Were Major League Doubleheaders a Mistake? Department of Economics Working Paper

Stephen K. Layson University of North Carolina at Greensboro

M. Taylor Rhodes University of North Carolina at Greensboro

February 2011 Working Paper 11-05 www.uncg.edu/bae/econ/ 1

Were Doubleheaders A Mistake?

Stephen K. Layson M. Taylor Rhodes Department of Economics Department of Economics UNC Greensboro UNC Greensboro Greensboro, NC 27402 Greensboro, NC 27402 [email protected] [email protected]

Abstract

This paper uses daily Major League Baseball (MLB) data from 1938 to 2009 as well annual MLB data from 1920 to 2009 to estimate the effects of doubleheaders on attendance. The annual data over various sub-samples from 1920-2009 indicate that the number of doubleheaders have either a negative or an insignificant effect on annual attendance. The daily data from 1938-2009 show that doubleheaders have a very positive effect on attendance on the day of the doubleheaders but that this is substantially offset by reduced attendance at games 3 days surrounding doubleheaders. This leads us to question the widespread use of doubleheaders.

File: Complete_v5f Date: 2/1/11

I. Introduction

We use a large panel data set on daily attendance for every Major League Baseball

(MLB) team from 1938 to 2009 as well as annual MLB team attendance data from 1920 to 2009

to estimate the effects of doubleheaders on MLB attendance. Doubleheaders in this paper are defined to be two consecutive baseball games that are sold to a fan for the same ticket price as a 2

single game.1 Because a doubleheader is two baseball games for the price of one, we expect

attendance at doubleheaders to exceed attendance at single games, ceteris paribus. Using the

daily attendance data we find that doubleheaders have two effects on attendance: a positive direct

effect on attendance on the day of the doubleheader and a negative substitution effect on

attendance at single games surrounding doubleheaders. Both the direct effect and the

substitution effects of doubleheaders, however, appear to have changed over the 1938 to 2009

period.

In the period between 1938 and 1956 when the structure of MLB was relatively stable

and doubleheaders were common, we estimate attendance on the day of a doubleheader increases

by 48% relative to single games. This positive direct effect of doubleheaders on game day

attendance, however, is substantially but not completely offset by lower attendance at single

games 3 games before and 3 games after the doubleheaders as fans rationally substitute

doubleheaders for single games. After 1956 when the structure of MLB underwent many

changes and the use of doubleheaders declined, we find the direct effect of doubleheaders on

attendance is still positive and significant, but smaller than in the 1938-1956 period. Also, in the

post-1956 periods we find the total effect of doubleheaders are negative but not significantly

different from zero.

The daily regression results concerning the total effect of doubleheaders on attendance

are for the most part confirmed by the use of annual MLB team attendance data. From 1920-

1956 and from 1938-1956 the number of team doubleheaders per year has insignificant effects

on annual attendance and for the post-1956 periods we find the effect of doubleheaders per year on annual attendance is always negative and marginally significant in the 1957-1980 period. The

1 To be more precise by doubleheader we mean single-priced doubleheaders as opposed to separate-priced doubleheaders which are two baseball games played on the same day with separate ticket admissions. 3 most important difference between the annual and the daily regressions is that the daily regressions over the 1938-1956 period indicate a small positive, but significant total effect of doubleheaders on attendance whereas the annual regressions indicate an insignificant effect of doubleheaders on annual attendance. It could be that the annual regressions over the 1938-1956 period are not finding a significant effect of doubleheaders on attendance because they are capturing substitution effects of doubleheaders beyond 3 days.

II. Literature

To date, only four studies – Siegfried and Eisenberg (1980a, 1980b), Hill, Madura and

Zuber (1982), Marcum and Greenstein (1985) and Bruggink and Eaton (1996) – examine the relationship between attendance and doubleheaders. The only panel data study was by Siegfried and Eisenberg (1980a, 1980b), which analyzed annual attendance for various teams from 1973 to 1977 and surprisingly found that the number of team doubleheaders per year had no statistically significant effect on annual team attendance. The other three studies used cross-sectional daily attendance data from a single year and all find that doubleheaders have a positive impact on daily attendance on the day of the doubleheader.

