Last round I gave three teams to look for going forwards, (one hit, but the other two missed wildly). The round there are two teams that are getting underestimated. I swear I picked these before today's games.
Miami: People are down on the Heat because they haven't lived up to their lofty expectations. Nonetheless, they are number one in the power rankings and have home court advantage. They should take care of business relatively quickly over the Celtics. Today's 9 point win belonged to the Heat the whole way, and is a trend that will likely continue.
Memphis: The Grizzlies are not the favorites in the second round, but are the most likely team to pull an upset. The have even become a dark horse championship contender almost on the level of the Celtics and Thunder. With their game 1 win, they now have a 60.8% chance of winning the series.
Last year the second round spat in the face of my rankings, giving me only 1 winner and adding three sweeps to boot. Things look like they should go better this year, but no winner are decided. What is certain though is that there are four terrific matchups to watch in the second round. I'm pumped.

True Hoop 2011 Second Round

After the first round of the NBA playoffs I've accumulated 29 total points which would put me in 5th in the TrueHoop Stat Geek Smackdown. It's not as good of a start as last year, but I'm still in the game. Here are my picks for the second round (full odds and analysis will come sometime tomorrow).

Chicago over Atlanta in 5
Miami over Boston in 5
Oklahoma City over Memphis in 7
Los Angeles over Dallas in 7

It's pretty bland, going with all favorites, but I'm hoping to gain a couple points in series length. 2.83 expected series wins plus .97 expected series length picks means I should hope for about 16 points this round. A little better would be a nice boost too.

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.

Wednesday, March 30, 2011

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.

Tuesday, March 29, 2011

Final Four Odds and Analysis

Okay, I haven't fared well so far, but I still ran the bracket predictor for final four teams (both Men's and Women's). Who gonna be the champ?
Men's Odds
Kentucky 46.7
Connecticut 30.1
Butler 17.8
VCU 5.4

Kentucky was actually (yeah Dad, actually) the sixth highest rated team in the polls, and a has had a reasonable chance to win it all along. Now they should definitely be considered the favorites, but as this tournament has shown anybody can win (even VCU, although the odds are still not good).

Women's Odds
Connecticut 47.7
Stanford 26.9
Texas A&M 17.7
Notre Dame 7.7

The odds look shockingly similar to the men's odds, but the women's tournament has been light on upsets. Why are they so spread out? There are two reasons: first, the top few women's teams are comparatively better than the top few men's teams (look at the power ratings), so UConn and Stanford spread it out a little bit. The best teams are also on opposite sides of the bracket, as opposed to the men where either Butler or VCU has to make the final. Either way, both final fours look to be exciting with a clear favorite but a couple strong underdogs.

Tuesday, March 22, 2011

The Game Theory of 21

On Sunday a great basketball rivalry was renewed. It was not the Kings and Timberwolves fighting to stay out of last place, it was Andy, Jimmy and I playing 21 (a basketball game). In general when we play I win probably two thirds of the time, Andy will win one third, and Jimmy will never win (Burn!*). Recently though, Jimmy has started winning, highlighted by a game Sunday when Jimmy had 19, I came back to 17, and then Andy let Jimmy get a free layup for 21! With two victories in the last nine games (and zero for Andy) it appears that my secret has been uncovered: don't guard Jimmy.
Turns out, this is a classic Prisoner's dilemma. In all situations it is better for both Andy and me to not guard Jimmy (example odds of winning in each case are illustrated in the table). As a result though, both of us have significantly lowered our odds of winning the game.
This sort of idea comes up often in life, and a fair bit in recreational sports too. The same phenomenon applies to capture the flag: Offense is fun, but defense wins, so both teams play defense and have no fun, but still each have 1/2 chance of winning.
Could this phenomenon happen in national sports leagues? Absolutely. Off the top of my head here are a couple examples.
Helmet hits in NFL: Knocking the other team's star player out helps you win, but both teams are better off if there are no helmet to helmet hits.
College Recruiting Violations: Paying to get the best players can help you win (SMU), but if everybody does it then everybody loses.
Steroids in Baseball: Again, it's an advantage for you if you're the only one on the juice, but once everyone does it then the playing field is level again and your health sucks.
How do you get out of a Prisoner's Dilemma? Put a negative incentive on the negative behavior, including fines, sanctions, and suspensions. The leagues are all actually controlling for it fairly well. That doesn't mean I'll guard Jimmy though.
*Jimmy actually played really well when we played today. Somewhere over the past couple years he has learned to shoot and take advantage of his athleticism on the boards. He should probably get better than 0% odds on winning. That wouldn't amuse me as much though.

Sweet 16 Odds and Analysis

My personal bracket has been busted, and some of the ratings favorites (Texas, Purdue) didn't fare well either. Fortunately there's still four rounds left to go, and places like Yahoo! have bracket contests for them too (here's the stats bracket for the last four rounds). What? You say you need the odds for the last rounds to fill that out? Here they are:

Rd 3 Rd 4 Rd 5 Rd 6
Ohio St 0.628 0.456 0.278 0.177
Kentucky 0.372 0.228 0.111 0.058
Marquette 0.414 0.113 0.038 0.014
North Carolina 0.586 0.203 0.083 0.037
Duke 0.731 0.49 0.286 0.178
Arizona 0.269 0.115 0.04 0.016
Connecticut 0.456 0.17 0.067 0.029
San Diego St 0.544 0.225 0.098 0.046
Kansas 0.826 0.676 0.462 0.256
Richmond 0.174 0.087 0.028 0.006
VA Commonwealth 0.286 0.04 0.008 0.001
Florida St 0.714 0.197 0.074 0.019
Butler 0.281 0.091 0.025 0.005
Wisconsin 0.719 0.393 0.183 0.075
BYU 0.583 0.32 0.146 0.058
Florida 0.417 0.196 0.075 0.024

