I got it! I got it! I really got it!
I haven't had much of a chance to get to ballgames this year. I normally go to about a dozen or so A's games during a typical season, but this year I basically haven't made it to any. Life has just filled up with other things to do. But last night, the mystical forces of the diamond converged in the form of a pair of free tickets and a free parking night at the O.co Coliseum. Athletics vs. Astros, woohoo!
It was a beautiful night for a ballgame. Temperature was in the mid sixties or so, with very little wind. At first pitch, it didn't seem like there would be a very large crowd. There were lots of empty seats. I guessed that fewer than 10,000 fans were in attendance, which was actually kind of okay with me. I like the relatively lay back atmosphere of these mid July games. But as the game wore on, more and more people began to sit down. Checking this morning, official attendance was 22,908. Not too bad.
A very nice game all in all. The A's gave up 2 runs in the top of the third, but scored in the bottom half and again in the sixth to tie the game. It remained that way until the end of regulation, but L.J. Hoes would end up hitting a home run for the Astros in the top of the 12th, and the A's went down 1-2-3 in the bottom half.
Ah, but I've buried the lead.
In all the years that I've been going to ballgames, I have never come away with a foul ball. I have been hit in the head by one, but my slow reflexes, and the near concussion meant that I didn't come up with the ball on my one best shot at getting one. But last night, I finally did it, in the most surprising way.
Carmen and I were seated in row 29 of section 113, which is directly (but far) behind the visiting teams dugout. The top of the third had just ended, so I was just sitting there, checking my phone when.... suddenly people around me are excited. I look up just in time to see a ball, which literally landed in my lap, bounced against my chest, and stopped. I'm guessing that one of the Astros lobbed this ball trying to get it to the very cool pair of Astros fans in row 20 or so, but had misjudged. And so, this time without the threat of head injury, I got my first game ball:
Awesome! Achievement unlocked.
MLB.TV still stupidly refusing to offer me a product that I want to buy…
Two years ago, I complained that MLB.TV's black out rules basically robbed them of a chance to get $120 of my hard earned cash in exchange for a product which they supply to others in the U.S., but which they refuse to sell me. Fast forward to today, and nothing has changed: I still can't buy live access to all Oakland Athletics games for any amount of money, even though if I lived in somewhere else, I could buy their product. Isn't it time (beyond time) for these silly exclusivity agreements to fade away?
I'm not the only one whose been complaining about this for years.
It seems startlingly anti-consumer for these blackout agreements to continue. The artificial scarcity created by these policies do nothing to enhance the fan experience. I've seldom seen an industry work so hard to avoid selling a product that they have and could sell to consumers.
Ridiculous.
Baseball and Pascal’s Triangle
I was standing in Tom's office, and asked him a simple probability question (and a timely one, given the World Series):
If the odds of a particular team winning against their opponent is some probability p, what are the odds that they will win a 7 game series?
If you had any probability at all, you probably have solved this problem before. I know I have: I blogged about it before.. But I was trying to remember the equations: I knew they had something to do with the binomial coefficients, but their exact form seemed problematic.
Tom pointed out that you could just write it down by making a table. We are looking for the best 4 out of 7, so let's make a 5x5 array. For each cell_{ij}, we are going to compute the odds that the series will reach team A having I wins and team B having
1 | ||||
Let's say that team A wins with probability p, and team B wins with probaility q (note that q = 1 - p). Each time team A wins, let's move one step to the right... Let's imagine that team A wins in a clean sweep, we can fill in those numbers quite easily:
1 | p | p^{2} | p^{3} | p^{4} |
Similarly, we can compute the odds that team B has a clean sweep by marching down the first column, multiplying each previous entry by q.
1 | p | p^{2} | p^{3} | p^{4} |
q | ||||
q^{2} | ||||
q^{3} | ||||
q^{4} |
But now, what are the odds that we reach (say) a 1-1 even series. Well, there are two ways of reaching 1-1, either team A wins then team B, or team B wins then team A. If the games are independent, then the odds are the same regardless of the path taken, and there are two paths. So, we can fill 1-1 in as 2 p q ...
1 | p | p^{2} | p^{3} | p^{4} |
q | 2 p q | |||
q^{2} | ||||
q^{3} | ||||
q^{4} |
We can continue this, being careful to keep track of the number of paths, and it will begin to look like Pascal's triangle...