Siegfried and Eisenberg (1980b, 64) list two alternative, mutually exclusive, reasons for their finding that doubleheaders have no impact on annual minor league attendance: (1) “rapidly diminishing marginal utility beyond nine of baseball per day” and (2) “much of the increased attendance at -headers may simply be people switching from alternative single games.” Using daily MLB attendance we demonstrate that the doubleheader substitution effects speculated on by Siegfried and Eisenberg (1980b, 64) do exist and appear to be the most likely explanation for their surprising finding that doubleheaders have no effect on minor league attendance. Also, using annual MLB data from 1920-2009 with a methodology similar to that of 4

Siegfried and Eisenberg (1980a, 1980b), we confirm their finding that the annual number of team

doubleheaders does not have a positive and significant effect on team attendance.

The three studies mentioned earlier that used daily data from a single year of cross-

sectional daily data on MLB attendance examined only the attendance effects of doubleheaders

on the day of the doubleheaders. They did not check for the possibility that doubleheaders steal

attendance away from single games. Hill, Madura and Zuber (1982) analyzed the 1977 MLB

season and found that doubleheaders had a highly significant statistical effect increasing

attendance on the day of a doubleheader by 4,814 relative to single games. Marcum and

Greenstein (1985) analyzed the 1982 season for two MLB teams, the St. Louis Cardinals and the

Texas Rangers. They found that doubleheaders had a statistically significant effect for St. Louis

increasing attendance on the day of a doubleheader by 32.5% compared to single games but the

effect of doubleheaders on attendance for the Rangers was insignificant at only 7.6%. Lastly,

Bruggink and Eaton (1996) studied the 1993 season and found that doubleheader games relative

to single games increased attendance for National League (NL) teams in a range of 8.8% to 10%

and a range of 12% to 14% for American League (AL) teams.2

III. Data and Descriptive Statistics

To investigate the daily attendance effects of doubleheaders, we use a collection of

individual regular season MLB game logs sorted by home team from retrosheet.org.3 Across

2 The weak finding by Marcum and Greenstein (1985) for the effect of doubleheaders on attendance for the Texas Rangers may be due to the fact that Texas played only 3 doubleheaders in 1982. Also, the weak findings by Bruggink and Eaton (1996) for the effects of doubleheaders attendance may be explained by the small number of doubleheaders played in 1993. The National League played only 13 doubleheaders in 1993 and the American League played only 14. 3 The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at www.retrosheet.org. 5

seasons, the game logs are arranged chronologically starting with the 1871 season and ending

with the 2009 season. Within a season, game logs record daily home team attendance and many

game-specific outcomes. For example, the game logs record if the game was a night or day

game, if the game was a single or a doubleheader game, and record the day, day of the week,

month, and year the game was played. Additionally, many of the game logs offer a

comprehensive list of offensive and defensive statistics for each game as well as other

information.

While the game logs contain a rich account of individual home games, prior to 1938 the

game logs have numerous missing values for attendance. Hence, our sample on MLB daily

attendance begins in 1938. As a rough check on the validity of the Retrosheet daily attendance

figures from 1938 -2009, we aggregate the Retrosheet daily attendance figures for each year and

then compare them with Lahman’s annual MLB attendance figures.4 Figure 1 reports the %

difference between the two series from 1938 to 2008.5

From 1950 onwards the two measures of aggregate attendance are very close, with the

largest occurring in 1952 when the Retrosheet aggregate attendance was 5% below

Lahman’s attendance figure. From 1938 to 1949 the Retrosheet aggregate attendance is

sometimes below and sometimes above Lahman’s but reasonably close except in 1949 when the

