In the history of Major League Baseball, Mike Schmidt was one of the best players. He played third base for the Philadelphia Phillies from the years 1972 to 1989. Schmidt was a great player from many aspects. He was an excellent fielder at third base, winning a large number of Gold Glove awards. He is probably better known for his hitting; in particular, he is best known for his ability to hit homeruns. Schmidt hit 548 homeruns over the span of his career, which places him seventh on the all-time list. He won the season homerun title in the National League seven times and tied for the title once.
The story of Mike Schmidt's baseball career can be told using his homerun statistics displayed in Table 1. This table gives the number of games he played, the number of opportunities to hit (at-bats), and the number of homeruns for each of his seasons in his baseball career. One measure of Schmidt's ability to hit homeruns is the ratio of the number of homeruns to the number of at-bats. This statistic gives the rate at which he hits homeruns. This homerun rate is displayed in the column ``Rate" in Table 1.
Table 1: Homerun statistics for Mike Schmidt.
We see from the table that Schmidt began his major league career with the Phillies in 1972. That year he started playing towards the end of the season, and only had a small number of plate appearances and only one homerun. The next year, 1973, was the first season in which Schmidt played regularly. This was a year where his hitting was relatively immature. He hit 18 homeruns, but he had many strikeouts and had a relatively poor batting average under .200. This is when the hometown fans in Philadelphia started to boo him. Unfortunately, this booing would become one notable aspect of his career. During the off-season following the 1973 year, Schmidt played winter baseball. This is when he adjusted his batting swing. In Schmidt's words ``I found a swing that made things happen." (Thorn and Palmer, 1993.) Schmidt's hitting was very productive starting with the 1974 season. We see from Table 1 that he hit at least 30 homeruns (with one exception) each year from 1974 to 1987. The only exception to this streak was 1978. Schmidt had a number of injuries that year, and these injuries had a significant impact on his power hitting.
One of the most exciting days in Mike Schmidt's career was April 18, 1976. On this day, Schmidt hit homeruns on four consecutive at-bats against the Chicago Cubs. Hitting four homeruns in a single game was a feat that had been accomplished previously by only nine players. In an interview described by Westcott (1995), Schmidt commented about his last homerun: ``I was feeling good, and I was nice and relaxed".
The climax of Schmidt's career was 1980, when the Phillies won the World Series, the championship of baseball. That year he hit homeruns at his highest rate, .088. He continued his hot hitting during 1981 which was significantly shortened by a two-month players' strike. After 1981, Schmidt's homerun skills decreased, but he still hit homeruns at a high rate. His hitting production dropped significantly during 1988. He did not play as regularly (only 108 out of 162 team games) and his homerun rate (.031) dropped to less than one half of his previous year's rate. Schmidt's career ended with the Phillies in 1989. Midway through the season, he felt that his defensive skills had deteriorated and believed it was the right time to retire from baseball.
Most baseball experts agree that Mike Schmidt was the greatest third baseman in baseball. Bill James, one of the foremost baseball statisticians, lists (in James, 1988) four assets of Schmidt that distinguished him from other third basemen.
First, he was a powerful hitter which was demonstrated in his large number of homeruns in his career. Second, he was very skillful in drawing walks. By getting on base many times with a walk, Schmidt contributed many runs to his team. Third, Schmidt was very durable. He played at least 89% of his team's games every year from 1974 to 1987. Finally, Schmidt was a very consistent player. James notes that he had only one off-season in a 14 year stretch and very few ``great" baseball players can match this record.
Mike Schmidt's consistency is mentioned by other baseball experts (Westcott, 1995). Paul Owens, the Phillies general manager in the 1980's, describes Schmidt as ``a true professional." ``He plays like a man fighting to keep his job." ``Consistency is the only word you can use to describe him." Another contemporary ballplayer, Dale Murphy said that ``Mike was so professional about his job." ``He was just so consistent." ``He continued to produce year after year."
Based on Schmidt's season homerun statistics shown in Table 1, he did appear to be a very consistent hitter. Most of his season homerun totals from 1974 to 1987 fell between 30 to 40. However, this data is just a summary of Schmidt's success over the stretch of a season and it hides possible inconsistencies in his homerun hitting during a season. Recently, more detailed information about Schmidt's homerun hitting became publicly available. The Philadelphia Phillies gave recognition to Schmidt's induction into the Baseball Hall of Fame with a special tribute during one of their recent baseball games. Every fan who attended the game was given a listing of the dates of each of the 548 homeruns that Schmidt hit during his career. (This list was posted by Jim Sweetman on the World Wide Web page http://users.aol.com/jweetman/phils/schmidt.htm.) This time series data has the potential to give us new understanding into this player's homerun hitting record.
In this article, this new dataset is used to explore the homerun hitting behavior of Mike Schmidt. The statistical notion of consistency is clarified in Section 2. Essentially, a consistent homerun model is coin tossing with a constant probability of success. Section 3 performs an exploratory data analysis on this time series. Graphs and associated statistics suggest that, during some seasons, Schmidt had an inconsistent or nonconstant pattern of homerun hitting. However, the patterns that we notice in this data analysis may not be meaningful. It is well-known that even simple coin tossing with a fair coin can give interesting patterns of streaks of heads or tails and other apparent nonrandom behavior. To see if the patterns we see in the plots are real, Schmidt's homerun data is compared with data of homerun hitters who are truly consistent. In Section 4, a procedure is outlined to produce simulated homerun data from the consistent coin-tossing model. This simulation procedure is repeated many times, producing a population of data from these consistent hitters. By comparing Schmidt's data with this population in Section 5, we get extra insight into Schmidt's homerun hitting. In Section 6, we summarize what we have learned in this analysis and relate this discussion with other papers analyzing baseball hitting data.