World Series Probability

I play World Series Superstars and they recently challenged us to predict how each game of the series would play out. A user asked on their forum, "What do you think the odds are that someone will actually pick the entire series correctly game for game?" I attempted to find the answer online, but the majority of the websites I found were either determining how many games the series would last or predicted the betting odds.

I took it upon myself to try to figure this out, but had to consider several items first:
1) It's a best of seven game series.
2) The winner must win four games.
3) There will either be four, five, six, or seven total games played.
4) The series ends when a team wins their fourth game.
5) Consider a team has a 50/50 chance to win a game.

I enjoy statistics, but I was not sure how to solve this scenario with a binomial distribution equation or what have you, so I typed it out by hand. If the following information is accurate and complete, then you have a 1 in 70 (1.429%) chance of selecting the correct outcome.

Feel free to look over my details and let me know if you find any mistakes. My prediction is highlighted in bold red letters. Leave your prediction in the comments.

Four game series (2 outcomes) 4-0

StL wins Tex wins

C-C-C-C R-R-R-R

Five game series (8 outcomes) 4-1

StL wins Tex wins

R-C-C-C-C C-R-R-R-R

C-R-C-C-C R-C-R-R-R

C-C-R-C-C R-R-C-R-R

C-C-C-R-C R-R-R-C-R

Six game series (20 outcomes) 4-2

StL wins Tex wins

R-R-C-C-C-C C-C-R-R-R-R

R-C-R-C-C-C C-R-C-R-R-R

R-C-C-R-C-C C-R-R-C-R-R

R-C-C-C-R-C C-R-R-R-C-R

C-R-R-C-C-C R-C-C-R-R-R

C-R-C-R-C-C R-C-R-C-R-R

C-R-C-C-R-C R-C-R-R-C-R

C-C-R-R-C-C R-R-C-C-R-R

C-C-R-C-R-C R-R-C-R-C-R

C-C-C-R-R-C R-R-R-C-C-R

Seven game series (40 outcomes) 4-3

StL wins Tex wins

R-R-R-C-C-C-C C-C-C-R-R-R-R

R-R-C-R-C-C-C C-C-R-C-R-R-R

R-R-C-C-R-C-C C-C-R-R-C-R-R

R-R-C-C-C-R-C C-C-R-R-R-C-R

R-C-R-R-C-C-C C-R-C-C-R-R-R

R-C-R-C-R-C-C C-R-C-R-C-R-R

R-C-R-C-C-R-C C-R-C-R-R-C-R

R-C-C-R-R-C-C C-R-R-C-C-R-R

R-C-C-R-C-R-C C-R-R-C-R-C-R

R-C-C-C-R-R-C C-R-R-R-C-C-R

C-R-R-R-C-C-C R-C-C-C-R-R-R

C-R-R-C-R-C-C R-C-C-R-C-R-R

C-R-R-C-C-R-C R-C-C-R-R-C-R

C-R-C-R-R-C-C R-C-R-C-C-R-R

C-R-C-R-C-R-C R-C-R-C-R-C-R

C-R-C-C-R-R-C R-C-R-R-C-C-R

C-C-R-R-R-C-C R-R-C-C-C-R-R

C-C-R-R-C-R-C R-R-C-C-R-C-R

C-C-R-C-R-R-C R-R-C-R-C-C-R

C-C-C-R-R-R-C R-R-R-C-C-C-R

Update...
I must admit my shameful inability to count as I originally stated there were 10 possible outcomes in a five game series when there are actually only 8. I corrected the error thanks to UofMWolv25 from Playfish forum. I can now support this claim as well.

Four game series:
One team must win the first four games in a row.
1/2^4 + 1/2^4 = 2/16

Five game series:
One team must win exactly 3 out of the first 4 games, and then win the fifth game.
C(4,3) 1/2^5 + C(4,3) 1/2^5 = 8/32

Six game series:
One team must win exactly 3 out of the first 5 games, and then win the sixth game.
C(5,3) 1/2^6 + C(5,3) 1/2^6 = 20/64

Seven game series:
One team must win exactly 3 out of the first 6 games, and then win the seventh game.
C(6,3) 1/2^7 + C(6,3) 1/2^7 = 40/128

If you add the numerator from each possible series (2, 8, 20, 40), then you get 70.

1 in 70 chance (1.429%)

Should the Pirates Keep Maholm

I have been talking a lot about the Postseason, simply because it's more exciting, but there has been a lot of talk about Paul Maholm lately. In case you have been too caught up with the Playoffs, living under a rock or are simply not a Pittsburgh resident, Maholm has a team option in his current contract worth $9.75 million.

Is he worth that much?
Many fans say, "No." Analysts say, "Probably." The Pirates are a hanging chad so far.

Maholm earned $6.25 million in 2011 or $5.75M, depending on where you look. He posted a respectable ERA of 3.66 and WHIP of 1.29; both of which were better than the league, team, and his career averages; but he has not posted a winning percentage on the positive side (in true Pirate fashion) since becoming a full-time starter in 2006.

His record in 2011 was a dismal 6-14. Many analysts have attributed his high loss count to poor run support. It's true the Pirates offense is lacking, to say the least, but how true is this assumption? The Pirates offense only scored an average of 3.77 runs per game (27th in the MLB), so it certainly seems likely.