Retrosheet attendance was 34% below Lahman’s attendance figure. Even though the aggregate

attendance for the Retrosheet data does not match Lahman’s data as closely in the 1938 to 1949

period as it does in the post 1950 data, we include this earlier period because it is rich in

4 For more on Sean Lahman’s Baseball Archive, see www.baseball1.com. 5 A similar plot was obtained when we compared the Retrosheet data to the total attendance data from two other sources: baseball-reference.com – made available by Rodney Fort at www.rodneyfort.com – and Total Baseball (1993). 6

doubleheaders. If there is measurement error in the daily MLB attendance figures prior to 1949

this would bias the coefficient on our doubleheader variable towards zero.

Figure 1: Percent Change in Attendance Data Reported by Retrosheet and Lahman (Data 1938 - 2008)

50 40 30 20 10 0 1938 1943 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008 Data) -10

Percent Change Percent -20 -30

(Base = Lahman's Attendance -40 -50 Year

As far back as 1920, the game logs have complete records on the annual number of doubleheaders and annual games per team. Thus for analysis using only annual observations similar to Seigfried and Eisenberg (1980a, 1980b), we use the number of doubleheaders from the

Retrosheet data from 1920 to 2009 along with Lahman’s annual baseball attendance figures for

1920 to 2009.6

Recall that when we use the word doubleheaders we mean single-priced doubleheaders because such games offer fans an opportunity to see two games for the price of one. Separate- admission doubleheader games offer no such incentive; they are merely two games held on the same calendar day. To distinguish between these two types of doubleheaders in the Retrosheet

6 See the attached data appendix for more details on the frequency of missing observations. 7 game logs we had to make some assumptions regarding how attendance was recorded for these two types of doubleheaders.7 For each home team that played doubleheaders between 1920 and

2009, the Retrosheet game logs record attendance in 4 different ways.

For the doubleheaders with attendance figures there are 3 different ways in which the game logs record attendance. The first and largest group (8,837 observations), record a single attendance figure for the doubleheader. We assume these values represent the attendance of single-priced doubleheaders. The second group (658 observations), record the attendance for the first game with a positive value and the attendance for the second game with a different positive value. We assume such paired observations represent a separate-priced doubleheader where fans were charged separate admissions for each game. The third group (537) observations, record the attendance for the first game with a positive value and the attendance for the second game with the same positive value. We assume that such observations redundantly entered the total attendance of a single-priced doubleheader. Thus we have 10,032 doubleheaders with attendance figures. We assume that 658/10,032=6.56% of these are separate-priced doubleheaders and 9,374/10,032=93.44% of these are single-priced doubleheaders.

There were also 2,115 doubleheader observations with missing attendance data for both the first and second games. These come mostly from the 1920-1937 sub-period. For our analysis using annual observations, we used team specific weights – the proportion of doubleheaders with attendance figures by team – to determine how many of the 2,115 doubleheader observations with missing attendance data represented single versus separate-priced doubleheader games. In our analysis of daily data, of course, we drop all observations for both single games and doubleheaders when there are missing observations.

7 For a more meticulous discussion, see the attached data appendix. 8

We investigated the validity of our data assumptions regarding doubleheaders by

contacting David Smith, President of the Retrosheet Board of Directors. He informed us that our

data assumptions regarding single-priced doubleheaders were correct but mentioned the

possibility of attendance inaccuracies prior to the 1980s. As an additional check, we used

scheduling data from ESPN on doubleheader games from 2002 until 2009.8 For these 216

games, we matched each doubleheader with press releases or news stories from the archives

available on MLB.com. Given our data assumptions, the Retrosheet data correctly distinguished

between single-priced and separate-priced doubleheaders in every case.

