The Law of Truly Large Numbers

The Law of Truly Large Numbers
With a large enough sample, any outrageous thing is likely to happen. The point is that truly rare events, say events that occur only once in a million [as the mathematician Littlewood (1953) required for an event to be surprising] are bound to be plentiful in a population of 250 million people. If a coincidence occurs to one person in a million each day, then we expect 250 occurrences a day and close to 100,000 such occurrences a year.

Going from a year to a lifetime and from the population of the United States to that of the world (5 billion at this writing), we can be absolutely sure that we will see incredibly remarkable events. When such events occur, they are often noted and recorded. If they happen to us or someone we know, it is hard to escape that spooky feeling.

http://www.wired.com/wiredscience/2012/05/methods-for-studying-coincidences/


02 January 2011

Position Battles: Cubs, Reds, Astros, Brewers, Pirates, Cardinals

Chicago Cubs
None

Cincinnati Reds
Left Field
Jonny Gomes (favorite) vs Chris Heisey (underdog) vs Todd Frazier (underdog) vs Juan Francisco (long shot)

Tale of the Tape
Gomes: 30 years old, $1.75M salary, .266/.327/.431 in 511 AB's, 5 SB, -19.1 UZR/150
Heisey: 26 years old, $440K salary, .254/.324/.433 in 201 AB's, 1 SB
Frazier: 25 years old, $414K salary, .258/.333/.448 in 480 AB's, 14 SB (AAA)
Francisco: 26 years old, $414K salary, .286/.325/.565 in 308 AB's, 1 SB (AAA)

Analysis: After hitting .266 with 18 HR's and 86 RBI's for the NL Central Champs, Gomes will go into spring training as the starting left fielder. It's important to note, however, that the 30 year-old did most of his damage against LHP's (.857 OPS) while his .709 OPS is barely passable for someone not making a difference defensively or on the base paths. Thus, there could be some competition coming his way. In limited playing time, the right-handed hitting Heisey had a .925 OPS against RHP's but was terrible against LHP's (.545 OPS). Frazier, who came into the 2010 season as the team's #1 prospect according to Baseball America, got off to a slow start in Triple-A but posted an .854 OPS over the second half of the season. Francisco would give the team a third left-handed hitting power threat, but he has limited experience in the outfield and probably isn't ready to make the move.

#5 Starter
Travis Wood (even) vs Mike Leake (even)

Tale of the Tape
Wood: 24 years old, $440K salary, 5-4, 3.51 ERA, 102.2 IP, 85 H, 26 H, 86 K in 17 starts
Leake: 24 years old, $440K salary, 8-4, 4.23 ERA, 138.1 IP, 158 H, 49 BB, 91 K in 24 games (22 starts)

Analysis: As would be expected from a rookie making the jump directly from college to the pros, Leake wore down in the second half of the season and was eventually shut down. It wasn't before he made quite an early impression, posting a 6-1 record and 3.53 ERA by the All-Star break. Wood filled in admirably, finishing the season strong with seven straight starts of 3 ER's or less. Both deserve to be in a major league rotation. Good problem to have for the Reds.

Houston Astros
#5 Starter
Nelson Figueroa (slight favorite) vs Ryan Rowland-Smith (slight underdog) vs Aneury Rodriguez (long shot) vs Lance Pendleton (long shot)

Tale of the Tape
Figueroa: 36 years old, $900K salary, 7-4, 3.29 ERA, 93 IP, 84 H, 34 BB, 73 K in 31 games (11 starts)
Rowland-Smith: 28 years old, $725K salary, 1-10, 6.75 ERA, 109.1 IP, 141 H, 44 BB, 49 K in 27 games (20 starts)
Rodriguez: 23 years old, $414K salary, 7-5, 3.71 ERA, 123.2 IP, 113 H, 51 BB, 100 K (AAA/AA)
Pendleton: 27 years old, $414K salary, 12-5, 3.61 ERA, 154.2 IP, 124 H, 57 BB, 133 K (AAA/AA)

Analysis: Thirty-six year-old journeyman or not, Figueroa was terrific last season, especially after he was claimed off waivers from the Phillies and eventually inserted into the rotation. His competition comes from Rowland-Smith, coming off of a nightmare season, and two Rule-V picks. Rowland-Smith was an effective pitcher prior to 2010 so there's a chance he can rebound and win the job in spring training. Rule V picks typically have a hard time even sticking as long relievers, so Rodriguez and Pendleton will have to be really good in spring training to get a look as starters.

Milwaukee Brewers
Center Field
Carlos Gomez (favorite) vs Chris Dickerson (underdog)

Tale of the Tape
Gomez: 25 years old, $1.5M salary, .247/.298/.357 in 291 AB's, 18 SB, 8.0 UZR/150
Dickerson: 28 years old, $440K salary, .206/.250/.268 in 97 AB's, 4 SB

Analysis: With Lorenzo Cain officially out of the competition after he was dealt to Kansas City, it appears that Gomez will get another chance to live up to his potential. Dickerson suffered through an injury-plagued and unproductive season but he had previously showed promise as an athletic left-handed hitter with an ability to get on base at a high rate. He'll likely need to outplay Gomez by a wide margin in spring training in order to win the job.  