Worst RS/9 for Starting Pitchers with 150 Innings Pitched or more, Fangraphs

There were 105 starting pitchers who accumulated 150 innings pitched or more, Maholm had the sixth worst run support over nine innings (RS/9) among them all. Ouch.

The 2011 RS/9 average was 4.59, which left three of the Pirates regular starters below the threshold, one near average, and one slightly above average. It was quite surprising to see Tim Lincecum beating everyone out for the top slot. If an amazing pitcher like Lincecum was on this list, then perhaps Maholm's pitching woes is driven by poor offense as well.

I am not a believer, so let's look over the data.

Maholm's total games started and innings pitched were both below average, but he went on the disabled list on August 19th. Otherwise he would have reached the league averages quite easily. His ERA and WHIP may have been better than average, but those are primitive statistics that rely too much on factors outside of what a pitcher can control. His BABIP and FIP were both slightly better than the norm, which would account for a little bit of defensive luck and explain his good ERA and WHIP scores. His SIERA score is slightly worse than average due to his poor strikeout count and rate.


The five pitchers who had worse run support than Maholm all accumulated a higher Wins Above Replacement value than him, as well as the rest of the Pirates starting rotation. They all recorded better values than him in regard to FIP, SIERA, K/9, and K/BB. The only statistic Maholm really has going for him is K/BB, which was better than average and the top five.

The average 2011 starting pitcher recorded 149 strikeouts at a rate of 6.75 K/9. Maholm was far below those averages with 97 strikeouts and 5.38 K/9. In fact the only Pirates starter who recorded an above average strikeout rate was James McDonald, which explains why he is the only pitcher I enjoy watching and hope the Pirates retain for a while.

Paul Maholm is a pitcher who relies too heavily on luck. He walks batters almost as rarely as he strikes them out, thus he has to rely on ground balls, fly balls, the defense behind him, and praying the ball stays inside the park. All that said, he is still an average pitcher with a WAR of 2.1. If a team values a win somewhere between $4 and 5 million, then he should collect a contract in the range of $8.4 and $10.5 million.

Should the Pirates keep Maholm? That's the 9.75 million dollar question.

Glossary
BABIP - Batting Average on Balls In Play
FIP - Fielding Independent Pitching
SIERA - Skill-Interactive Earned Runned Average

Irony

The St. Louis Cardinals will be facing the Texas Rangers in the World Series on Wednesday with home field advantage. The announcers for last night's NLCS game made a few interesting points regarding how the Cardinals got where they are today.

The Philadelphia Phillies swept the Atlanta Braves twice in September and ended the season with a series record of 12-6. If the Phillies would have opted to lose the final game of the regular season against the Braves, then it would have forced a one game playoff for the National League Wild Card. The Phillies could have faced the Brewers in the NLDS with whom they had a 4-3 record in the regular season, which would have been slightly favorable compared to their record against the Cards, 5-9. Knowing this, losing to the Cardinals in the NLDS was avoidable.

Prince Fielder hit a three-run homer in this year's All-Star game in Arizona and won the All-Star game MVP award. His home run provided the National League with home field advantage at the World Series. Funny how he inevitably helped the Cardinals, the team the Brewers were trying to beat in the NLCS, and gave them home field advantage.

My friend also suggested I should point out how long I waited for my childhood hometown team to make a run for the playoffs. I will continue waiting for the Pittsburgh Pirates to at least cross the .500 hump before I hope for a postseason run. Then I move to St. Louis and the Cards make it to the World Series during my first year with my new hometown team.

Oh, the irony.

Rangers and Redbirds

The Texas Rangers defeated the Detroit Tigers on Saturday to win the ALCS 4-2.

One day later the St. Louis Cardinals beat the Milwaukee Brewers to win the NLCS 4-2.

This Wordle image was created using the all the players on each Championship team's roster with a WAR of 0.5 or higher, then weighted as such.

World Series, St. Louis Cardinals and Texas Rangers (Wordle)

The Cards are my new home team and made a fantastic turnaround from 10 games behind in the Wild Card race in late August to where they are today: National League Champions. TLR may get criticized a lot, but you can't argue with results, especially with all the injuries they had to endure. I will be cheering for them on the outside.

The Rangers ball club appears to be built better with the best team batting average in the Majors (.283), second best slugging percentage (.460), and second most home runs (210). They can hit, run, and have great depth in the bullpen. Ron Washington is a great manager who is both intelligent and very entertaining to watch. This will be the Rangers' second consecutive appearance in the World Series, as well as their second appearance overall, and is among the six Major League organizations who have never won a World Series crown. To top it all off, Nolan Ryan was my childhood idol.

Will the Cardinals win their 11th World Series or will the Rangers win their first?

I'll be honest. I really don't mind who wins the World Series.

Happy Flight

The St. Louis Cardinals just defeated the Milwaukee Brewers 12-6 and won the NLCS 4-2. There were six homers hit in the first three innings, but the ball stayed inside the park from that point onward. That ties the record for most homers in a game, which the Texas Rangers and Detroit Tigers also tied yesterday.

David Freese received the award for the National League Championship Most Valuable Player. He was great in the regular season and outstanding in the postseason. A lot of credit has to go to the relief pitchers in the Cardinals bullpen since the starting pitching has been so poor as of late.

David Freese, NLCS MVP from ESPN.com

Congratulations to the Cards. Good luck in the World Series against the Rangers.

Have a happy flight home.