Lastly, we investigated a number of separate-priced doubleheader games in conjunction

with an article on holiday doubleheaders by Bevis (2004). Specifically, Bevis (2004) offers a

brief discussion on which teams’ scheduled separate- priced holiday doubleheader games from

1934 until 1958.9 For these teams, we were able to investigate 11 games using the Retrosheet data and given our data assumptions found that 2 games were possibly incorrectly recorded as

single-priced doubleheaders, 2 games had missing attendance figures and the remainder

indicated separate-priced doubleheaders. Thus in total, we believe that our data assumptions are

substantially correct and offer a first attempt at separating single-priced and separate-priced

doubleheaders.

Other data edits include dropping a few obvious attendance outliers and a small number

of games played in March. All such details are outlined in the appendix. Figure 2 which shows

the percentage of total games that are single-priced doubleheaders from 1920 to 2009

demonstrates the importance of doubleheaders in MLB prior to 1970. At their peak in 1945

single-priced doubleheaders accounted for 48% of the total games played! Also note that in

8 For the ESPN data on scheduled doubleheaders, see http://sports.espn.go.com/mlb/stats/doubleheaders. 9 According to Bevis (2004), such teams were the exception rather than the rule during this period. 9

every year from 1926 to 1967, the percentage of single-price doubleheaders accounted for at

least 20% of the total games played.

Figure 2: Percentage of Doubleheader Games by Year (Data 1920-2009)

100

90

80

70

60

50

40 Frequency (%) 30

20

10

0 1920 1924 1928 1932 1936 1940 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 Year

Doubleheaders

Figures 3 and 4, respectively, show the percentage of total games that are accounted for by single-priced doubleheaders by month and day of week from 1938 to 2009. For a comparison across months, Figure 3 shows the frequency of single-priced doubleheaders reaches a peak in

July and decreases thereafter. Similarly for the days of the week, Figure 4 shows the relatively flat frequency of single-priced doubleheaders from Monday to Saturday with a sudden spike on

Sunday.

10

Figure 3: Percentage of Doubleheader Games by Month (Data 1920-2009)

18

16

14

12

10

8

Frequency (%) 6

4

2

0 April May June July August September October Month

Doubleheaders

Figure 4: Percentage of Doubleheader Games by Days of the Week (Data 1920-2009)

35

30

25

20

15 Frequency (%) 10

5

0 Monday Tuesday Wednesday Thursday Friday Saturday Sunday Day of Week

Doubleheaders

11

Next, Figure 5 illustrates the difference in average attendance between single-priced

doubleheader and single games across years. As shown in Figure 5, the average attendance for

single-priced doubleheaders exceeded that of single games until the late 1980s; thereafter, the

comparison becomes noisy due to the relatively small number of doubleheaders played from

1990 to 2009.

Figure 5: Average Attendance of Double Header and Single Games over Time (Data 1938-2009)

40000

35000

30000

25000

20000

15000

Average Attendance 10000

5000

0 1938 1942 1946 1950 1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 Year

Doubleheaders Single Games

Lastly, Table 1 lists the average number of single-priced doubleheader games played per year by team from 1920 until 2009. The franchises with the highest average doubleheaders per year tend to be historic ball clubs that played most of their games in a period of time when doubleheaders were very common. In contrast, the relatively new expansion teams of the Tampa

Bay Rays, Washington Nationals and have played fewer doubleheaders per year. Such was expected given Figure 2, which illustrated the percentage of total games that are single-priced doubleheaders over time. 12

