AL East Playoff Projections

Throughout the entire MLB season, the AL East has stood out as the strongest division. For a big part of the year, all five teams had winning records. Currently four out of the five teams have a winning record, and Baltimore sits at five games under .500.

More important, the race to win the division is more exciting this year because of the Tampa Bay Rays. Not only have the Rays competed with the traditional powerhouse out of Boston and New York, but they currently lead the division by two-and-a-half games.

There are three very strong teams playing for a maximum of two playoff spots, with Toronto trying to join the sprint to the finish.

For those of us that are anxious to see how this race plays out, I have calculated projected standings for the teams involved.

The methodology was actually rather simple. I only looked at Tampa Bay, Boston, New York, and Toronto because Baltimore is currently out of reach. It’s clearly possible that the Orioles could have a hot streak and make a run at the playoffs, but it would be impossible to project that sort of results.

For each team, I listed out all remaining games. I then calculated the probability for that team to win each game.

To do this, I took into account whether the game was at home or away, and then averaged the appropriate winning percentages for the two competing teams.

Here is an example for Tampa Bay’s next game at Seattle:

Seattle has won 40.7% of their home games this year. This means their opponents have won 59.3% of games at Seattle.

Tampa Bay has won 44.2% of their road games this year.

So essentially Seattle is giving teams, on average, a 59.3% winning percentage and Tampa Bay is taking, on average, a 44.2% winning percentage (since the game is in Seattle). I average these two numbers to come up with a compromised probability that Tampa Bay will win.

The average is a 51.8% chance that Tampa Bay will beat Seattle. Tampa Bay loses most of their games on the road, but since Seattle loses a lot at home, the Rays chances of winning is boosted.

Now I repeated this process for each team for each remaining game. I took the final win probabilities and took that as a fractional win for the team in question. So, from the example, Tampa Bay gets .518 wins for that one game against Seattle.

This is a common practice in statistical projections and actuarial work. If there are questions about the process and it’s validity I would be more than happy to answer them in the comments section.

After a fractional amount of wins is assigned for each team for each game, all I had to do was add these together to get the total wins and losses for the remaining games. The losses are just the compliment of the wins.

I added the records for teams to date to the projected records to get final standings for these four teams. I show both the record rounded to two decimal places and the record rounded to the nearest whole numbers for comparison.

1^st Place: Tampa Bay Rays: 92.44 – 69.56 (92-70)

2^nd Place: Boston Red Sox: 91.08 – 70.92 (91-71)

3^rd Place: New York Yankees: 86.53 – 74.57 (87-75)

4^th Place: Toronto Blue Jays: 81.86 – 80.14 (82-80)

As you can see, the spread of teams is very similar to what the standings look like today. This is very good news for the Rays. If these projections were to hold then the Rays would make the playoffs by winning the division and the Red Sox would have a good chance at the Wild Card.

It is important to remember that these projections are assuming that each team performs the same for the rest of the season as they have been for the season to date. What the projections really account for is the strength of schedule remaining along with the mix of home and away games.

The main interpretation of the projections I think is that the Red Sox have the most favorable remaining schedule. The Sox are currently 2.5 games back of the Rays, but the projections (assuming both teams perform as they have been) moves the Sox only 1 game back of the Rays at the end of the season.

This means the Rays have even less breathing room than they may think. It would only take a slight improvement for the Red Sox or a slight choke by the Rays for Boston to claim the division crown.

It is also clear that the Yankees and Blue Jays will need to improve their play in order to move up in the rankings. Either that or the teams above them must play worse.

As you can see, the final rankings are very close for all teams. And the Orioles still aren’t too far behind.

This race should be a great one to watch play out. As we near the end of the season, the teams are still separated by the slightest of margins. One significant winning streak could make the difference as to who makes the playoffs and who stays home.

Washington Nationals' Injury Report

In a 162-game season, injuries will undoubtedly play a role on almost every major-league team. The key to a successful season lies in part with avoiding too many significant injuries to key players.

