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: White Sox, Indians, Detroit Tigers, Royals

Chicago White Sox
Third Base
Brent Morel (slight favorite) vs Dayan Viciedo (slight underdog) vs Mark Teahen (underdog)

Tale of the Tape
Morel: 23 years old, $414K, .322/.359/.480 in 490 AB's, 8 SB (AAA/AA)
Viciedo: 22 years old, $1.25M salary, .308/.321/.519 in 104 AB's
Teahen: 29 years old, $4.75M salary, .258/.327/.382 in 233 AB's

Analysis: Morel ended the season as the starting third baseman but the free-swinging Viciedo also showed enough to also be given strong consideration for the job. With plenty of veteran firepower throughout the lineup, the team can afford to go with one of the youngsters at the bottom of the order. If neither is ready to take over as the full-time third baseman, however, Teahen would get the call. He'd likely get the majority of AB's vs RHP's with Viciedo playing vs LHP's and Morel heading back to the minors.

Closer
Matt Thornton (favorite) vs Chris Sale (underdog) vs Jesse Crain (underdog)

Tale of the Tape
Thornton: 34 years old, $3M salary, 5-4, 2.67 ERA, 60.2 IP, 41 H, 20 BB, 81 K, 8 Sv, 21 holds
Sale: 22 years old, $414K salary, 2-1, 1.93 ERA, 23.1 IP, 15 H, 10 BB, 32 K, 4 Sv, 2 holds
Crain: 29 years old, $4M salary, 1-1, 3.04 ERA, 68 IP, 53 H, 27 BB, 62 K, Sv, 21 holds

Analysis: Thornton looks to be the front-runner after another dominating season that included eight saves. Crain was an effective setup man in 2010 who throws in the mid-90's but he has never been a closer and has exactly one less save (3) in his career than the rookie Sale recorded (4) in 21 relief appearances late last season. Along with Sergio Santos, this foursome will make it tough on White Sox opponents late in games regardless of who is closing.

Cleveland Indians
Second Base
Jason Donald (favorite) vs Luis Valbuena (underdog) vs Jason Kipnis (long shot) 

Tale of the Tape
Donald: 26 years old, $440K salary, .253/.312/.378 in 296 AB's, 5 SB
Valbuena: 25 years old, $440K, .193/.273/.258 in 275 AB's 
Kipnis: 24 years old, $414K salary, .307/.386/.492 in 518 AB's, 9 SB (AA/HiA)

Analysis: On paper, it doesn't look like much of a competition. Donald is a solid prospect entering his first full big league season while Valbuena regressed from a decent rookie season in '09 (.250-10-31). Kipnis has yet to play a game above Double-A ball it's not out of the realm of possibility that he proves to be the better player in Spring Training. 

Third Base
Jayson Nix (favorite) vs Jared Goedert (underdog) vs Lonnie Chisenhall (long shot)

Tale of the Tape
Nix: 28 years old, $440K salary, .224/.281/.396 in 331 AB's
Goedert: 25 years old, $414K, .283/.358/.532 in 481 AB's (AAA/AA)
Chisenhall: 22 years old, $414K salary, .278/.351/.450 in 460 AB's (AA)

Analysis: Nix is the leading candidate at the hot corner after hitting 13 HR's in 76 games after being claimed off waivers from the White Sox in June. But he also struck out 75 times while posting just a .283 OBP. Goedert, who was added to the 40-man roster last month, could have a shot with a strong performance in Spring Training but he doesn't appear to be very good defensively (.923 fielding pct in '10). They could be on the lookout for a veteran stopgap (i.e. Pedro Feliz or Felipe Lopez) until Chisehnall is ready. Adding Chisenhall to the competition is a bit of a stretch but he is the team's top hitting prospect and this is a rebuilding year with the Tigers, Twins, and White Sox expected to dominate the division. So why not give him a full year in the big leagues so he's better prepared for 2012 when the team might be more competitive? Like I said, it's a stretch. He will likely be up later in the season after a few months worth of Triple-A at-bats.

