March Madness Underdog Comparison: Davidson vs. George Mason

What Davidson and Stephen Curry accomplished in this year's NCAA Basketball tournament was amazing... but how does it stack up to the 2006 George Mason team that went to the final four?

There are many different methods of comparison, and I will only look into some of the main ones in this article. For starters, lets compare over-all record.

Season-ending record:

Davidson - 29-7 George Mason - 27-8

This is a very slight advantage to Davidson. Now I compare their successes prior to the NCAA tournament.

RPI - rating and rank:

Davidson - .5875, #35 George Mason - .5984, #26

This is a clear advantage to George Mason, which is surprising. Many people thought George Mason would not even make the 2006 NCAA tournament (they lost in their conference tournament), while Davidson was a lock to make the 2008 tournament. However, it is George Mason who had the higher RPI rating.

Conference Success:

Davidson - 20-0 in the Southern Conference (RPI #21)

George Mason - 15-3 in the Colonial Athletic Association (RPI #10)

There is no clear advantage here. Davidson went undefeated, but they did so in an easy conference. George Mason won a very difficult conference. The CAA had another team qualify for the tournament that year (UNC-Wilmington) and two other teams on the bubble (Hofstra and Old Dominion). It's only fair to give Davidson a slight edge here, but it's impossible to know how their success would have changed if they played in a more competitive conference.

Strength of Schedule Rank:

Davidson - #129 overall, #4 non-conference

George Mason - #89 overall, #32 non-conference

It is easy to see how much playing in the Southern Conference hurt Davidson's strength of schedule. Their non-conference schedule was one of the toughest in the country, but their overall schedule strength was still weak. George Mason had a relatively difficult over-all strength of schedule, even though they played in a non-major conference. The edge has to go to George Mason, although Davidson certainly gets an "A" for effort by scheduling such difficult teams.

Now I look at how these teams actually fared in the tournament.

Tournament Results:

Davidson -

1st Round: Gonzaga (7) - W 82-76

2nd Round: Georgetown (2) - W 74-70

3rd Round: Wisconsin (3) - W 73-56

Elite Eight: Kansas (1) - L 57-59

George Mason -

1st Round: Michigan State (6) - W 75-65

2nd Round: North Carolina (3) - W 65-60

3rd Round: Wichita State (7) - W 63-55

Elite Eight: Connecticut (1) - W 86-84 (OT)

Final Four: Florida (3) - L 58-73

There are actually several striking similarities in the runs of Davidson and George Mason, but also some key differences. They both ultimately lost to the eventual champions. Davidson gave eventual-champion Kansas a much closer game than George Mason gave to eventual-champion Florida. Mason was, however, Florida's third closest game of the tournament. Davidson was Kansas' second closest game, behind their overtime championship thriller against Memphis.

They both won their games in somewhat similar fashions; by using very strong second halves. Davidson outscored Gonzaga 46-35 in the second half, outscored Georgetown 47-32 in the second half, and outscored Wisconsin 37-20 in the second half. George Mason outscored Michigan State 42-35 in the second half, outscored UNC 45-33 in the second half, and outscored UConn 40-31 in the second half.

However, there is one enormous difference in the two teams... George Mason won one more game. And not just any game, they beat #1 seed and tournament-favorite UConn to qualify for the final four. They were the first mid-major team since UPenn and Indiana State in 1979 to make the final four. They also tied LSU's record, set in 1986, for highest seed to play in the final four.

While Davidson lost an extremely close game against Kansas with a shot to win the game at the buzzer, Mason recovered from squandering a lead at the end of the second half to beat UConn in overtime. Davidson likely would have had a better final four performance than Mason had (they lost a close game to UNC, who would have been their opponent, earlier in the season). But it was George Mason who rose to the occasion to defeat a #1 seed in the elite eight, while Davidson fell just short.

Another big difference, in my opinion, is that many fans and analysts expected a strong run from Davidson in the 2008 tournament. I'm not sure that anyone expected them to beat the quality of teams that they beat in the way that they did, but there were very few people that expected any tournament wins out of George Mason in 2006. Many thought they didn't even deserve to be in the tournament.

All in all, both teams were extremely well-talented and thrilled the entire country with their success. The team of better strength is debatable, and I would even say the edge might go to Davidson. The media certainly portrayed Davidson as the stronger team prior to the tournament, but as we saw with RPI rankings there was also indication that George Mason was better.

But in the end, George Mason's run went deeper into the tournament and was more unexpected, so the title of better underdog has to go undebatably to George Mason.

2008 College World Series: Inning-by-Inning Scoring Breakdown

This year’s College World Series will always be remembered because of what Fresno State was able to accomplish in winning the National Championship as an extreme underdog. However, there was also another very interesting phenomenon in Omaha this year: the ninth-inning rally.