In my following of Major League Baseball this season, along with the Washington Nationals, I have noticed an abnormal amount of injuries.

Here is the injury report for the Nationals this season:

1B Nick Johnson: Out for season (only played in 38 games this year), making $5.5 million this year.

Closer Chad Cordero: Out for season (only pitched in six games this year), making $6.2 million this year.

3B Ryan Zimmerman: Out since May 26, making $465,000 this year.

1B Aaron Boone: Out since July 7, making $1 million this year.

OF Elijah Dukes: Out from beginning of season until May 9, and has been out since July 6, making $392,500 this year.

Starting Pitcher Shawn Hill: Out from March 20 to April 18 and has been out since June 25, making $402,000 this year.

OF Lastings Milledge: Out since June 29, making $402,500 this year.

C Paul Lo Duca: Out April 18 to May 2 and May 9 to June 17, making $5 million this year.

1B Dmitri Young: Out from April 8 to May 15 and out since July 19, making $5 million this year.

OF Austin Kearns: Out from May 22 to July 3, making $5 million this year.

OF Wily Mo Pena: Out March 20 to April 13 and out since July 18, making $2 million this year.

2B/3B Ronnie Belliard: Out May 20 through June 10, making $1.6 million this year.

Relief Pitcher Ryan Wagner: Out since March 20, making $450,000 this year.

C Johnny Estrada: Out from March 26 to April 9 and from May 9 to July 18, making $1.25 million this year.

Starting Pitcher Odalis Perez: Out from June 14 to June 26, making $850,000 this year.

This is a very long list, and these are all players who played, or would have played, significant roles on the Nationals this year.

The only position-player starters from the beginning of the season that have avoided the DL are the middle infielders: SS Cristian Guzman and 2B Felipe Lopez. However, Lopez has lost his starting spot at multiple times throughout the year.

The Nationals payroll this season is $43.3 million. Calculated from this list of players, $35.5 million of those players have spent some time on the disabled list.

That is, financially 82 percent, of the team.

The Nationals currently have just over 50 percent, financially, of their team on the DL.

This is not normal, and from what I remember, this does not seem to be much different from last year, either. Nick Johnson missed almost the entire season last year as well, and Cristian Guzman missed the whole second half.

For a team that has been a bottom dweller for all of recent memory, it makes it extremely difficult to rebuild when all of your players are injured.

The list of players the Nationals have used in left field this season is longer than most team’s available infielders: Rob Mackowiak, Wily Mo Pena, Elijah Dukes, Willie Harris, Paul Lo Duca, Ryan Langerhans, and Kory Casto.

I am not one to think the injury bug in DC is coincidence, and I have two possible explanations.

The first is that the Nationals’ medical staff and trainers are totally incompetent.

And the second, more viable explanation, is that players have no interest in coming off the disabled list.

Who can blame them? Who wants to play for a team that has been outscored by more than 100 runs this season?

The Washington Nationals have a lot of issues to address. But first and foremost, they need to get, and keep, their players healthy.

Even the players that have been healthy have no risk of being demoted because there are no available replacements. For most of the first half of the season, both Willie Harris and Wily Mo Pena struggled to hit .200. Aside from Guzman, the rest of the averages haven’t been much higher, either.

MLB All Star Break Report: Statistical Predictions

Teams that outscore their opponents, on average, should win a lot of games. Likewise teams that get outscored on average should lose most of their games.

This is a very simple concept, and I will use it to analyze the MLB season before the All-Star break and make some predictions for the rest of the year.

I have used the run differential (total runs scored minus total runs allowed) in a linear regression to try to explain the win percentage of each major league team.

In general, it would make sense that teams with the highest positive run differential would also have the highest winning percentage. And vice versa; that teams with the highest negative win differential would have the lowest win percentage. Teams with a run differential around 0 should have a win percentage around .500 because, on average, they should win just as many games as they lose.

Of course this would never work out in real life. In addition to random variation and luck, some teams also just perform really well in close games while others do not. Some teams are more over-matched by the better teams and some teams are better at pounding the bad teams.

