Is Mark Teixeira REALLY worse than last year?

So yesterday Blaine made some claims that I led him down the wrong path by encouraging him to draft Mark Teixeira. He cited many valid stats showing how Teixeira's production has dropped thus far this year. I will now examine those stats to see if differences between this year and last year are statistically significant.

Batting Average
Batting Average can be treated as a Bernoulli Distribution. This means that every at bat will be given a value of 0 (out) or 1 (hit). The true probability of him getting a 1, or a hit, is his true batting average. If you then take the sum of each trial and add them up (total number of hits) and divide by number of trials (total number of at bats), you are left with the hitter's batting average. We will do a t-test (with level 0.05) to determine if the difference between batting average this year and batting average last year is statistically significant. Our null hypothesis will be that his true batting average this year is .308, which it was last year. Our alternative hypothesis is that his true mean batting average is less than .308.

Data values:
Sample Proportion = X/n = 14/77 = 0.182
Sample Variance = p(1-p) = 14/77(1-14/77) = 0.14876
n = 77
t-critical value with 76 df at 0.05 level = -1.9917
t = (0.182 - 0.308)/sqrt(0.14876/77) = -2.87

Because our t of -2.87 is less than our t-critical value of -1.9917, we reject the null hypothesis in favor of the alternative, concluding that Mark Teixeira's true batting average for 2009 is less than last year's average of .308.

On Base Percentage
On-Base percentage can be treated the same as Batting Average in that they are both proportions, but now 0 means not getting on base, while 1 means getting on base. We will perform the same t-test as before with significance level 0.05. Our null hypothesis is that Teixeira's true on base percentage is .410 as it was last year, and our alternative hypothesis is that Teixeira's true on base percentage is less than .410.

Data Values:
Sample Proportion = X/n = 35/99 = 0.354
Sample Variance = p(1-p) = 35/99(1 - 35/99) = 0.228548
n = 99
t-critical value with 98 df at 0.05 level = -1.9845
t = (0.354 - 0.410)/sqrt(0.228548/99) = -1.166

Because our t value is greater than our t-critical value of -1.9845, we fail to reject the null hypothesis and conclude that Teixeira's on base percentage is not statistically significantly different than last year.

Slugging Percentage
Slugging Percentage must be treated slightly differently than OBP or AVG, as it is not a proportion. Rather, Slugging Percentage is essentially an average of total bases obtained in each at bat, 0 for not getting on base, 1 for a single, 2 for a double, 3 for a triple, 4 for a home run. So, we will do the same t-test (level 0.05) but our sample variance will be calculated differently. Note that I am violating the assumption of normally distributed data (which come to think of it, I think I also violated in the previous two problems), but the test is still somewhat valid and useful. Our null hypothesis is that Teixeira's true slugging percentage is .552, as it was last year, and our alternative hypothesis is that his true slugging percentage is less than .552.

Data Values:
Sample Mean = 26/77 = 0.338
Sample Variance = 0.88273
n = 77
t-critical value with 76 df at 0.05 level = -1.9917
t = (0.338-0.552)/(0.88273/sqrt(77)) = -2.13

Our t of -2.13 is less than our t-critical value of -1.9917, so we (barely) reject our null hypothesis in favor of the alternative that Mark Teixeira's true slugging percentage is less than last year's.

Conclusion
So, it appears that Teixeira's AVG and SLG are significantly worse than last year. However, OBP does not appear to have suffered as much, and as that is the statistic that matters in our fantasy league, all is not lost for Blaine. Still, Teixeira's numbers really are noticeably worse than last year, and statistically significant or not, Blaine should be slightly worried. Even I can't always be right I suppose (but I am in first place nonetheless).

Interesting Baseball Fact of the Day: Today is former Major Leaguer Ben Grieve's birthday. Lifetime on his birthday, Grieve was 5-17 (.294) with 2 2B, 1 HR, 4 RBI, 3 R, 5 K, and 2 BB.