1 | p | p^{2} | p^{3} | p^{4} |
q | 2 p q | 3 p^{2} q | 4 p^{3} q | |
q^{2} | 3 p q^{2} | 6 p^{2} q^{2} | ||
q^{3} | 4 p q^{3} | |||
q^{4} |
If you are familiar with Pascal's triangle, or with binomial coefficients, those numbers are beginning to look pretty familiar to you. But you have to be a little careful in filling in the remaining squares: for instance, it's perfectly possible for the series to end 4-1, but there are no paths that end up there that pass through 4-0 (when the first team wins 4 games, the series is over). So you don't continue to add in the same way. for these remaining squares. And, of course the series won't end 4-4, so the final square will remain unfilled.
1 | p | p^{2} | p^{3} | p^{4} |
q | 2 p q | 3 p^{2} q | 4 p^{3} q | 4 p^{4}q |
q^{2} | 3 p q^{2} | 6 p^{2} q^{2} | 10 p^{3} q^{2} | 10 p^{4} q^{2} |
q^{3} | 4 p q^{3} | 10 p^{2} q^{3} | 20 p^{3} q^{3} | 20 p^{4} q^{3} |
q^{4} | 4 p q^{4} | 10 p^{2} q^{4} | 20 p^{3} q^{4} |
So, what are the odds that team A wins? We can just sum up the probabilities in the final column. That team B wins? We can sum up the final row (and the combination better add up to one).
Let's say that p = 0.5. That means p = q, and we'd expect the odds to be the same. Just staring at the equations, substituting p for q should convince you that the probabilities are the same. If we've filled in our formulas correctly, we'd expect the overall probability to be 0.5 as well. It's far from obvious to me, staring at those equations that it's true, but if you go ahead and plug in the numbers, you'll find that it does indeed work out.
So, let's say that in a (for examples) Rangers vs. St. Louis matchup, the Rangers would win 60% of their games. What are the odds that the Red Birds win the Series? About 26.4% of the time. But if the Series is all tied up 3-3, then of course their probability is 40%.
Of course all this doesn't take into account the difference in home field advantage, or pitching matchups, or any of a million other factors, so it's relation to any games being played tonight is strictly theoretical.
St. Louis hangs in, there will be a Game 7 tomorrow!
Absolutely the most amazing World Series Game I've seen. I'm speechless. My words aren't sufficient: I'll post some links when I find someone better than me to put the game in perspective. Amazing.
Nifty paper on Batting Average…
For some reason, I never do much reading about baseball during the season itself. But as the World Series approaches its end (still hoping for a game seven) I have started to dust off some of my reading materials. A couple years ago, I mentioned this work by Lawrence Brown on this blog, but the paper that he was writing was still a work-in-progress. But it's available now:
Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number
of qualifying attempts (called “at-bats”), an observed number of successes (“hits”) distributed according to the binomial distribution, and with a true (but unknown) value of pi that represents the player’s latent ability. This is a common data structure in many statistical applications; and so the methodological study here has implications for such a range of applications.
There is a lot of meat to chew in it, but some easy take aways are that simply imagining that the batting average of a player in the first half of the season is indicative of their performance in the last half is just not true: it turns out to be a relatively poor measure. A better measure is simply to average that performance with the mean batting average of all players (best predictor is that the player will regress towards the mean). I've been aware of this principle for quite some time, but Brown goes on to derive some more interesting statistical techniques, well outside my normal comfort zone. If math/statistics is your thing, check it out.
Movie Review: Moneyball
I must admit, I had my misgivings about the prospects of a movie based upon Michael Lewis' book Moneyball. After all, Moneyball is a book about how Billy Beane took the Oakland Athletics to unheard of success on one of the most meager payrolls in the major leagues using a (then) unconventional view of baseball based upon discovering and exploiting inefficiencies in the market for players. How can that be turned into a movie?
And yet, they did. And it's a great movie.
Mind you, part of it is my own nostalgia and romance for the game. I was a budding fan of baseball during this era of Athletics baseball. I watched Hudson, Mulder, and Zito. I cheered Chavez, Tejada and both Giambis. I was amazed by Koch and Bradford. I grew to love and appreciate the beauty of the game. I enjoyed the story of each season as it unwound. The glorious victories. The agonizing defeats. I still love this part of the game.