However, I propose that teams with a run differential much higher than their record would suggest have a strong potential to find more success in the remainder of the season because they have shown the ability to consistently outscore opponents. The reverse is also true; teams that have a win percentage much higher than their run differential would indicate (teams that are getting “lucky”) a potential for a less successful second season.

Under these assumptions, I interpreted the results from my regression and will exhibit them below. The graph of predicting win percentage from scoring difference can be seen at the top of the article.

I was very pleased with how the graph turned out for several reasons. The regression equation is:

Winning Percentage = .500 + .000941(Run Differential)

This says that for every run a team scores more than their opponent, their winning percentage will increase by .0941%. It is a very good sign that this is a positive number, or else scoring more runs than you’re opponent would be a bad thing.

The equation also says that a team with a run differential of exactly 0 would be expected to have a winning percentage of .500. This makes sense and I was very pleased that this worked out exactly. It is a good sign that run differential is a good predictor of winning percentage.

Finally, the R-squared value for the regression was 71.3%. This means that 28.7% of the variability in team winning percentage is left unexplained by only using run differential. This makes sense from my discussion before; some teams get lucky and some teams also have a knack for winning or losing close games. However, 71.3% is fairly high for only using one variable. While run differential is not necessarily a good precise predictor for win percentage, it is a very reasonable approximation.

Now that I feel fairly safe with my assumptions, here are the interpretations for the results.

First, the most interesting teams on the graph are ones that fall far from the regression line. Teams underneath the line have won fewer games than their run differential would suggest (“unlucky”), and teams above the line have won more games than their run differential would suggest (“lucky”). The further a team is from the line, the more lucky or unlucky they have been. Note that I use the term lucky and unlucky very loosely here, as there is certainly some skill involved in winning close games.

Based on the results, here are ten teams that should expect the biggest change in winning percentage for the rest of the season. The over-achievers will likely perform worse, and the under-achievers should do better.

Top 5 Over-Achievers

1. Angels

2. Marlins

3. Twins

4. Rays

5. Rangers

Top 5 Under-Achievers

1. Indians

2. Braves

3. Mariners

4. Phillies

5. Blue Jays

Now I will break down the MLB pre-All Star break season, still based on my results, for each division. I have calculated a modified version of the standings assuming that win percentage only depends on scoring margin. I included the original standings for comparison. Teams with significant changes in standings have strong potential to have differing success for the rest of the season.

AL East:

Team	Modified Standings	Original Standings
Red Sox	-	-
Rays	5	.5
Yankees	7	6
Blue Jays	7	9
Orioles	10	10

The biggest flag here is the Tampa Bay Rays. They could be much further behind the Red Sox now, so don’t be surprised to see them fall further behind after the All-Star break.

Also, look out for the Blue Jays in the second half. It will be difficult for any team to dethrone the Red Sox, but the Blue Jays could have a strong run and at least contend for the Wild Card.

AL Central:

Team	Modified Standings	Original Standings
White Sox	-	-
Twins	6	1.5
Indians	7	13
Tigers	7	7
Royals	13	12

While many consider the White Sox season to date to be a fluke, the numbers suggest otherwise. They have a comfortable division lead in the division standings, so I wouldn’t expect them to fade very much.

After some small glimmers of hope, Royals fans should expect another very poor end of the season results.

The Tigers still need to improve a lot to make a run at the division, and the Indians could also move up the standings a lot in the second half of the season.

The Twins may have already played their best baseball of the season, but could still hang around for a while.

AL West:

Team	Modified Standings	Original Standings
A’s	-	6
Angels	4	-
Rangers	8	7.5
Mariners	11.5	20

The modified standings show a huge reversal at the top of this division. Even though the A’s just traded away their ace, the Angels should be a lot more worried about being caught than most people think.

The Rangers have over-achieved so far, so don’t expect them to make a serious run towards the playoffs.

