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 have been the better team for most of the year; 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. However, the actual 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. 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.
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.
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.
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 surprised 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.
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