Was There a Seven Way Game? Seven Ways of Reaching First Base

A common trivia question among baseball fans is, “How many ways are there for a batter to reach first base?” According to Question 5 in the individual primary round of the trivia contest at the 2009 SABR 39 National Convention in Washington DC, there are eight different ways. The Wiki Answers web site lists 23. There is even a book called 23 Ways to get to First Base: The ESPN Uncyclopedia. In my family, the answer is seven, and my children are required to know them all: hit, walk, error, fielders’ choice, hit by pitch, dropped third strike, and defensive interference.1,2,3

For simplicity of reference in this paper, each of the seven ways that a batter can reach first base will be referred to as a Way (capitalization intentional).

On June 16, 2007, I attended a minor league game at Prince George’s Stadium between the hometown Bowie Bay Sox and the visiting New Britain Rock Cats (Class AA Eastern League) and kept a scorecard throughout the game. During the sixth inning, a batter reached first base due to defensive interference by the catcher, also known as catcher’s interference. I did not know how to score catcher’s interference; this was the first time I had seen it happen during a game. In the seventh inning, a batter reached on a dropped third strike. Since there had already been a hit by pitch in the second inning, a fielders’ choice in the second inning and one in the sixth, two walks (fourth and seventh innings), and 14 hits during the game, that was six of the seven Ways occurring in the same game. When a batter reached first base due to an error by the first baseman in the top of the ninth inning, the set was complete: batters had reached first base by all seven Ways in the same game.

A natural question is, “Has this ever happened in a major league game?”

Methodology

I made use of Retrosheet, whose database at the time included every event in (almost) every major league game from 1945 through the 2012 season.4 Although there is some incompleteness, I examined every game for which individual plate appearances (called “events” in Retrosheet parlance) were recorded during this time period, a total of 124,146 games. For the 1940s, I was able to examine 65 percent of the games played, and from 1974 through 2012, I was able to examine 100 percent of the games played (see Table 1).

 

I queried the database using the Perl scripting language.5 Statistics were accumulated per game without regard for team; that is, the number of batters reaching first base by any of the seven Ways was counted for each game regardless of whether the event represented a batter from the home team or a batter from the visiting team.

The Perl script that I wrote read each line of the database. If the line indicated an event, then it was parsed to determine whether the batter reached first base, and if so, by which Way. A complete list of Retrosheet event codes was constructed to ensure that each plate appearance was assigned to the correct outcome (batter reaches first base, batter does not reach first base) according to the event code. Table 2 gives the Retrosheet event codes that indicated each of the seven Ways for a batter to reach first base. Table 2 also includes a list of all of the Retrosheet event codes that correspond to the batter not reaching first base.

Statistics

I counted the number of times each Way occurred in each of the 124,146 games examined, and I counted the number of games in which each Way occurred. The most common Way is a hit. There is at least one hit in 100 percent of all games. (There has never been a game where neither team got a hit, though it is theoretically possible.6) The average number of hits per game per team is nine. The least common Way is defensive interference which occurs in less than 1 percent of all games. Among the games searched, defensive interference occurred twice in a single game only 15 times. Table 3 shows the frequency and rate of occurrence for each of the seven Ways. Table 4 and Figure 1 show the distribution of the number of Ways that occur in a single game.

 

Figure 1. The frequency of different numbers of Ways occurring in the same game, taken from Table 4, are displayed. (a) The diamonds/dashed line show the probability exactly N different Ways occurring in the same game, where N ranges from 1 to 7. (b) The squares/solid line show the probability of at least N different Ways occurring in the same game, where N ranges from 1 to 7.

Assuming the probability of one Way occurring in a game is independent of the probability of a different Way occurring in the same game, I can use Table 3 to estimate the probability of various combinations occurring. From Table 3, the predicted probability of no Way occurring in a game other than a hit is ~0.01 percent.7 From Table 4, one can see that there were 39 games where the only Way that a batter on either team reached first base was with a hit; that is ~0.03 percent of the games searched, which is not very good agreement. The most obvious conclusion is that the probabilities of the different Ways occurring in the same game are not independent; demonstrating that is beyond the scope of the current paper.