#4 and #5 starter
Josh Tomlin (favorite) vs Carlos Carrasco (favorite) vs David Huff (underdog) vs Jeanmar Gomez (underdog) vs Anthony Reyes vs Zach McAllister (underdog) vs Corey Kluber (long shot) vs Alex White (long shot)

Tale of the Tape
Tomlin: 26 years old, $425K salary, 6-4, 4.56 ERA, 73 IP, 72 H, 19 BB, 43 K in 12 starts
Carrasco: 24 years old, $425K, 2-2, 3.83 ERA, 44.2 IP, 47 H, 14 BB, 38 K in 7 starts
Huff: 26 years old, $440K salary, 2-11, 6.21 ERA, 79.2 IP, 101 H, 34 BB, 37 K in 15 starts
Gomez: 23 years old, $414K salary, 4-5, 4.68 ERA, 57.2 IP, 73 H, 22 BB, 34 K in 11 starts
Reyes: 29 years old, $500K, 1-1, 6.57 ERA, 38.1 IP, 40 H, 23 BB, 22 K in 8 starts (2009)
McAllister: 23 years old, $414K salary, 9-12, 5.29 ERA, 149.2 IP, 185 H, 45 BB, 99 K in 27 starts (AAA)
Kluber: 24 years old, $414K salary, 9-9, 3.49 ERA, 160 IP, 169 H, 56 BB, 165 K in 29 games (AAA/AA)
White: 22 years old, $414K salary, 10-10, 2.45 ERA, 150.2 IP, 123 H, 46 BB, 117 K in 26 games (AA/HiA)

Analysis: Lots of options, although Tomlin and Carrasco don't appear to have too many serious threats for the last two rotation spots. Gomez was solid in 11 starts and Reyes was a promising prospect before his career was derailed by injuries the past two seasons. Huff is likely to get another look but he's coming off of a terrible season. Kluber and McAllister could get the call sometime during the season, although not likely before June. White appears to be the organization's top pitching prospect after a very good pro debut in 2010 so the team might want to take a long look at him this spring. As with the third base competition, the team could add an affordable veteran or two to the competition before the start of Spring Training. 

Detroit Tigers
#5 Starter
Armando Galarraga (favorite) vs Andy Oliver (underdog) vs L.J. Gagnier (long shot)

Tale of the Tape
Galarraga: 29 years old, arb. eligible (1st time), 4-9, 4.49 ERA, 144.1 IP, 143 H, 51 BB, 74 K in 25 games
Oliver: 23 years old, $414K salary, .9-8, 3.45 ERA, 130.1 IP, 117 H, 50 BB, 199 K in 23 starts (AAA/AA)
Gagnier: 26 years old, $500K salary, 10-7, 3.35 ERA, 155.2 IP, 146 H, 52 BB, 122 K in 27 games (AAA)

Analysis: Things could be a lot worse than having a guy who is capable of throwing a perfect game as your #5 starter. Still, Galarraga will have to hold off Oliver, the team's 2nd Round pick in '09, and Gagnier, who put together a very good minor league season between Double-A Erie and Triple-A Toledo. Oliver made five starts with the Tigers in 2010, struggling badly in his last three, but the team showed a lot of faith to promote the 22 year-old with only a handful of minor league starts on his professional resume.

Kansas City Royals
Third Base
Wilson Betemit (favorite) vs Mike Moustakas (underdog)

Tale of the Tape
Betemit: 29 years old, $1M salary, .297/.378/.511 in 278 AB's
Moustakas: 22 years old, $414K salary, .322/.369/.630 in 484 AB's (AAA/AA)

Analysis: Betemit resurrected his career with a solid 2010. But if he wants to continue being a starting third baseman, it won't be with in Kansas City for much longer. Moustakas emerged from the 2010 season as one of the top hitting prospects in baseball and the Royals' third baseman of the very near future. Knowing that the team doesn't have much of a chance in 2011, they could choose to be patient with the youngster and hope that Betemit maintains his value with another good half-season before he's traded to open the spot sometime in June or July.