Table 1: Average Number of Games Played as Doubleheaders per Year by Team (Data 1920-2009) Team Avg Boston Braves (1920-1952) 30.00 Philadelphia Athletics (1920-1954) 27.84 New York Giants (1920-1957) 24.05 St. Louis Browns (1920-1953) 23.36 Brooklyn Dodgers (1920-1957) 19.69 Washington Senators (1920-1960) 19.18 Washington Senators (1961-1971) 19.09 Philadelphia Phillies (1920-2009) 17.74 (1920-2009) 16.89 (1920-2009) 16.37 Seattle Pilots (1969) 16.00 (1920-2009) 15.59 (1920-2009) 15.00 (1920-2009) 14.62 Los Angeles Angels (1961-1964) 14.50 Milwaukee Braves (1953-1965) 14.31 Boston Red Sox (1920-2009) 13.57 Kansas City Athletics (1955-1967) 13.37 (1920-2009) 12.99 (1920-2009) 12.24 (1962-2009) 11.46 St. Louis Cardinals (1920-2009) 10.86 Baltimore Orioles (1954-2009) 10.75 Montreal Expos (1969-2004) 6.39 San Francisco Giants (1958-2009) 6.23 Milwaukee Brewers (1970-2009) 5.80 (1966-2009) 5.55 Kansas City Royals (1969-2009) 5.07 (1968-2009) 5.00 (1961-2009) 4.65 San Diego Padres (1969-2009) 4.20 Texas Rangers (1972-2009) 4.05 California Angels (1965-1996) 3.63 Los Angeles Dodgers (1958-2009) 2.77 Toronto Blue Jays (1977-2009) 2.73 Houston Astros (1962-2009) 2.17 Florida Marlins (1993-2009) 1.88 (1977-2009) 0.97 Colorado Rockies (1993-2009) 0.82 Washington Nationals (2005-2009) 0.40 Anaheim Angels (1997-2009) 0.31 (1998-2009) 0.17 Arizona Diamondbacks (1998-2009) 0.00

13

IV. Empirical Results for Daily MLB Attendance Data

To measure the impact of single-priced doubleheaders on home team attendance, we begin with the following general model:

(1) ln(attendit,12 )   Double it , Xβ  i t it ,

where attendit, measures daily attendance for home team i in year t , Doubleit, is a dummy variable which equals one of if the game is a single-priced doubleheader and zero otherwise, Xβ represents any remaining observable factors that influence daily attendance for home team i in year t and their corresponding coefficients, i is a team specific year invariant effect, t is a year effect common to all teams, and it, is the remaining disturbance term capturing all remaining factors. 10

In Table 2, we estimate model (1) starting with a simple specification – a pooled OLS regression of log attendance on a dummy variable indicating a single-priced doubleheader. We build upon this simple specification by adding various dummy variables in order to control for various game characteristics and time effects. For example, in column 2 we add a vector of game characteristics including the dummy variable Night Game, which equals one if the game is played at night and zero otherwise, the dummy variable , which equals one if the game is played on opening day and zero otherwise, and lastly a collection of dummy variables for Memorial Day, Independence Day and Labor Day.11 In column 3, we add dummy variables indicating the day of the week with Monday as the base group. In column 4, we add month dummy variables with April as the base group. In column 5, we add year dummy variables, with

10 Our notation follows Baltagi (2008) and his treatment of two-way error component models. 11 Data on the specific calendar dates for each of the holidays was taken from www.timeanddate.com. 14

1938 as the base group, to control for any unobserved year effects common across team.

Continuing, in column 6, we remove the year dummy variables and add team dummy variables

in order to control for any unobservable team fixed effects. Lastly, in column 7, we add both

year and team dummy variables to control for both year and team fixed effects.