Can Money Buy Happiness? Update on the 2009 New York Yankees, and Their Free Agent Acquisitions

As ESPN continues to tell us, money cannot buy the front row seats at Yankee Stadium. Or at least any reasonable amount of money. As the Yankees have proven thus far, even an absurd amount of money can't buy wins either. The Yankees spent nearly a half a billion dollars over the offseason on free agents, and so far these free agents have been far from their expectations. Lets have a look

Mark Teixeira-Signed a contract January 6th worth $180 million over 8 years
Teixeira was brought into NY with enormous expectations. He has the short right field to work with, and people were expecting a .375 BA, 75 HR, and 200 RBI every season. Maybe not that high, but his expectations were certainly quite hefty, given his contract and reputation as arguably the best switch hitter in baseball. All of these factors, as well as the persuasion of Tom Nielsen, got me to pick Teixeira in the 1st round, 12th overall pick, in my fantasy draft this year. Thus far, that's been a pretty terrible choice. Mark Teixeira is batting a whopping .182. He has 3 HR, 10 RBI, and the same amount of triples and SBs that I do this season. Historically, Teixeira is a relatively slow-starter, with a .272 average over the last 3 Aprils, and only 9 HR and 36 RBI, so maybe this isn't as bad as it seems, but he certainly has been terribly disappointing so far, both for my fantasy team and for the Yankees.

CC Sabathia-Signed a contract December 18th worth $161 million over 7 years
The Yankees brought in CC Sabathia to be the #1 starter, the horse, the stopper, whatever else you want to call him. He has been one of the most consistently horse-like pitchers in the majors his entire career, having pitched 180+ innings every year of his major league career. As many of you probably remember, CC pitched terribly last April, with an ERA of 7.76 and a 1-4 record. This did not stop CC from coming back and having another terrific season, and quite the contrary, he was in serious discussion for the NL Cy Young/MVP Award despite only playing there for half the season. This season, CC has started slowly yet again, with a 1-3 record and a 4.85 ERA. He has shown signs of brilliance, including his 2nd start of the year, when he pitched 7 2/3 scoreless innings, but he's been below average overall. Last year, CC's early problems were generally contributed to his workload the previous season, where he threw 241 innings, including quite a few in October. If that really was the case, then the Yankees have little cause for concern, as he threw 253 innings last season, including some in October, so its very possible that he'll come around and dominate again this season.

A.J. Burnett-signed a contract December 18th worth $82.5 million over 5 years
Considering Burnett's contract, its just incredible to think that he was by a pretty wide margin the Yankees' 3rd biggest signing, in both money and publicity. At the time of this signing, I had a lot of problems with it, the foremost being that they'd signed a 32 year old who's been very inconsistent and has had some elbow problems to a 5 year deal. Throw in the $80 million+ and you've got all the makings of a bad signing. Burnett has had Tommy John surgery, and was a relatively inconsistent pitcher during his time in Toronto. So far this season, Burnett is 2-0, although his ERA is 5.40 and his WHIP is 1.33. His strikeout rate is about where it should be, at nearly 1 per inning, but he's walking nearly 4.5 batters per 9 IP, and has been pretty unimpressive overall. Frankly, the Yankees can't expect very much out of Burnett, considering he's just not that good to begin with. The Yankees went out and paid far too much for a pitcher that had a few very good seasons and strikes out a lot of hitters. Another thing to consider with Burnett's injury history is the workload he carried last season. He threw 221 innings, the most in his career, and his first 200+ inning season since 2005. Overall, I wasn't a big fan of this signing at the time, and Burnett has failed to change my opinion on that at all. The Yankees paid ace money to a #3 starter.

Other Various Signings
Chien Ming Wang-1 year, $5 million-Wang is currently on the DL after starting the year with a 34.50 ERA. That is not a typo. 34.50. WHIP of 4.83.

Andy Pettitte-1 year, $5.5 million-Pettitte has been about as good as someone can be when 1/2 of the letters in their last name are "t". His ERA is 3.82, and his 2-1 record in 5 starts is nothing to be ashamed of. He's also already thrown 33 innings, and has overall been consistently decent. I also like that they only signed him to 1 year, as he's 34 years old. They should have done the same for Burnett.

Currently spending all this money has not been able to buy the Yankees their desired results, as they're a mediocre 13-11, and 3.5 games back of 1st place Toronto. If Mark Teixeira continues to produce at this rate, I'll probably just drop him by June, but until then, it should be interesting to see how these signings continue to go.