Also, the Mariners aren’t quite as bad as their record would suggest. They could win a lot more games in the second half and build some momentum going into next season.

NL East:

Team	Modified Standings	Original Standings
Phillies	-	-
Mets	3.5	.5
Braves	3.5	6.5
Marlins	9.5	1.5
Nationals	17.5	16

Like the other Florida team that had a lot of first half success, the Marlins should continue to slide in the standings.

The Phillies look like they are going to be tough to beat this year, but they will have to watch out not only for the Mets but the Braves as well.

The Nationals are flat out bad and should easily secure the worst record in baseball after the All-Star break.

NL Central:

Team	Modified Standings	Original Standings
Cubs	-	-
Cardinals	7.5	4.5
Brewers	8	5
Astros	13.5	13
Reds	14	11.5
Pirates	15.5	12.5

From these results, the Cubs look to have the safest division lead out of all the division leaders. Every team in this division has actually over-achieved, but the Cubs and Astros have over-achieved the least.

The Brewers may be the only team with hope of making a run at the Cubs after adding C.C. Sabathia to the top of their starting rotation.

NL West:

Team	Modified Standings	Original Standings
Dodgers	-	1
Diamondbacks	.5	-
Giants	6	7
Rockies	9	8.5
Padres	9	10

Amazingly, all of these teams under-achieved in the first part of the season. That’s a very good sign considering how bad these teams have been so far. No team has a winning record.

The Dodgers and Diamondbacks should have a very close race for the division lead, and the Giants will be looking to make it a three-way race.

The defending N.L. Champion Rockies might need another miraculous win streak to have a chance to defend their title.

Of course it is impossible to predict what is really going to happen in the future, but hopefully this analysis provides some good insight for what to expect. It will be interesting to see how well these discrepancies match up with what actually plays out, and I will be sure to keep an eye on that.

For those interested, detailed MLB Standings can be found here. I found it interesting to look at the probabilities for each team to make the playoffs, win the division, and win the Wild Card.

New York Yankees' Playoff Chances

I’d like to start off with a question: What’s wrong with the Yankees?

And an answer: Nothing.

Entering the All-Star break, the New York Yankees sit in third place in the AL East. At 50-45, they sit 6 games behind the Boston Red Sox and 5.5 games back of the surprising Tampa Bay Rays.

In this article I will explain why I think the Yankees will still make the playoffs, and discuss some trade moves/additions they could make in the next part of the season.

The first reason is the most important. Last year at this time the Yankees were in an even worse position. Heading into the All-Star break last season they were 9.5 games behind the Red Sox and had a winning percentage of only .500, at 43-43.

They then went on to go 51-25 the rest of the season and win the wild card to qualify for the playoffs. They finished only 2 games behind the Red Sox.

This season the Yankees have a better record than last, and also are 3.5 games closer to the division leaders in the standings. They came back in the standings easily last year, so why not this year too?

Reason number two is the Tampa Bay Rays. The Rays have never won more than 70 games in a season and have finished something other than last (second to last) in the division only once in their franchise history.

While the Yankees have more experience than any other team as far as qualifying for the playoffs, the Rays have absolutely zero experience of playing meaningful games towards the end of the season.

The Rays also enter the All-Star break on a seven game losing streak. Despite the current margin, it would be very surprising for the Rays to end the season ahead of the Yankees in the standings.

In fact, the Rays should even help the Yankees catch their ultimate foe, the Red Sox. The Rays have swept the Red Sox at home this season thus far (6-0), and have a home series against the Sox late in the season. The Rays host Boston in a three game set from September 15-17. If Tampa Bay’s winning trend at home against the Red Sox continues, the Yankees could gain a lot of ground quickly on the Red Sox late in the season.

The third reason is pitching. This may come as a surprise, considering pitching is usually pointed to as the Yankees most glaring weakness. Post All-Star break, their pitching will be better; and here’s why:

Joba Chamberlain has a 2.81 ERA through 41.1 innings pitched as a starter. He will only get better as he gets accustomed to his starting role and will emerge as the ace of this staff.