LF/CF/RF
Melky Cabrera (favorite) vs Jeff Francoeur (favorite) vs Alex Gordon (favorite) vs Lorenzo Cain (underdog) vs Mitch Maier (underdog) vs Gregor Blanco (underdog) vs David Lough (long shot)

Tale of the Tape
Cabrera: 26 years old, $1.25M salary, .255/.317/.354 in 458 AB's, 7 SB
Francoeur: 27 years old, $2.5M salary, .249/.300/.383 in 454 AB's, 8 SB
Gordon: 27 years old, arb. eligible (2nd time), .215/.315/.355 in 242 AB's
Cain: 24 years old, $440K salary, .306/.348/.415 in 147 AB's, 7 SB
Maier: 28 years old, $440K salary, .263/.333/.375 in 373 AB's, 3 SB
Blanco: 27 years old, $440K salary, .283/.360/.367 in 237 AB's, 11 SB
Lough: 25 years old, $414K salary, .280/.346/.437 in 460 AB's, 14 SB (AAA)

Analysis: The Royals may have been the only teams in the majors willing to give Cabrera and Francoeur starting jobs this offseason. In a rebuilding season, giving the veterans a chance to rebuild their value might not be a bad idea. It's a few million bucks down the drain if it doesn't work out but both players were considered very good ballplayers just a few years ago. This is a make-or-break season for Gordon, who like Cabrera and Francoeur, has struggled at the big league level after a promising start to his career. There will be plenty of competition this spring. Cain looks to be the team's centerfielder of the future while Maier and Blanco are still trying to prove that they are more than just solid reserves. Lough is coming off of a very productive Triple-A season in which he had 15 2B's, 12 3B's, 11 HR's, and 14 SB's.

#5 Starter
TBD (favorite) vs Kevin Pucetas (underdog) vs Nathan Adcock (underdog) vs Steven Shell (underdog)

Tale of the Tape
Pucetas: 26 years old, $414K salary, 5-7, 5.69 ERA, 136 IP, 172 H, 61 BB, 95 K in 26 starts
Adcock: 23 years old, $414K salary, 11-7, 3.38 ERA, 141.1 IP, 131 H, 38 BB, 113 K in 27 games (HiA)
Shell: 28 years old, $414K salary, 3-2, 3.59 ERA, 72.2 IP, 76 H, 19 BB, 51 K in 21 games

Analysis: I'll go out on a limb and say that none of these three contenders will be in the starting rotation on Opening Day. There are too many decent options on the free agent market for the Royals not to end up with at least one more pitcher who is better than Pucetas, who was roughed up in Triple-A last season before he was claimed off waivers from the Giants this offseason. Adcock is a Rule V pick who was successful starter in HiA last season. He's more likely for long relief if he makes the team. Shell is a former big leaguer with the Nationals who was pitching well as a starter in Triple-A Tacoma last season, earning our 'Knocking Down the Door' honors on May 17th, before going down with an elbow injury that landed him on the DL.

Minnesota Twins
Second Base or Shortstop (Tsuyoshi Nishioka will fill one of the two spots)
Alexi Casilla (favorite) vs Trevor Plouffe (underdog) vs Luke Hughes (underdog) vs Matt Tolbert (underdog)

Tale of the Tape
Casilla: 26 years old, arb. eligible (1st time), .276/.331/.395 in 152 AB's, 6 SB
Plouffe: 24 years old, $414K salary, .244/.300/.430 in 402 AB's, 5 SB (AAA)

Hughes: 26 years old, $414K, .257/.313/.405 in 74 AB's (AAA)
Tolbert: 28 years old, $440K, .230/.293/.379 in 87 AB's

Analysis: Casilla appears to be an overwhelming favorite at the moment, coming off of a solid season as a backup. He can play 2B or SS, giving the team flexibility once they figure out where Nishioka will best fit. Plouffe is an option at shortstop while Hughes and Tolbert would be options at second base, although none of the three should strike much fear into Casilla.
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