Table 2: Estimating the Effect of Doubleheader Games on Daily Home Team Attendance (Data 1938-2009) Dep Var: ln(attend) (1) (2) (3) (4) (5) (6) (7) Basic Add Game Add Day of Replace Year Add Both Year Add Month Add Year Model Controls Week Add Home Team and Home Team Doubleheader 0.0022 0.0661 -0.0396 -0.0651 0.3398** 0.0849* 0.3652** (0.0482) (0.0484) (0.0415) (0.0390) (0.0228) (0.0350) (0.0197) Night Game 0.2100** 0.5168** 0.5082** 0.2202** 0.4604** 0.2718** (0.0478) (0.0643) (0.0640) (0.0400) (0.0638) (0.0369) Opening Day 0.6555** 0.9142** 0.9857** 0.9888** 1.0108** 1.0133** (0.0519) (0.0679) (0.0709) (0.0644) (0.0709) (0.0658) Memorial Day 0.3079** 0.5573** 0.6520** 0.5256** 0.6256** 0.5439** (0.0452) (0.0573) (0.0617) (0.0470) (0.0619) (0.0501) Independence Day 0.4196** 0.5475** 0.4019** 0.2734** 0.3691** 0.2833** (0.0357) (0.0425) (0.0450) (0.0352) (0.0375) (0.0349) Labor Day 0.2210** 0.5598** 0.8031** 0.6222** 0.7619** 0.6447** (0.0520) (0.0754) (0.0771) (0.0574) (0.0756) (0.0587) Dummies Added: Days of Week N N Y Y Y Y Y Months of Year N N N Y Y Y Y Year N N N N Y N Y Team N N N N N Y Y

Observations 119,174 118,477 118,477 118,477 118,477 118,477 118,477 R-squared  0 0.027 0.132 0.160 0.417 0.321 0.514 Notes: Robust standard errors in parentheses, clustered by home team. * Significant at 5%; ** significant at 1%

This approach clearly illustrates the importance of controlling for year fixed effects, as

can be seen by the large increase in the point-estimate for doubleheaders once year dummy

variables are added. Specifically, the point-estimate of .34 on doubleheaders in column 5 would

imply that home team attendance rises by about 41% as a result of a doubleheader relative to 15 single games.12 This is in stark contrast to the specifications shown in columns 1 through 4 and column 6 which exclude year dummy variables. For these specifications, the percent increase in attendance as a result of a doubleheader relative to single games ranges from a small negative effect of -6% to a small positive effect of 9%.

A similar although less dramatic result holds with respect to the exclusion of team fixed effects. This is shown by comparing the point-estimate on doubleheader games in column 5, which controls for year fixed effects but not team fixed effects, to that of column 7, which controls for both year and team fixed effects. Thus, the inclusion of year but not team fixed effects tends to under estimate the marginal effect of a doubleheader.

Given these concerns regarding omitted variables bias, it follows that the preferred specification is column 7, which controls for both year and team fixed effects. From this specification, night games increase daily attendance by about 31% relative to day games.

Opening day illustrates the initial interest in all teams at the start of the season with an estimated increase in daily attendance by 175%. For the holidays, Labor Day increases daily attendance the most (91%) followed by Memorial Day (72%) and Independence Day (33%). Lastly, the point-estimate for doubleheader games implies that home team attendance increases by approximately 44% for doubleheader games relative to single games. This marginal effect of

44% is larger than the estimated 32.5% increase reported by Marcum and Greenstein (1985) when they studied the St. Louis Cardinals in 1982 and the estimated 8% to 14% increase by

Bruggink and Eaton (1996) when they studied the 1993 season. We also estimated the model in

12 Since Double enters our model as a dummy variable and the log of daily attendance is the dependent variable, the percent increase in attendance as a result of a doubleheader game relative to a single game can be calculated by using the following formula: 100*(exp(  2 ) – 1). For a formal treatment regarding this formula see Halvorsen and Palmquist (1980).

16 levels and found that doubleheader games increased attendance by 4,786, holding all else constant and controlling for team and year fixed effects. This is comparable to the findings of

Hill, Madura and Zuber (1982); however, our log specification allows a degree of flexibility in that the marginal effect of a doubleheader game will have the same percent change in attendance for each team but does allow the change in the underlying levels to vary across teams.

While our initial estimate of a 44% increase in attendance seems to indicate doubleheaders are a powerful marketing tool, this estimate as well as the estimates by Marcum and Greenstein (1985), Bruggink and Eaton (1996) and Hill, Madura and Zuber (1982) is valid only if the substitution effect of fans from single games towards the doubleheaders is zero.