Mike Mussina and Andy Pettite are both extremely experienced pitchers, and have posted double-digit wins and ERA’s under 4 so far.

Chien-Ming Wang is the arguably the most reliable pitcher on the Yankees staff. He has an 8-2 record and an ERA just over 4. Amazingly, he has given up only four home runs this year in 95.0 innings.

That is four solid starting pitchers the Yankees will use for the rest of the season. The fifth and final spot belongs to Sidney Ponson for the time being. Ponson is an accomplished pitcher who has performed reasonably well in his first three starts as a Yankee. Ponson has had some struggles at this point in his career, so the Yankees are sure to keep a sharp eye on him for his next few starts.

Should Ponson falter in the slightest, expect the Yankees to make a deal for another starting pitcher. While big names like Harden and Sabathia have already been traded, there are several good pitchers the Yankees could still go after. This includes Cleveland’s Paul Byrd, Toronto’s A.J. Burnett, Seattle’s Erik Bedard, and Washington’s Tim Redding. It would be in the Yankees best interest to get another young pitching prospect in the long term, but for the short term they just need another reliable arm to send out to the mound.

Also, the Yankee bullpen is one of the best in the game. Mariano Rivera is still a lights out closer. He has 26 saves and a miniscule 1.06 ERA.

Kyle Farnsworth is a tall, hard throwing right-hander that is very difficult to score runs off of. His ERA is a little high at 3.51, but he has added approximately 1.45 wins to the Yankees cause thus far (measured by WPA, or Win Probability Added).

Jose Veras and Edwar Ramirez have also been very successful in the Yankee bullpen; both have ERA’s under 3.

With a fantastic closer and three very good relievers, the Yankee bullpen should have no trouble through the end of the season and into the playoffs.

Derek Jeter is my fourth reason. While he is the starting shortstop for the AL in the upcoming All-Star game, Jeter’s statistics have been below his career mark across the board thus far. I expect him to have a big second half of the season.

Jeter is striking out far less this year than other year during his career, at only 11.8% of his at-bats. So his problem is certainly not putting the ball in play.

However, his batting average only on balls hit in play (BABIP) is far lower than his career average. Jeter’s BABIP to date this season is a modest .315. Compare this to .368 last year, .394 the year before, and a .356 BABIP for his career. In fact, the .315 mark would be the lowest for Jeter’s entire career if the season ended today.

A lower BABIP means that more of your hits are being successfully fielded. The only explanations for this is either Jeter is getting unlucky and hitting the ball right to fielders, or that his is mis-hitting balls. This would mean either his timing or contact point is slightly off, which would be a rather easy mechanical fix with enough work.

Since Jeter is the Yankee captain and has come up big when the Yankees have needed him most throughout his career, I expect Jeter would put the necessary work in to fix any of these problems. His BABIP should stabilize and move closer to his career mark of .356. This means his productivity will increase, and this should be (along with my next reason) enough to catalyze the Yankee offense into some explosive run production.

The fifth reason is injuries. While all teams deal with injuries, the Yankees have had four different starters injured during the first part of the season. Alex Rodriguez and Jorge Posada both missed significant time at the beginning part of the season, but have since returned to the lineup. The Yankees also currently have outfielders Johnny Damon and Hideki Matsui on the DL.

Damon and Matsui were both hitting well above .300 before their injuries. Damon is expected to return shortly after the All-Star break and the Yankees are hopeful to get Matsui back soon as well. Matsui has started rehab assignments after injuring his knee in June.

With a healthy lineup, the Yankees still pose the biggest offensive threat in baseball. The return of Damon and Matsui not only gives the Yankees two more very successful bats in their already potent lineup, but it allows them to stop using Melky Cabrera in a starting role.

Cabrera has been the Yankees least productive position player by far this season. Melky has 356 at bats and only a .244 average. He also has a WPA (win probability added) of -1.6, which means he has cost the Yankees approximately 1.6 wins already this season. Cabrera has seen a decline in most of his statistics over his few years with the Yankees, so there is not a lot of hope for significant improvement in the second half of the season.