Defensive interference is the least common Way for a batter to reach first base, occurring in fewer than one out of every one hundred games. At that rate, two or more batters should reach first base through defensive interference in the same game about once every ten thousand games. This prediction is in pretty good agreement with the observed occurrence of 15 games out of 124,146 games where two (or more) batters reached first through defensive interference.8

For those who divide defensive interference into catcher’s interference and fielder’s interference, such as the judges of the SABR 39 trivia contest, the 1,073 occurrences of defensive interference in Table 3 consisted of 1,059 occurrences of catcher’s interference and 14 occurrences of fielder’s interference (by the pitcher or the first baseman). The only game in which both catcher’s interference and fielder’s interference occurred was the August 1, 2008, game between the Toronto Blue Jays and the Texas Rangers. If catcher’s interference and fielder’s interference are counted as separate Ways, then batters reached first base by 7 (out of 8) different Ways in this game (hit, walk, fielder’s choice, error, hit by pitch, catcher’s interference, fielder’s interference); there was no batter reaching first by way of a dropped third strike. In no other game would the number of Ways change if catcher’s interference and fielder’s interference were considered separate Ways.

One can also see from Table 4 that batters reach first base in four or fewer Ways in about 78 percent of games. Again assuming the probability of one Way occurring in a game is independent of the probability of a different Way occurring in the same game (which I have already shown to be a questionable assumption), I can use Table 3 to estimate the probability of all seven Ways occurring in the same game; that predicted probability is 5.5×10-5, or about once every 18,000 games. So it should happen about six or seven times in the 124,146 games that were examined.

In fact, that is an excellent prediction.

The Seven Way Games

There have been six major league games (from 1945 to 2012) where batters reached first base by all seven Ways.

May 13, 1976: Texas Rangers at California Angels

This game was won 7–5 by the home team Angels. 16 different batters reached first on a total of 16 hits, 5 walks, 2 fielder’s choice, 3 errors, 2 hit by pitch, 1 dropped third strike, and 1 defensive interference. Rangers batters reached first base six different Ways (no fielder’s choice) and Angels batters reached first base five different Ways (no dropped third strike, no defensive interference).

July 9, 1979: Chicago Cubs at Atlanta Braves

This game was won 7–4 by the visiting Cubs. 22 different batters reached first on a total of 23 hits, 8 walks, 5 fielder’s choice, 1 error, 2 hit by pitch, 1 dropped third strike, and 1 defensive interference. Cubs batters reached first base five different Ways (no error, no defensive interference) and Braves batters reached first base six different Ways (no dropped third strike).

May 1, 1988: Montreal Expos at Houston Astros

This game was won 7–3 by the visiting Expos in 14 innings. 19 different batters reached first on a total of 25 hits, 10 walks, 1 fielder’s choice, 4 errors, 1 hit by pitch, 1 dropped third strike, and 1 defensive interference. Expos batters reached first base five different Ways (no fielder’s choice, no hit by pitch) and Astros batters reached first base five different Ways (no dropped third strike, no defensive interference). After nine innings of this game, batters had reached first base in six different Ways; the seventh Way, dropped third strike, did not occur until the top of the 10th inning.

July 23, 1996: San Diego Padres at Houston Astros

This game was won 7–4 by the visiting Padres. 17 different batters reached first on a total of 18 hits, 8 walks, 1 fielder’s choice, 1 error, 2 hit by pitch, 2 dropped third strike, and 1 defensive interference. Padres batters reached first base six different Ways (no error) and Astros batters reached first base four different Ways (no fielder’s choice, no hit by pitch, no defensive interference).

May 23, 1999: Anaheim Angels at Tampa Bay Devil Rays

This game was won 4–0 by the visiting Angels in 10 innings. 16 different batters reached first on a total of 7 hits, 5 walks, 1 fielder’s choice, 2 errors, 1 hit by pitch, 1 dropped third strike, and 1 defensive interference. Angels batters reached base six different Ways (no dropped third strike), and Devil Rays batters reached base four different Ways (no fielder’s choice, no hit by pitch, no defensive interference). After nine innings of this game, batters had reached first base in five different Ways; the sixth and seventh Ways, fielder’s choice and defensive interference, did not occur until the top of the 10th inning.