But it was more than just the on field game. I started reading. I got exposed to the works of Bill James and sabermetrics. Here was a guy who tried to systematically understand the game, and why it was the way it was. To really be able to say something definitive about the players, and how to evaluate them. The approach appealed to me, and gave me insights that I didn't have before. It helped explain why the Athletics did what they did.
And I began to appreciate the business game. How clever, low payroll teams could still compete against big market teams like the Yankees.
But how could you make a movie that conveys all these things on screen?
Well, the Moneyball story is a fascinating story. And Aaron Sorkin has done an amazing job of adapting it to the screen. Brad Pitt does a great job portraying Billy Beane. And in the end, I was blown away at how powerful the movie was.
I know part of it is my own love for my adopted home team. It's awesome to see angles of the Oakland Coliseum up on the big screen. It's not like Fenway, which seemingly appears in every movie of baseball. The Coliseum isn't an immaculate temple to baseball. It isn't even that historic. But it's where I remember seeing some amazing baseball, and where I grew to appreciate and love the game. And as I watched it in a theater in Emeryville (an Oakland suburb), I could tell that some of the audience members (a suprisingly large number) felt it too.
When people asked me what the greatest baseball movie was, I always used to say Bull Durham. That's still a great movie, but Moneyball may in fact be greater. Greater because it's a true story, about the real game. If you have any love of the game, watch it. If you don't have any love of the game, give it a try.
Update: Was Hank Aaron really that good?
Back in 2007, I was looking at the career total bases expressed as miles, mainly to demonstrate what an outstanding career Hank Aaron had.
brainwagon » Blog Archive » Was Hank Aaron really that good?
I expressed with certainty that Bonds would never catch (and indeed, nobody may ever catch) Aaron's numbers for total bases. In his career, Aaron had 6856 total bases. If you multiply that by 90 feet, you get that Aaron ran 116.86 miles in his career.
Bonds finished with 5976 bases, for a total of 101.86 miles. That places him just above Ty Cobb (99.78 miles) but below Aaron, Musial and Mays.
Among active players, only Alex Rodriguez seems remotely possible, but he's already in his 18th season, and has 5057 total bases (as of today). He'll probably catch Griffey (5271 in 22 seasons) by the end of the year, but it would take about six or eight more years of playing at his current level to reach Aaron.
Congratulations to the 2010 World Series Champion San Francisco Giants
Okay, I'm really more of an Oakland fan, but ultimately I'm a baseball fan, and the Giants provided one of the most compelling post-season runs in recent memory. Narrowly winning the pennant on the last day of the season, avoiding a potential three-way tiebreaker. Agonizing, one inning games in round one against Atlanta. A great victorious round as underdogs against the Phillies. And ultimately triumphing over the Texas Rangers (again as underdogs) in five games to capture the series.
It's really difficult to win the World Series. Among professional sports, baseball has the greatest parity: the best teams might win 60% of their games or so. The idea that the best team will prevail just isn't that likely in reality (ask the Yankees). But this year, from September until the culmination on October 1, the Giants were arguably the best team in baseball, and certainly provided this fan with some amazing baseball moments.
Congratulations to Edgar Renteria for winning the World Series MVP as well. A fitting end to a great career.
Giants lead Phillies in the NLCS, 3-1
Wow, last night's Game 4 of the NLCS was a real nailbighter, with the Giants ultimately prevailing 6-5 in a game which saw three different lead changes. I've begun to look at baseball-reference.com for play-by-play and statistical analysis, since it breaks down the outcome of each play and gives the change in winning percentage as results. The graphs of winning percentage seem to me a more natural (and more meaningful) statistic than "momentum" or other similar measures. They also identify the top plays (which are plays which significantly change the winning percentage). If you click through here, you can see the NLCS, and its up and down nature.
National League Championship Series (NLCS) Game 4, Phillies at Giants
If you compare this to the snoozer that was the Yankees defeating Texas 7-2, you can judge for yourself what the more interesting game was.
American League Championship Series (ALCS) Game 5, Rangers at Yankees
The Giants have the opportunity to close out the series tonight at home. I was at the Game 6 where the Giants closed out against St. Louis to earn their last trip to the big show. Sadly, I'll have to watch this one at home, but I'm still pretty excited.
Lincecum vs. Halladay. It doesn't get much better than that.
Why are baseball managers so stupid? Or is it just me?