If any other injuries come up, or even if they don’t, I wouldn’t be surprised if the Yankees try to trade for another hitter as well. Jason Giambi has been having a fantastic season, but they could use someone who could play first base and/or DH, and maybe more importantly a utility fielder. Someone that could play second base to spell Robinson Cano, who is the next least productive Yankee behind Cabrera, and someone to fill in the outfield for injured players as needed.

Unfortunately for the Yankees, there are not many of these type players considered to be on the trading market right now. But the Yankees seem to always find ways of making rich enough offers to lure the players that they want.

Finally, the last reason I’m going to give why the Yankees will come back to make the playoffs is Yankee Stadium. Yankee Stadium as we know it is going to be demolished after this season. There is simply too much tradition, spirits, and memories that lie within the confines of Yankee Stadium to not give way to one last chance at baseball’s highest crown.

The Yankees have made the playoffs every year in recent memory, and there is no reason to think this year will be any different. Catching the Red Sox may prove difficult, especially after Boston finally broke through to win the division last year (first non-Yankee AL East Champion since 1997).

However, the Yankees will certainly give the Sox a run for their money. And if they fail to win the division, the Wild Card team from the American League has traditionally come out of the AL East as well in the modern era. The Yankees should have no problem locking up the second position in the division.

Alex Rodriguez: MLB's Best Player?

Alex Rodriguez of the New York Yankees is making more money this year than the entire Florida Marlins team. This is an astounding fact in itself, especially considering the Marlins currently have a better record than the Yankees, but it is even more disturbing if you consider the value A-Rod actually adds to the Yankees. Of course he is widely considered the best player in the league, and he is on pace to break every offensive record ever set as long as he stays healthy... but how much has he really improved the teams he has played for? Each player on a team, in some way contributes to the success of that team and, intuitively it seems, individual success for a player should imply positive contributions to team success. However, Alex Rodriguez is a perfect contradiction to this hypothesis.

To analyze A-Rod’s contribution to his team throughout his career, I did a simple before-and-after comparison of consecutive seasons where he switched teams. He began his career in 1994 with the Seattle Mariners; however he did not earn significant playing time until 1996. In 2001 A-Rod was traded to the Texas Rangers, where he stayed three seasons until joining the New York Yankees in 2004. Following the hypothesis that A-Rod should provide positive value to his team, and assuming all other factors to be equal: A-Rod leaving a team should cause that team to be worse the next season and A-Rod joining a team should likewise bring improvement. Here is a table showing how the involved teams fared after either losing or gaining A-Rod.

Teams Losing & Gaining Alex Rodriguez

Team	Last Year w/ A-Rod	Year After A-Rod	Team	First Year w/ A-Rod	Year Before A-Rod
2000 Mariners	91-71	116-46	2001 Rangers	73-89	71-91
2003 Rangers	71-91	89-73	2004 Yankees	101-61-1	101-61

The pattern is largely the opposite of what we expect. The year after Rodriguez left the Mariners, they raised their win total by 25 games, tying the Major League record for most regular season wins in the process. One year after A-Rod departed the Rangers’ team, Texas upped their win total by 18 games. They went from win totals in the low 70’s for all of A-Rod’s tenure to just barely missing the playoffs. There is no real jump present for the Rangers or Yankees to indicate improvement after A-Rod has joined a team either. Texas won two more games with A-Rod than without, and the Yankees win total stayed exactly the same.

A little more analysis shows the Rangers and Yankees actually performed worse once Rodriguez joined. The Rangers were a division powerhouse prior to his arrival (see table below). They won 95 games two years before adding A-Rod, and won at least 88 games in three of the last five years without him.