#5 Starter
Chris Narveson (favorite) vs Manny Parra (underdog) vs Mark Rogers (underdog)

Tale of the Tape
Narveson: 29 years old, $440K, 12-9, 4.99 ERA, 167.2 IP, 172 H, 59 BB, 137 K in 37 games (28 starts)
Parra: 28 years old, arbitration eligible (1st time), 3-10, 5.02 ERA, 122 IP, 135 H, 63 BB, 129 K in 42 games (16 starts)
Rogers: 25 years old, $414K, 6-8, 3.71 ERA, 111.2 IP, 86 H, 69 BB, 111 K in 24 starts (AA)

Analysis: Narveson looks like a solid #5 going into 2011 after a strong second half performance (5-3, 3.89 ERA in 14 starts) but Parra was equally impressive at times. Parra pitched well after he was moved to the bullpen (2.39 ERA in 26 relief appearances) after struggling as a starter. If the Brewers think he turned the corner as a pitcher, and believe Parra's success wasn't a result of him being better suited as a reliever, maybe he gets a long look in spring training. Regardless of what happens between the two lefties, it might not matter because Rogers is on the fast track. The 25 year-old, who was recently named the team's #1 prospect by Baseball Prospectus, showed what he can do in a late-season stint with the club. After throwing no-hit ball over five scoreless innings in three separate outings, Rogers pitched five solid innings in his final appearance of the season with 6 K's and just one walk. No need to rush him, now that the rotation has turned into a strength following the acquisitions of Zack Greinke and Shaun Marcum, but he'll still be considered for the #5 spot in spring training.

Pittsburgh Pirates
Right Field
Garrett Jones (favorite) vs Ryan Doumit (underdog) vs John Bowker (underdog) vs Steve Pearce (underdog) vs Alex Presley (long shot)

Tale of the Tape
Jones: 29 years old, $440K, .247/.306/.414 in 592 AB's, 7 SB
Doumit: 30 years old, $5.1M, .251/.333/.406 in 406 AB's
Bowker: 27 years old, $440K, .313/.382/.587 in 288 AB's (AAA)
Pearce: 27 years old, $414K, .326/.424/.535 in 129 AB's, 7 SB (AAA)
Presley: 29 years old, $414K, .320/.373/.494 in 518 AB's, 13 SB (AAA/AA)

Analysis: After Jones' breakout season in '09 (.293-21-44 in 82 games), many people were wondering what kind of numbers he'd put up in a full season. Well, he was given that chance in 2010 and the results (.247-21-86) were a bit disappointing. Going into 2011, he's expected to platoon with Matt Diaz in right field but he'll have to hold off a slew of competitors, including Bowker and Pearce, who are looking for a chance to prove that they can carry over their minor league success to the big leagues. Doumit might be the best hitter of the group, but he could be on the trade block at the moment and there's no telling how the catcher would do in the outfield. Presley had a breakout season in the minors but will likely need to duplicate his success in Triple-A to prove 2010 was no fluke. He had been a fringe prospect in the low minors prior to last season.

#5 Starter
Scott Olsen (favorite) vs Jeff Karstens (underdog) vs Charlie Morton (underdog) vs Daniel McCutchen (underdog) vs Brad Lincoln (underdog)

Tale of the Tape
Olsen: 27 years old, $500K, .4-8, 5.56 ERA, 81 IP, 93 H, 27 BB, 53 K in 17 games (15 starts)
Karstens: 28 years old, $1.1M, 3-10, 4.92 ERA, 122.2 IP, 146 H, 27 BB, 72 K in 26 games (19 starts)
Morton: 27 years old, $440K, 2-12, 7.57 ERA, 79.2 IP, 112 H, 26 BB, 59 K in 17 starts
McCutchen: 28 years old, $414K, 2-5, 6.12 ERA, 67.2 IP, 83 H, 28 BB, 38 K in 28 games (9 starts)
Lincoln: 25 years old, $414K, 1-4, 6.66 ERA, 52.2 IP, 66 H, 15 BB, 25 K in 11 games (9 starts)

Analysis: Olsen was signed, presumably, to be the team's #5 starter. He'll have to prove that he is healthy after battling through injuries the past two seasons. Previously, he had been an effective starter for the Marlins. Karstens was tendered a contract, signing for $1.1 million, so the team must have been happy with his work in 2010. He could be more valuable as a versatile swingman who could start, if needed. Morton, McCutchen, and Lincoln have all been highly-ranked prospects at one time but have yet to show much as major league starters.

Closer
Joel Hanrahan (slight favorite) vs Evan Meek (slight underdog)

Tale of the Tape
Hanrahan: 29 years old, arbitration eligible (1st time), 4-1, 3.62 ERA, 69.2 IP, 58 H, 26 BB, 100 K, 6 Sv
Meek: 27 years old, $440K salary, 5-4, 2.14 ERA, 80 IP, 53 H, 31 BB, 70 K, 4 Sv

Analysis: Based on their 2010 performances, the Pirates can't go wrong with this decision. Hanrahan had a dominant 12.9 K/9, Meek had a dominant 6.0 H/9. One of these guys will pitch the 8th, one will pitch the 9th. How they decide could come down to who is better in spring training. Hanrahan has more closing experience so I give him a slight edge.

St. Louis Cardinals
None
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