Four different games were run with a significant amount of runs scored in the ninth inning (Stanford over Florida State, Georgia over Miami, LSU over Rice, UNC over LSU) and two other ninth-inning rallies fell just short (Florida State against Miami and Stanford against Georgia). Talented and experienced teams were making mistakes, while those in danger of losing refused to go down without a fight.

I performed an analysis of the total scoring breakdown in the 2008 College World Series to see if there were significantly many runs being scored in the last inning as opposed to occurring from random chance. To do this, I used a Chi-Square Goodness-of-Fit test and assumed that the runs scored should be evenly distributed across all of the innings. This should mean each inning should expect to hold approximately 1/9 of the total runs scored…but actually it’s a little more complicated in that.

If the home team is winning in the ninth inning they do not get a turn to bat, so I adjusted for this by multiplying 1/9 by 23/32 (the proportion of total ninth inning half-innings that were actually played out throughout the CWS) to get the proportion of total runs expected in the ninth inning. Then the rest of the runs should be spread out evenly across the first eight innings.

Here is the table summarizing the results of the test:

Inning	Runs Scored	Proportion Expected	Runs Expected	Chi-Square Contribution
1	14	0.115017	23.0035	3.5239
2	11	0.115017	23.0035	6.2635
3	28	0.115017	23.0035	1.0853
4	33	0.115017	23.0035	4.3442
5	21	0.115017	23.0035	0.1745
6	20	0.115017	23.0035	0.3922
7	18	0.115017	23.0035	1.0883
8	25	0.115017	23.0035	0.1733
9	30	0.079861	15.9722	12.32
Total	200	1	200	29.6352

The test results in a p-value of 0 to three decimal places, meaning that if runs were really distributed evenly across each inning, then the run distribution observed in this year’s College World Series could essentially never happen.

Looking at the table, it is easy to see which inning messes up the distribution the most: the ninth inning. There were 14 more runs scored than we would expect, and the ninth inning by itself generated 42% of the overall chi-square statistic. For those with no statistics background, the larger the chi-square statistic is the further the results are from expected.

For whatever reason, teams scored way more runs in the ninth inning than we would expect. One team in particular, Stanford, scored 15 runs (half of the total for all teams) in the ninth inning. What is even more interesting is that Fresno State, the ultimate champion, scored zero runs in the ninth inning. This is very surprising, especially since they played more games than any other team in the CWS.

I decided to break Fresno’s run distribution down even further. Here is the inning-by-inning breakdown for the total runs Fresno scored in the CWS.

Inning	1	2	3	4	5	6	7	8	9	Total
Runs	1	7	9	17	9	10	3	6	0	62

Fresno State actually scored the vast majority of their runs in the middle innings. They scored 36/62, or 58%, of their runs in the 4^th, 5^th, and 6^th innings. Amazingly, Fresno also allowed zero runs in the ninth inning to their opponents.

So while the rest of the field was scoring a lot of runs in the last inning of games, Fresno utilized the middle innings to produce most of their runs. Based on the results Fresno had, scoring runs in the middle innings looks like a good avenue towards success.

One can only guess at why other teams scored so many runs at the end of games, but one possible explanation could be the national stage that all of these games were on. College Baseball is very rarely televised until the post-season, and usually not made into a focus of media attention until the teams reach Omaha. Teams in the lead could have been getting more tense than usual and teams behind at the end of games could have been unable to relax until the sense of urgency was finally realized. However, it should not be too much of a surprise that the one team that took care of their scoring earlier in the game and allowed no scoring at the end of the games ended up as Champion.

Congratulations Fresno State, and hopefully you’re success will serve as a model to all hopeful underdogs.

Decade's Best NCAA Basketball Champions: Objective Rankings

OK, so I know we still have two more years to go until the end of the decade, but I wanted to rank all of the tournament champions for the past few years. At first I wanted to give my opinions on each team, but then I thought of a simple formula that would be much more accurate and relevant.

I only looked at each team's performance in the NCAA tournament, and my main barometer of success was margin of victory throughout the tournament. Because some teams may have tougher roads than others, I then weighted the average margin of victory by the average seed number defeated.

For example, the 2008 Kansas team defeated (in order) 16, 8, 12, 10, 1, 1 seeds and won by (in order) 24, 19, 15, 2, 18, and 7 points. Note that I decided to ignore overtimes for simplicity, and also Kansas had the only overtime game that I knew of. Kansas' average margin of victory was 17 points and average seed defeated was 9.6. Thus their rating is 17/9.6 or 1.77.

I generally agreed with the rankings, but numbers can never be 100 percent accurate. I'd be interested in hearing everyone's feedback.