Okay, I'm currently reading The Book: Playing the Percentages in Baseball because I hate to see intentional walks. Case in point: last night's 7th inning walk of Chase Utley with one out and pitcher Roy Oswalt on second. You'd expect him to score on a double, but he's not a huge immediate threat. In any case, they walked Utley, and Placido Polanco singles. Oswalt actually runs hard and scores, and you have two men on with one out, except now you are down a run, with Ryan Howard at bat. "Our situation has not improved." During Howard's at bat, the Phillies pull a double-steal. Howard strikes out, but now we have first base open, with Jayson Werth batting. Argh! Because of the double steal, they intentionally walk Werth to load the bases. Yes, Werth has been a hot hand in the playoffs, and Rollins was underachieving. But all those statistics are meaningless: it's not like Rollins was really as bad as his recent slump would indicate. He's a .272 career hitter (same as Werth), and if you give him plate appearances, he'll show you it. He doubles, three runs scores, and it's a sad day for the Giants.
Intentional walks really annoy me. Perhaps wrongly though. I was rereading some analysis of a game I remember from 2005.
Back in 2005, I blogged a tiny bit about the following game, which courtesy of baseball-reference.com, now has a very interesting analysis. In this game, the Astros were leading 4-2, and with the Cardinals batting in the bottom of the 9th, they got two quick outs, but Eckstein singles, and then steals second due to fielder indifference. "The theory" says at that point that the Cardinals only have a 4% chance of winning if the Cardinals played as an "average" team. Brad Lidge walks (on five pitches, not intentionally) Jim Edmonds, and St. Louis rises to a 7% win expectancy, again, assuming an "average team". But the next batter isn't an average batter: it's Pujols. He cracks a home run, St. Louis scores three, and St. Louis wins (the Astros would win the series though).
So, here's the question: on average teams, walking Edmonds only cost an additional 3% chance of handing the win to the opponents, but given that Pujols was the next batter, what's a reasonable estimate for how costly that walk is? And if we did a similar analysis on the IBB's in last night's game, what would we find?
Well, you can go here and find out. The Giants only have a 1:4 chance of overcoming their deficit, and the intentional walk only changes that by a single percentage point. Polanco's single increases that to 1:9, and the double steal increases that by 3%. Again, the intentional walk to Werth costs them about 1%, which frankly, I can't argue with too much. The game is practically over, and these plays (as dramatic as they seem to me) hardly do much to harm SF's small chance of making a comeback.
I hate it when I find out that my indignation is probably not righteous.
What do I know about baseball?
Back in 2004, I blogged a short message about the game four performance of the Red Sox against the Yankees.
brainwagon » Blog Archive » Red Sox 6, Yankees 4, 12 innings.
I had turned off the game after 7 innings, missing Bill Mueller's RBI single in the bottom of the ninth to tie the game, and ultimately Ortiz's game winning homer in the bottom of the 12th to win the game for Boston.
In my post, I warned the Red Sox that their defeat was inevitable.
Of course, this was 2004, where despite trailing the Yankees 3-0, the Red Sox rallied with four wins in a row in some of the most thrilling post season baseball I can remember, and ultimately going on to win the World Series.
I apparently don't know much about baseball. "Inevitable doom" indeed.
A question from the ballgame…
Can someone (preferably somebody whose very keen on baseball, especially sabermetrics) answer me a question?
Tonight I was at the game between the Athletics and Twins in Oakland. After trailing 1-3, the A's score twice in the bottom of the eighth inning to tie the game up going into the ninth. Danny Valencia strikes out. With nobody out, Justin Morneau replaces Brendan Harris.
Okay, here's the question: you are in a tie game, with nobody on base. Justin Morneau is batting .376, to be followed by Nick Punto, who is batting around .200. What do you do?
The Athletics chose to intentionally walk Morneau. Sadly, they also ended up walking Punto, after they pulled Morneau for a pinch runner. Span then hits a grounder and Punto is out at second, but Span beats the throw, and we have runners at the corners with two out. Tolbert (batting about .167) pokes a shot out to center field, and the Twins score.
I can't understand the utility of walking Morneau. Yes, he's batting .375 or whatever, which means that over 60% of the time, he doesn't reach base, and you then have two outs, facing Punto, Span, and Tolbert. If he singles, you are in exactly the same place you were if you intentionally walked him. So you are betting that 63% of the time making an out is less desirable than 34/191 (34 extra base hits in 191 at-bats) chance of getting an extra base hit. Sure, I haven't quite factored in chance that you accidently walk Morneau, but I can't help but think that the intentional walk is the wrong play.
