This is the standings for the American League East after the games on Sunday, May 16 were completed. It is the first time the New York Yankees have had a .500 winning percentage since early April. Their current 8 game winning streak has created a feeling of hope among both their fans and the media. The newspaper headlines no longer talk about the “Slumping Yankees”. Instead, it is now the “Surging Yankees” who are “climbing” up in the standings.

How likely is it that the Yankees will win the Eastern Division? Did their poor start doom the team in the playoff race this year? In this analysis, I will not consider the F-Rays since they have such a strong affinity for the bottom of the standings. The Toronto Blue Jays are at best a .500 team so that leaves us with the Baltimore Orioles, Boston Red Sox, and the Yankees.

If the Orioles continue to win at their current pace, the Yankees would have to play like the Yankees of 1998 with a .700 winning percentage to finish ahead of them. Fortunately for the Yankees and their fans, it is very unlikely that the Orioles will continue to play this well. Last year, the Orioles finished around .500. If they win at this rate for the rest of the year, the Yankees would have to win around 55% of their games to catch them. If we give the O's credit for significant improvement over last year's team and assume that they are more likely a .550 team (89 wins over a full season), the Yankees have to win almost 60% of their remaining games. That would mean that this year's team would have to play as well as last year's team for the rest of the season. It is quite possible that the Yankees will finish in front of the Orioles.

Even though the Red Sox are currently behind the Orioles in the standings, they are by far the better team. The Red Sox have won about 60% of their games so far in the 2005 season. There is no reason to think that they cannot continue winning at this pace since they are doing it right now without two of their top starting pitchers in Curt Schilling and David Wells. If they do maintain their current winning ways, the Yankees will need to have a winning percentage of .630 from today forward to place ahead of the Red Sox. The Yankees have only had a winning percentage this high in two of the years of their current run starting in 1996. It is not looking good for the Yankees finishing ahead of the Red Sox this year.

All of this is from a fairly optimistic perspective—that the Yankees are showing their true ability now as opposed to the April version of the team. If the team's future performance is actually closer to the team that was crushed by the Devil Rays than the one that did the same to the Mariners and Athletics, neither a division crown nor a wild card spot is in the team's future.

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This was taken from the Associated Press recap of Friday night's baseball game featuring the New York Yankees and Oakland Athletics. This type of reporting bothers me considerably. It is primarily an issue of sample size. Four at-bats is not enough data points to make the determination that Jason Giambi's slump is over. This is especially true when going 1-for-4; it is not that different statistically from getting 4 hits over 41 at-bats. We just cannot tell the difference between a .300 hitter and a .100 hitter from a 1-for-4 night. Let me explain this.

First, let's model the probability of whether a player gets a hit during an at-bat using a binomial random variable. For those of you who don't like math, you can stop reading now...or you can think of this as replacing the player with a coin. Heads and he gets a hit. Tails and he heads back to the bench. In this scenario, we are not dealing with a fair coin meaning that the probability of getting a hit (heads) is not 50%. For most players, it is much lower than half—somewhere between 25% and 30%. We can think of a slump as replacing the normal coin for that player with one that is even more weighted towards making outs. Breaking the slump would mean returning to the normal coin. In Giambi's case, let's say that his normal coin returns a hit 30% of the time since his career average is .295. In his current slump, he is getting hits around 10% of the time. Now the question is how certain can we be that he has gone back to the normal coin (broken the slump) given the evidence of a 1-for-4 game.

We plug the numbers into our handy binomial distribution formula and get some answers. A player who gets hits 10% of the time will get a single hit in four at-bats about 30% of the time. A player who hits around .300 will go 1-for-4 around 40% of the time. Given the small sample size, it is basically impossible to tell the difference between a .100 hitter and a .300 hitter if they both have a 1-for-4 night. The same holds true for telling whether Giambi has broken his slump or not. Now, if he had gone 2-for-4 or 3-for-4, the numbers would have come out differently. In four at-bats, a .300 hitter is about five times more likely to get two hits, twenty times more likely to get three hits and eighty times more likely to get a hit every time. Then maybe we could do a hypothesis test to determine how much confidence we have that Giambi broke his slump. As it is, I am expecting an 0-for-4 today.

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For the past two or three years, he has poorer than normal stats and this has been attributed to various injuries he has suffered. A question to consider is whether the decline is due to the injuries or are both the decline and the injuries due to old age (for a baseball player). Take a look at the graph. This shows Bernie's OPS for every year he has been in the major leagues. OPS is on-base percentage plus slugging percentage. The number of runs scored by a team over a season has a higher correlation to OPS than team batting average so it is a good metric for evaluation. A star player will generally be around or above .900 in OPS.

You will notice that the decline started in the late 90's. This looks like a gradual deterioration of skills that was masked by injuries in the past three years. Another perspective is that the injures are chronic conditions and are what led to the decline, but the end result is the same. It is unlikely that we will see the Bernie Williams from the championship Yankees teams of the late 90's again.

Most likely, the Yankees will become tired of Tony Womack's defense in left field and the growing pains that a rookie like Robinson Cano will suffer through and return Bernie Williams to a more full-time role. The Yankees picking up the option on his contract for next year is not likely though so this may be the last year of Bernie in pinstripes with the interlocking NY.

Bernie does have his next career lined up which is a lot better than most professional athletes. Take a look.

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