Texas Rangers 1996-2003

Year	Record
1996	90-72-1
1997	77-85
1998	88-74
1999	95-67
2000	71-91
2001	73-89	* A-ROD
2002	72-90	* A-ROD
2003	71-91	* A-ROD

The chart below shows the effect of Rodriguez on the Yankees is even more intriguing. In the eight years prior to acquiring A-Rod, the Yankees played in six World Series’ and won four of them. In the five years that he has been a part of their team, the Yankees have played in, and won, ZERO World Series.’ The Yankees winning percentage in the regular season has remained constant, but the playoff success has clearly not been the same after acquiring A-Rod. Also note that the first year Alex was a member of the Yankees was the first year the Yankees’ rival, the Boston Red Sox, won the World Series since 1918.

Major League Baseball World Series: 1996-2007

Year	Champion	Runner-Up
1996	Yankees	Braves
1997	Marlins	Indians
1998	Yankees	Padres
1999	Yankees	Braves
2000	Yankees	Mets
2001	Diamondbacks	Yankees
2002	Angels	Giants
2003	Marlins	Yankees
2004	Red Sox	Cardinals	*A-ROD
2005	White Sox	Astros	*A-ROD
2006	Cardinals	Tigers	*A-ROD
2007	Red Sox	Rockies	*A-ROD

The evidence appears very strong, but does not seem to make sense. How could A-Rod possibly make teams worse? I decided to look more into this. The change in team success can only be attributed to A-Rod if the make-up of the team remains generally the same with and without him. I looked at individual player’s who played on the team both successive year’s around an A-Rod arrival or departure. I assumed the only players that A-Rod might actually have an effect on were position players. This is because, as a position player, he would have no real need for interaction with pitchers and very little need for interaction with designated hitters, since hitting is such an individual piece of baseball. In addition, I was only interested in players who received significant playing time, because A-Rod would not interact as much with bench players. I set an arbitrary cutoff at a minimum of 200 at bats for players, with players needing to have the minimum in both years of comparison (and for the same team). Finally, I excluded players that were new to the league. The assumption here is that a change in performance would more likely be due to growing accustomed to the league (or the league growing accustomed to them) rather than any "A-Rod effect". I disallowed players if the two years used for comparison were the first two years that the player was in the Major Leagues.

Here is the list of qualified players, along with their batting averages, that were part of a team that Rodriguez left:

A-ROD LEAVING: Batting Average Comparison

Player	Team	Last Season w/ A-Rod	Season After	Improvement
David Bell	Mariners	.247	.260	.013
Mike Cameron	Mariners	.267	.267	.000
Carlos Guillen	Mariners	.257	.259	.002
Stan Javier	Mariners	.275	.292	.017
Mark McLemore	Mariners	.245	.286	.041
John Olerud	Mariners	.285	.302	.017
Dan Wilson	Mariners	.235	.265	.030
Hank Blalock	Rangers	.300	.276	-.024
Michael Young	Rangers	.306	.313	.007

Here is the same list for players that were part of a team that Rodriguez joined:

A-ROD JOINING: Batting Average Comparison

Player	Team	Season Before	First Season w/ A-Rod	Improvement
Frank Catalanatto	Rangers	.291	.330	.039
Rusty Greer	Rangers	.297	.273	-.024
Gabe Kapler	Rangers	.302	.267	-.035
Ricky Ledee	Rangers*	.236	.231	-.005
Rafael Palmeiro	Rangers	.288	.273	-.015
Ivan Rodriguez	Rangers	.347	.308	-.039
Jason Giambi	Yankees	.250	.208	-.042
Derek Jeter	Yankees	.324	.292	-.032
Jorge Posada	Yankees	.281	.292	.011
Bernie Williams	Yankees	.263	.262	-.001
Enrique Wilson	Yankees	.230	.213	-.017

*played only a partial season with the Rangers in 2000 (season before A-Rod)

The numbers again are convincing. Players averaged an improvement in batting average of .01144 the first year after A-Rod left their team, and players averaged a decrease in batting average by .01455 the year after A-Rod joined their team. Only one out of nine players had a worse batting average after A-Rod departed, and only two out of eleven players improved their batting average after his arrival.