Here are the complete rankings, from 2000 to the present, from top to bottom:

1. 2001 Duke Blue Devils—rating: 2.50

Duke's closest game was 10 points. They were a one seed and beat Arizona in the finals. Their average margin of victory was boosted significantly by a 43-point first round victory over 16th seeded Monmouth.

Average Margin of Victory—20 points, Average Seed Defeated—8

2. 2007 Florida Gators—rating: 2.36

Florida's closest game was seven points and also had a 43-point blowout in the first round over a 16th seed. They became the first team to repeat as National Champions since Kentucky in 1998 by beating Ohio State in the finals.

Average Margin of Victory—17 points, Average Seed Defeated—7.2

3. 2002 Maryland Terrapins—rating: 2.33

First-seeded Maryland's closest game was eight points and helped their average victory margin by beating eighth seeded Wisconsin by 30 in the second round. They played the lowest seed possible in every round until the championship, where they defeated fifth seed Indiana.

Average Margin of Victory—16.8 points, Average Seed Defeated—7.2

4. 2000 Michigan State Spartans—rating: 2.14

Michigan State's closes game was 11 points and they defeated Florida in the finals. Their average seed defeated was hurt by playing an eighth seed and then a fifth seed in the Final Four. They were a one seed.

Average Margin of Victory—18.4 points, Average Seed Defeated—8.6

5. 2006 Florida Gators—rating: 2.09

Florida won the first of their two consecutive National Championships as a number three seed by defeating second seeded UCLA in the finals. They recorded double-digit wins over every team except number seven Georgetown in the Sweet Sixteen. Their average seed defeated was raised significantly by playing 11th seeded George Mason in the Final Four.

Average Margin of Victory—19.2 points, Average Seed Defeated—9.2

6. 2004 Connecticut Huskies—rating: 2.00

Second seed UConn had only one close call against Duke in the semifinals. They defeated number three seed Georgia Tech in the finals. Before the Final Four, their closest game was 16 points.

Average Margin of Victory—16 points, Average Seed Defeated—8

7. 2005 North Carolina Tar Heels—rating 1.98

UNC was a number one seed and gave fellow number one seed Illinois only their second loss of the season in the finals. Their closest call was a one point game against Villanova in the Sweet 16.

Average Margin of Victory—16.6 points, Average Seed Defeated—8.4

8. 2008 Kansas Jayhawks—rating 1.77

Kansas was one of the number one seeds to create the first Final Four of all one-seeds, and won the final game in dramatic fashion over Memphis in overtime. They also had a close call against 10th-seeded Davidson in the Elite Eight. Their average seed defeated was hurt severely by playing Davidson and also 12th-seeded Villanova in the Sweet Sixteen.

Average Margin of Victory—17 points, Average Seed Defeated—9.6

9. 2003 Syracuse Orangemen—rating 1.53

Third-seeded Syracuse led by Carmelo Anthony defeated second seed Kansas in the finals by only three points and also survived a one-point scare from 10th seeded Auburn in the Sweet Sixteen. They did however, beat two number one seeds by an average of 13.5 points.

Average Margin of Victory—10.4 points, Average Seed Defeated—6.8

The Real Problem (and Solution) of the BCS

The Bowl Championship Series playoff and ranking system is one of the most scrutinized and debated topics in the world of sports. No other sport, professional or college, lacks a postseason playoff. Further, no other division in college football besides 1-A lacks a postseason playoff. It seems like more seasons than not there is controversy over the two teams that should play for the national championship game. This was extremely evident this past season, as we saw the first two-loss championship game participant since the institution of the BCS in 1998. Many fans, analysts, and others argue that a playoff is the only way to crown a true champion. This off-season the BCS even went through a proposal of a “Plus 1” format to create a four team post-season playoff.

However, I argue that a BCS playoff would be a bad idea. The current bowl system is very entertaining to watch and great for those teams involved. Even though many bowls have become “watered down,” fans affiliated with teams in these bowls still strongly support their teams. The best thing about Division 1-A College Football though is the regular season. It is in theory, and with a little tweaking can be in reality, a regular season playoff. More than that, it has longer duration and includes more teams than any other major collegiate playoff system.

In my opinion, and often in reality, once a team loses a game in the regular season they are no longer deserving of a national championship. This is different from basically any other sport imaginable, but it is what makes college football so unique and exciting. However, because of pre-set schedules it would be impossible to end the season with exactly two undefeated teams each year.

That is why the BCS ranking system is so important. If either more than or less than two teams finish the season undefeated a selection has to be made. The worse of the two problems is by far when more than two teams are undefeated, because then more than two teams are deserving. When one loss teams (or even two loss teams) are looked at, then it is still important to make a good selection; but each team in this situation should really consider themselves fortunate to be getting an opportunity.