June 28, 2000: Baltimore Orioles at Boston Red Sox

This game was won 8–7 by the visiting Orioles in 11 innings. 20 different batters reached first on a total of 27 hits, 11 walks, 4 fielder’s choice, 2 errors, 1 hit by pitch, 1 dropped third strike, and 1 defensive interference. Orioles batters reached base all seven Ways, and Red Sox batters reached base four different Ways (no hit by pitch, no dropped third strike, no defensive interference). After nine innings of this game, batters had reached first base in six different Ways; the seventh Way, defensive interference, did not occur until the top of the 11th inning.

There have been six games (since 1945) where both teams together reached first base in all seven ways, but this has been accomplished in 9 innings only three times. Only one time has a single team reached first base in all seven Ways in the same game (the Baltimore Orioles on June 28, 2000), but it took them 11 innings to do it. These results are summarized in Table 5.

There has not been a nine inning major league game (since 1945) in which batters from one team reached first base using all seven Ways.

I’ll keep watching. 

PAUL HERTZ has been a SABR member since 2000. He holds a Ph.D in astronomy and is currently the Director of the Astrophysics Division at NASA Headquarters in Washington, D.C. He has been a fan of the local team wherever he has lived, which has been (in order): the Atlanta Braves, the Boston Red Sox, the Baltimore Orioles, and he is currently a season ticket holder of the Washington Nationals. This is his first contribution to the Baseball Research Journal.

 

Acknowledgments

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at www.retrosheet.org/. The information used here was retrieved from Retrosheet on January 12, 2013. The play-by-play summaries of the Seven Way Games were taken from Baseball-Reference.com (http://baseball-reference.com/). Thanks to Bruce Brown for providing Question 5 of the individual primary round from the SABR 39 trivia contest. Thanks to JP Caillault, Robert Fogel, and Michael New for critical readings that improved this article.

 

Notes

1. http://wiki.answers.com/Q/How_many_ways_can_a_batter_reach_ first_base.

2. Gary Belsky and Neil Fine, 23 Ways to get to First Base: The ESPN Uncyclopedia (ESPN Publishing, 2007).

3. Defensive interference resulting in the batter reaching first base can be committed by the catcher or by an infielder. This accounts for the eighth Way of reaching first base in the answer to the SABR 39 trivia question: catcher’s interference and fielder’s interference are considered separate Ways.

4. www.retrosheet.org.

5. I used the Strawberry Perl 5.15.2.1 version that is available at http://strawberryperl.com.

6. There have been 5 games since 1945 among the 124,146 games that I examined where the winning team had no hits. Two of these five games are listed as official no hitters that resulted in a loss (April 23, 1964, Cincinnati Reds at Houston Colt 45s; April 30, 1967, Game 1, Detroit Tigers at Baltimore Orioles). The other three are not listed as official no hitters (July 1, 1990, New York Yankees at Chicago White Sox; April 12, 1992, Game 1, Boston Red Sox at Cleveland Indians; June 28, 2008, Los Angeles Angels of Anaheim at Los Angeles Dodgers). In the first two games, the no hitter was pitched by the losing home team, so the home team pitched 9 innings in a losing effort. In the latter three games, the near no hitter was pitched by the visiting team, so there was no bottom of the ninth inning played, and the losing visiting team only pitched eight innings. By definition of Major League Baseball, a no hitter must be pitched over nine or more innings, so the latter three games are not official no hitters. But the definition does not require that the no hitter result in a win, so the first two games are official no hitters.

7. This is calculated by multiplying the probability of there not being a walk in a game times the probability of there not being an error in the games times the probabilities of there not being any of the other Ways in a game, other than a hit.

8. To be precise, if defensive interference is observed to occur in 1058 out of 124,146 games (0.85%), then it is predicted to happen twice in the same game about 0.85% times 0.85% of the time, or once every 13,770 games. Defensive interference is observed to happen twice in the same game in 15 games out of 124,146 games, or about once every 8,276 games. In 14 of the 15 games where defensive interference occurred twice, it was committed twice by the same team. If the second occurrence of defensive interference in a game occurs randomly, than half of the games should have had both teams committing defensive interference. It appears that a team which has committed defensive interference once in a game is more likely to commit it the second time. This may help explain the fact that defensive occurrence occurs twice in a game more often than predicted.