What do others think?
Perfect Game, Imperfect Call
Yesterday was an intereseting day in baseball. In the last month, we've seen two perfect games pitched: the first by Dallas Braden, and the second by Roy Halladay. For those of you who aren't big baseball fans, those were only the 19th and 20th perfect games recorded in Major League Baseball history. The last time two had occurred in the same year was in 1880.
Which brings us to yesterday. June 2, 2010, in a matchup between the Detroit Tigers and the Cleveland Indians. The pitcher for the Tigers was Armando Galarraga, who had recently been called up from the Detroit Triple-A affiliate and placed in the starting rotation. His ERA going into the game was an unremarkable 4.50.
He pitched eight and two thirds innings, with no hits, and no walks. Another perfect game in the making? The batter was Jason Donald, who hit a grounder to right field which was fielded by Miguel Cabrera, who tossed to Galarraga, who was covering first base. A perfect game!
But wait... the umpire Jim Joyce called Donald safe!
Wow. If there is one thing that is even rarer than perfect games, it's perfect games that are spoiled by the 27th batter. There were nine prior to last night. I actually was lucky enough to see one (on TV, not live) when Mike Mussina of the Yankees gave up a hit to Carl Everett of the Red Sox in September, 2001 (the last time it happened).
But here's the tragic thing: the umpire completely blew the call. Donald was out by a step. A long step. Joyce just flat out blew the call. Upon seeing the replay, he admits he blew the call. But baseball doesn't have instant replay, so the ruling stands, and Galarraga misses out on being the 21st perfect game hitter.
Okay, that;'s the background: here's my take.
Give the kid the perfect game. Donald was clearly out. As far as I can tell, everyone involved, from teams on both sides to the umpire agree that he should have been called out. It would have been the end of the game, so there is no needless speculation of how it would have changed the game: the game would have been over, except that Donald has one less hit in his batting average, and Galarraga would be properly recorded as the 21st pitcher to throw a perfect game. Any other outcome is a travesty of rules over substance. The rules should enable us to get the call right, not require that a wrong call be made official.
And cut Jim Joyce some slack. He blew a call. Yes, it was a bad call, but he freely admits and would absolutely reverse his call if it were in his power to do so. You don't make mistakes at your job? Get over it.
False advertising for MLB.TV?
I've got opening night tickets for the Athletics/Mariners opener next Monday, and once again, baseball is beginning to creep into my brain. I'm an XM radio subscriber largely because they broadcast pretty much every MLB game, and I enjoy listening to the play by play while driving around. Last year I also had a lot of fun with the very good iPhone app, which includes streaming audio of every game, which extends my ability to listen to live games.
So, with the new season, I was considering the possibility of adding MLB.TV and get video streaming. It seems like a very nice package, and costs about $120 for the entire season. They advertise:
Seems like a good pretty good deal. I like to track the A's, and there are other teams/games I would certainly watch. The only problem with it is that it is false advertising.
You can't actually watch 2,430 games live because of blackout restrictions. I'm in Northern California, where according to MLB both the Athletics and the Giants are blacked out. And not just for games played locally, but even away games. In other words, MLB.TV doesn't help me see even a single game for the two teams that play locally, even when they aren't playing locally, or even if they aren't being broadcast locally at all.
But it doesn't even stop there: there are lots of Saturday and Sunday blackouts too. Live games starting after 1:10 ET and before 7:05ET are blacked out in the entire United States. I dunno about you, but those are kind of the premium baseball watching times for me. The fact that I can't use my premium package to watch live baseball then seems pretty damned lame.
Yes, you can watch them on demand. As long as you demand them later.
This is ridiculous. I want to spend money to watch these games, but the MLB is apparently doing all they can to keep from delivering the product which every single baseball fan wants.
Sorry MLB.TV, I'm keeping my $120 for now.
Batting Stance Guy on Letterman
Thanks to Bob @ work for mentioning this to me. I think I appreciate this guy not just for his knowledge of batters and their stances, but for the self-deprecating way in which he presents his "least marketable skill". That, my friends, is a baseball fan.
httpv://www.youtube.com/watch?v=4sPakL5On3Y