The worst season for the BCS was in 2003 when USC, Oklahoma, and Auburn all went undefeated. A deserving team, Auburn, was left out. In other years the ranking system has done a reasonable job of picking championship game participants based on information available. However, a huge problem in many cases is a lack of information available. A good example of that is this past season with Kansas. Kansas barely qualified for a BCS bowl, even though they were a major conference team with only one loss (recall that LSU played in the National Championship with two losses). Kansas’ only loss was to Missouri, who was another top 10 team. The only other team in the country who could make a similar argument was Ohio State, whose only loss was to Illinois. However, Missouri was a better team than Illinois (they actually played at the beginning of the season). The knock on Kansas was that they hadn’t beaten any quality opponents. I find that to be a very poor argument. Kansas beat who they were scheduled to play during Big 12 play and they beat up on smaller schools in their non-conference schedule. Almost every other team in the country does the same thing – they schedule extremely weak non-conference teams and then play the schedule they are given for in-conference. Just because Kansas wasn’t given the opportunity to beat good teams does not mean they were incapable. They actually proved their capability in the Orange Bowl by beating Virginia Tech convincingly.

That brings me to the real problem with college football: the regular season scheduling. Many teams do not play enough quality competition to allow the BCS to accurately rank them at the end of the season. This is the reason why teams like Kansas and Boise State (two years ago) get very little respect but end up performing extremely well in Bowl Games. On the other side of the coin, there are teams like Hawaii that get much more respect than they deserve. It’s simply too difficult to gauge how good a team is if they have not played quality competition.

To solve this problem, I propose a modified scheduling structure. This structure will give a stronger likelihood to teams having more losses at the end of the season, but it will allow teams to play more games against other teams that have performed at their level and also eliminate strong teams from having so many non-conference games against much weaker opponents.

There should be two games (“Match-Up games”) for every team in a season that matches them with another team of approximately their level. For college basketball fans, this is a similar idea to what Bracket Buster Sunday gives the mid-major teams. Here is a sample schedule for a college football team to show you my proposed solution:

Game	Current Schedule	Proposed Schedule
1	Non-Conference (Home)	Non-Conference (Home)
2	Non-Conference (Away)	Conference (Home)
3	Non-Conference (Home)	Conference (Away)
4	Conference (Away)	Conference (Away)
5	Conference (Home)	Conference (Home)
6	Conference (Away)	Match-Up (Away)
7	Conference (Away)	Conference (Away)
8	Conference (Home)	Conference (Home)
9	Conference (Home)	Conference (Home)
10	Conference (Away)	Conference (Away)
11	Conference (Home)	Match-Up (Away)
12	Non-Conference/Rivalry (Home)	Non-Conference/Rivalry (Home)
13	Conference Championship (Neutral)	Conference Championship (Neutral)
14	Bowl (Neutral)	Bowl (Neutral)

The two match-up games would give lower rated teams a chance to prove themselves, over-rated teams a chance to fall, and strong teams two games that are less likely to be decided by 50 points. The goal would be not as much to match up the teams who are absolutely closest in ability, but rather to match up teams that are generally the same level. This solution should also diminish the reliance on pre-season rankings, which are often highly inaccurate. It is no secret that it takes a team ranked low to start the season a long time to climb to the top, while teams ranked at the top tend to not fall as much when they lose (unless you are Michigan and lose to a Division II team).

The bowl system would remain the same. It will just be much easier to pick qualified teams for the BCS games and for the national championship game because of more teams having better competition. This way the entire season will truly be like a playoff with every game being extremely important.

Some potential problems may be in preparation for the match-up games. Teams usually know their opponents well in advance and can collect tapes and other preparation materials for these teams. However, because there is no Match-Up game at the very beginning of the season teams can still be given at least two or three weeks notice of their opponent before-hand. This would be just as much time as for a bowl game and much more time than for a conference championship game. Also, in addition to wanting easy wins, many teams schedule weaker teams at the beginning of the season to make sure their teams get confidence and are ready for more challenging teams. I suggest allowing teams a pre-season exhibition game to solve this issue. The game would not count towards any standings but would allow teams to be better prepared. It would also allow teams to generate more money from an extra game.

The first thought to fix college football is always a post-season playoff, but with more thinking better solutions are out there. A few NCAA-scheduled non-conference games, as I have suggested, is one way to fix that problem, and is something that I believe the NCAA should look into. A true proposal would naturally have to be more detailed, but I just wanted to give an outline of what I think would improve the system. I also look forward to hearing opinions and any modifications to these ideas.

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.