However, if doubleheaders cause fans to substitute away from single game and towards doubleheaders, then our initial estimate of 44% overstates the total attendance return of a doubleheader. To account for any substitution effects of a single-priced doubleheader on attendance for MLB at the individual game level, we estimate the following model:

(2) ln(attendit,12 )   Double it , Xβθ 11GP δ GA  i t it ,

Model (2) above is identical to model (1) except that θ1GP is a collection of dummy variables indicating if a single game was played prior to a doubleheader by home team i in year t , and

δ1GA is a collection of dummy variables indicating if a single game was played after a doubleheader by home team i in year t . Thus, estimates for GP and GA will help account for any fan substitution effects resulting from doubleheaders.

As a reference, we first estimate model (2) without the inclusion of GP orGA . The results are shown in Table 3 and are merely our standard fixed effects estimates, which predict that doubleheader games increase attendance by 44%. Next, we allow GP to include a single 17 dummy variable which equals 1 if a single game was played one day prior to a doubleheader and zero otherwise. Similarly, we allow GA to include a single dummy variable which equals 1 if a single game was played one day after a doubleheader and zero otherwise. Estimates for this specification are shown in column 2 of Table 3.

Table 3: Effect of Doubleheader Games on Daily Home Team Attendance (Data 1938-2009) Dep Var: ln(attend) (1) (2) (3) (4) FE Add 1P, 1A Add 2P, 2A Add 3P, 3A Doubleheader 0.3652** 0.3302** 0.3203** 0.3141** (0.0197) (0.0194) (0.0200) (0.0206) 1 Day Prior -0.2412** -0.2422** -0.2432** (0.0233) (0.0236) (0.0239) 1 Day After -0.1441** -0.1442** -0.1440** (0.0195) (0.0194) (0.0192) 2 Days Prior -0.0421 -0.0434 (0.0267) (0.0266) 2 Days After -0.0989** -0.0985** (0.0178) (0.0177) 3 Days Prior -0.0882** (0.0173) 3 Days After -0.0449* (0.0176) Night Game 0.2718** 0.2588** 0.2583** 0.2585** (0.0369) (0.0362) (0.0361) (0.0360) Opening Day 1.0133** 1.0028** 1.0001** 0.9991** (0.0658) (0.0651) (0.0653) (0.0653) Memorial Day 0.5439** 0.5384** 0.5391** 0.5392** (0.0501) (0.0495) (0.0497) (0.0498) Independence Day 0.2833** 0.2743** 0.2731** 0.2716** (0.0349) (0.0348) (0.0344) (0.0343) Labor Day 0.6447** 0.6301** 0.6303** 0.6308** (0.0587) (0.0585) (0.0585) (0.0586)

Days of Week, Month, Y Y Y Y Team and Year Dummies

Observations 118,477 118,477 118,477 118,477 R-squared 0.514 0.518 0.518 0.519 Notes: Robust standard errors in parentheses, clustered by home team. * Significant at 5%; ** significant at 1%

Notice the point-estimates for both the one game prior and one game after dummy variables are statistically significant and negative in sign. Specifically, column 2 suggests that 18 while doubleheader games increase attendance by about 39%, single games played one day prior to a doubleheader decrease attendance by 21% and single games played one day after decrease attendance by 13%. This finding indicates that there are sizeable fan substitution effects.

To calculate the total effect of a single-priced doubleheader based on the estimates in column 2, we considered all the various combinations involving the following : one single game prior to a doubleheader, a doubleheader and one single game after a doubleheader. All such combinations are listed in Table 4.

