thanks for the reminder!
thanks for the reminder!
from excellent blog "THE NUMBERS GUY"
Carl Bialik examines the way numbers are used, and abused.
October 21, 2008, 3:50 pm
Why Free Tacos Are a Good Bet
If there is at least one successful stolen base in the World Series that begins Wednesday between the Philadelphia Phillies and Tampa Bay Rays, Taco Bell will give away crunchy seasoned beef tacos ? normally 89 cents each on the Yum Brands Inc. chain?s value menu.
Carl Crawford and the Rays have stolen 17 bases in 11 postseason games against the White Sox and Red Sox.
?What are the chances?? the restaurant chain asks in its promotional text. ?Let?s just say history is on your side.? Math is on your side, too. There?s less than a one in 1,000 chance of zero steals during the World Series, according to two statisticians.
History isn?t quite as definitive, but it?s encouraging for a taco giveaway. In 102 of 103 prior World Series, at least one base was stolen, according to Baseball Reference. The lone exception was the all-St. Louis World Series in 1944 between the Cardinals and the Browns, two teams that combined for just 81 stolen bases in the regular season and ranked sixth and seventh, respectively, among eight teams in each league in steals. Cardinals second baseman Whitey Kurowski was picked off twice in Game 6, though the Cardinals still managed to clinch the series with a 3-1 victory.
But there have been many near-misses: Thirteen times the World Series has seen just one stolen base. Six of those came between 1929 and 1940, when power was on the rise as a factor in the game, and speed on the decline. In 1940, the only seven-game series on the list, five times players tried stealing in the first six games between the Reds and Tigers. In Game 7, Reds catcher Jimmie Wilson, who?d thrown out two of those runners, broke the baserunning drought. The World Series also finished with just one steal in 2000 and 2004. Last year, which marked the debut of the Taco Bell offer, the Red Sox and Rockies combined for three steals in four games. (?We gave away millions of free tacos,? said spokesman Will Bortz, who couldn?t be more specific because most Taco Bell restaurants aren?t company-owned.)
As three of the last four Series have ended in AL sweeps, the giveaway might seem to be at risk. However, the Rays led the majors with 142 steals in the regular season, and the Phillies ranked fourth ? and second among playoff teams ? with 136. Philadelphia?s Jimmy Rollins (47 steals) and Tampa Bay?s B.J. Upton (44 steals) each equaled or topped both lead-footed St. Louis teams? totals in 1940.
At my request, statisticians Phil Birnbaum and Jim Lackritz each attempted to calculate how likely these two speedy teams are to swipe at least one bag between them in the World Series. Birnbaum used a more-empirical approach: He examined 382 games in 2007 that pitted two of the top 13 baserunning teams of that season against each other (expanding beyond the top few teams to expand the sample size). He found that 284 of those games featured at least one stolen base, for a percentage of 74.3%, which he rounded up slightly to 75% because Philadelphia and Tampa Bay get more steals than the group he studied.
Then Birnbaum assumed that the Rays and Phillies are evenly matched and that each World Series game is, essentially a coin flip (a simplification that admittedly ignores home-field advantage, the AL?s regular-season superiority and pitcher matchups). That gives a 1/8 chance of a sweep (because each team has a 1/16 chance of winning each of the first four games) a 1/4 chance of a five-game series (because half the time one team will win three of the first four games, and half of those times that same team will win Game 5) and an identical 5/16 probability for six games or seven games (because 3/8 of the time a series ends in the first five games, so 5/8 of the time it doesn?t, and half the time the team leading the series 3-2 wins Game 6, and half the time it doesn?t). In each scenario, by his calculations, there would be a 25% chance of no steals in each game, and you?d have to multiply 0.25 by itself for each additional game. The total probability of no steals in the World Series, then, is one in 1,200.
To check that it makes sense to apply regular-season statistics to the World Series, when runs tend to be harder to come by, Birnbaum checked the last 20 World Series and found that teams stole 2.1% more bases than you?d expect in the Fall Classic ? a negligible effect.
Lackritz came up with an even lower probability of that taco-free outcome by giving more credit for the Rays and Phillies baserunners. To both their regular-season stolen-base rates and their playoff rates ? a little lower for the Phillies? regular-season rate but much higher for the Rays ? he applied what?s known in statistics as the Poisson Distribution to calculate the probability of stealing a base in any given game. Using the regular-season totals, that gives the teams an 82% chance of stealing at least one base between them in a game; with the postseason totals, that goes up to 90%. Then he used the same assumptions as Birnbaum?s about the length of the series to calculate the probability of no steals throughout the series (Lackritz also tested an assumption that the home team has a 60% chance of winning each game, and found little effect). Using the lower percentage, the total probability of no steals in the World Series is one in 5,300; use the higher percentage ? if you believe the Rays continue to steal more bases in October than in the prior six months, and the Phillies slightly less ? and you get a whopping one in 71,000.
Why choose such a sure thing as a stolen base for the taco promotion? ?It?s a fun part of the game,? Bortz said. He made clear the intent is to hand out food. ?It?s more a question of when? than if.
Even that?s not too hard a question. Expect to collect your free taco between the local hours of 2 p.m. and 6 p.m. next Tuesday, the giveaway day for a steal in the first four games of the series. That?s 99.6% sure, according to Birnbaum?s assumptions, and at least 99.9% according to Lackritz?s.