I actually thought of two different statistical tests to try to see the significance of the A-Rod effect. The first was to see if significantly many players were having better batting averages after A-Rod left and if significantly many players were having worse batting averages after A-Rod joined their team. The null hypothesis was to assume A-Rod has no effect on the change in batting average, so that 50% of the players should have an increase and 50% should have a decrease. The alternative hypothesis was then that a majority of players improved their batting averages after A-Rod left and a majority of players worsened their batting averages after A-Rod joined. For A-Rod leaving a team, the p-value was .09, which means if A-Rod had no effect on player batting averages, the observed changes or more extreme changes (even more players improving) would only happen 9% of the time. This is moderately strong statistical evidence for an A-Rod effect. Note that Mike Cameron’s batting average was exactly the same in both years, however without rounding it was slightly lower the year after Rodriguez left. So Cameron was included as a player who experienced a decrease in batting average, even though as reported it stayed the same. Had he been excluded or been moved to the other group (and considered to have not worsened his average), the evidence would be even stronger. For A-Rod joining a team the p-value is .033, which provides strong statistical evidence for an A-Rod effect.

The second test was to assess the magnitude of the A-Rod effect on players. For this, I used the change in each player’s batting average. The null hypothesis was that the average change was 0, and the alternative was that the average change was greater than zero (improvement) for A-Rod leaving and the average change was less than zero (decrease in average) for A-Rod joining. For A-Rod leaving a team, the p-value is .051, which says that if the players on teams A-Rod left averaged the same batting averages as the year before, then the observed changes or more extreme changes (players increasing their average by more) would occur only 5.1% of the time. This is moderately strong statistical evidence for an A-Rod effect. For A-Rod joining a team, the p-value is .038, which again provides strong statistical evidence for an A-Rod effect.

It is important to note that statistically, it is difficult to say from these results that Rodriguez causes teams and players to be worse because this is not a controlled environment and so there could be other variables affecting the outcome. In restrictions placed on selection of players I attempted to account for some of this, but it would be impossible to eliminate all possible variables. However, it should be noted that despite so little data available the statistical results are all still very strong.

So what does this really mean? The changes that Alex Rodriguez has brought about to his team’s performances are entirely counterintuitive to how a player with such outstanding individual success should affect a team. His departure gave way to one of the best regular seasons in Major League history for the Seattle Mariners in 2001 and his addition to the Yankees in 2004 appears to be the event that has reversed the Curse of the Bambino. Since he has only been traded twice, it is very difficult to rule out coincidence as the cause of the differences in team successes. Still, the evidence available is startling. Even if A-Rod is the victim of coincidence, he still appears to carry a great deal of bad luck with him. Further, players who play with Rodriguez tend to do better after he is traded away and players who are new to playing with him tend to do worse than the prior season. This claim is a slight, but reasonable, extrapolation from the fact that there is undeniable evidence of (1) a correlation between A-Rod's arrival and a decrease in teammate's batting averages and (2) a correlation between A-Rod's departure and an increase in teammate's batting averages. The reasons behind this A-Rod effect are still totally unclear, but also relatively unimportant. The goal of any Major League franchise should be to win as many games as possible; and so to maximize team success it would be logical to avoid Alex Rodriguez at all costs. This is the complete opposite approach of the New York Yankees, who are paying him more than any other player in the history of sports. Admittedly, it is undeniable that A-Rod is an outstanding individual player but all available data shows his presence is not at all helpful for a Major League team.

For some final notes, I would hypothesize that other superstars in baseball and in other sports may negatively affect teammate’s individual performance. Ideally the superstar’s own performance would more than compensate for this, but clearly this has not been the case with Rodriguez. I also found it interesting that the few players who did not follow the pattern of the rest of A-Rod's teammates (Gabe Kapler, Frank Catalanatto, and Jorge Posada) all had relatively large changes in batting averages. I was suprised that the statistical evidence found was so strong in spite of these three, and also am curious to what made these players immune to what happened to the rest of their teammates.