Of particular interest here is the improvement of Kansas's odds thanks to weak opponents. From the championship odds below it's easy to see that Kansas is now the favorite to win it all, in large part because they have a 67.6% chance of making the final four.
Remaining Championship Odds
Team Odds
1 Kansas 0.2559
1 Duke 0.1779
1 Ohio St 0.1774
4 Wisconsin 0.075
3 BYU 0.0581
4 Kentucky 0.0575
2 San Diego St 0.0465
2 North Carolina 0.0369
3 Connecticut 0.029
2 Florida 0.0244
10 Florida St 0.0194
5 Arizona 0.0158
11 Marquette 0.0137
12 Richmond 0.006
8 Butler 0.0055
11 VA Commonwealth 0.001

A lot of weird things happened earlier in the tournament (chances VCU makes the sweet 16: 1.26%), and I started wondering if momentum actually played a role in college basketball. I weighted the Power Rankings to give the last 4 weeks 3 times the weight, and the last 2 weeks got 5 times the weight, expecting to see that Louisville/Purdue/Texas would drop significantly. The top 15 shows otherwise though:
Top 15 with Mo'
1 Ohio St
2 Duke
3 Louisville
4 Kansas
5 Notre Dame
6 Kentucky
7 San Diego St
8 Pittsburgh
9 Texas
10 Connecticut
11 Syracuse
12 Purdue
13 Washington
14 North Carolina
15 West Virginia

There were 5 surprise losses in the first round (LV, ND, Pitt, TX, Purdue). Adding up their rankings in the regular rankings they add to 38, and here? 37. Looks like momentum doesn't explain why the ratings have fared poorly so far. I think the real reason that my computer (and other stats ratings) haven't fared well is that sometimes, these things happen.


Tuesday, March 15, 2011

Bracket Analysis 2011

There were a lot of number in that last post, but what can you really get out of it? Here are some key bits o' knowledge.

Ten Most Likely Champions
Seed Team Chance
1 Ohio St 0.148
1 Duke 0.136
1 Kansas 0.121
1 Pittsburgh 0.088
4 Texas 0.065
3 Purdue 0.045
4 Louisville 0.039
4 Kentucky 0.039
2 San Diego St 0.033
3 BYU 0.033

This year is dominated by the one seeds and... the four seeds? The strength of the four seeds shows up throughout this bracket.

Best Final Four Odds By Region
1 Ohio St 0.368 1 Duke 0.357
4 Kentucky 0.148 4 Texas 0.207
7 Washington 0.13 2 San Diego St 0.152
3 Syracuse 0.112 3 Connecticut 0.097
2 North Carolina 0.095 5 Arizona 0.048
1 Kansas 0.318 1 Pittsburgh 0.325
3 Purdue 0.177 3 BYU 0.178
4 Louisville 0.155 4 Wisconsin 0.131
2 Notre Dame 0.14 2 Florida 0.105
6 Georgetown 0.042 5 Kansas St 0.04

Each Region's 4 seed is better than it's two seed? Maybe I was too early in praising the selection committee. Also notable are Washington's strong Cinderella chances.

Most Likely First Round Upsets
1 11 Marquette 6 Xavier 0.583
2 9 Villanova 8 George Mason 0.545
3 9 Illinois 8 UNLV 0.541
4 10 Michigan St 7 UCLA 0.53
5 11 Gonzaga 6 St Johns 0.497
6 10 Forida St 7 Texas A&M 0.495
7 12 Utah St 5 Kansas St 0.489
8 10 Penn St 7 Temple 0.474
9 9 Tennessee 8 Michigan 0.469
10 11 Missouri 6 Cincinnati 0.465

I know everybody likes 12-5 upsets, and everybody wants Arizona and Vandy to lose. But that's not what's good this year, instead it's time to look at the 11-6 games. They've got the best bang for your buck.

Compared to how their seed usually does, here are the top 5 over/under achievers by number of wins better/worse than usual, and by number of times as many wins (i.e. Belmont can expect 2.16 times as many wins as a normal 13 seed, but still not many).
5 UNDER Wins 5 OVER Wins
2 North Carolina -0.716 7 Washington 0.902
2 Florida -0.655 4 Texas 0.654
6 Xavier -0.63 4 Louisville 0.514
1 Pittsburgh -0.575 11 Marquette 0.512
1 Kansas -0.545 4 Kentucky 0.441
5 UNDER Perc 5 OVER Perc
14 St Peter's 0.483 13 Belmont 2.16
6 Xavier 0.507 7 Washington 2.06
10 Georgia 0.511 11 Marquette 2.02
13 Morehead St 0.537 11 Gonzaga 1.69
12 Memphis 0.56 11 Missouri 1.65

As we saw before, 4 seeds are good here while 2 seeds are bad. 11 seeds also show strongly, as does Washington. If you're looking for someone to make a run this tournament, Washington and Marquette may be the way to go.

There you have it, the expected trends at a glance going into the tournament. Not all of these are going to happen, and I'll probably feel like a fool, but expect at least some of these trends to show up.