Table 4: Total Effect of a Doubleheader Game (Model 2 w/ 1 Day Prior and 1 Day After) Sum of Regression Sequences Frequency Weight Estimates Total Effect 1 Day Prior - DH - 1 Game After 2367 0.2862 -0.0551 0.1046 1 Day Prior - DH - No 1 Day After 2774 0.3354 0.0889 No 1 Day Prior - DH - 1 Game After 1973 0.2386 0.1861 No 1 Day Prior - DH - No 1 Day After 1156 0.1398 0.3302 Total 8270 Note: The regression estimates of 1 Day Prior, Doubleheader and 1 Day After used in the total effect calculation are shown in column 2 of Table 3.

The first row in Table 4 represents the sequence where we have a single home game played one day prior to a doubleheader, a home doubleheader and a home single game played one day after a doubleheader. The second row represents a single home game played one day before a doubleheader, a home doubleheader and no home game after a doubleheader. The last sequence is no home single game prior to a doubleheader, a doubleheader and no home game after a doubleheader. The contribution of each sequence to the total effect of a doubleheader game will be the relative frequency of this triple occurring in the sample times the relevant sum of the regression point-estimates in column 2 of Table 3. Repeating in this fashion for all possible sequences yields an estimate of the total effect of a doubleheader game which accounts 19 for fan substitution away from single games and towards the doubleheader game. Shown in the last column of Table 4, our estimate for the total effect suggests that doubleheaders increase attendance by approximately 11% relative to single games, controlling for fan substitution effects from single games occurring at most one day before or after doubleheaders. Lastly, notice this simple total effect estimate reduced the attendance impact of doubleheaders by 33 percentage points when compared to our standard fixed effect direct estimate.

Next, we allowed GP to include separate dummy variables for home single games that occur one day prior and two days prior to a doubleheader. Similarly, we allow GA to include separate dummy variables for single home games that occur one day after and two days after a doubleheader. Estimates for this specification are shown in column 3 of Table 3. Relative to column 2, the point-estimates for the dummy variables controlling for home single games one game prior and after a doubleheader as well as for doubleheader remain stable. Additionally, the estimates in column 3 suggest that fans may be substituting away from home single games and towards a home doubleheader as far as two days. However in either direction, the substitution effect is diminishing and the point-estimate for single games played two days prior to a doubleheader is statistically insignificant.

In calculating the total effect, we followed a similar procedure as aforementioned yet applied it to the all combinations involving the following quintuple: 2 single home games prior,

1 single home game prior, home doubleheader, 1 single home game after, and 2 single home games after. This resulted in 16 total sequences. The contribution of each sequence to the total effect of a doubleheader game continued to be the relative frequency of this quintuple occurring in the sample times the relevant sum of the regression point-estimates in column 3 of Table 3. 20

Summing over all 16 sequences yielded an estimated total effect of .035.13 This suggests that doubleheaders increase attendance by approximately 4% relative to single games, controlling for any fan substitution effects from single games occurring at most two days before or after a doubleheader. Thus, the total effect of doubleheaders on attendance is reduced by nearly 40 percentage points when compared to our standard fixed effects direct estimate.

Lastly, we allowed GP to include separate dummy variables for single home games that occur one day prior, two days prior and three days prior to a doubleheader. Similarly, we allow

GA to include separate dummy variables for single games that occur one day after, two days after and three days after a doubleheader. Estimates for this specification are shown in column 4 of Table 3.

To calculate the total effect, we identified all the combinations involving the following septuple: 3 home single game prior, 2 home single games prior, 1 single home game prior, doubleheader, 1 single home game after, 2 single home games after and 3 single home games after. This resulted in 64 total sequences. For a given sequence, the contribution to the total effect continued to be the relative frequency of that sequence occurring in the sample times the relevant sum of regression point-estimates in column 4 of Table 3. Summing over the sequences yields an estimated total effect of -.0114.14 This suggests that the direct increase in daily attendance effect from doubleheaders is completely offset by fan substitution effects.

V. Stability of the Regressions over Time.

Our full sample daily regressions with the appropriate controls, offer strong evidence for both a positive effect of doubleheaders on attendance on the day of the doubleheaders as well as

13 Results not shown but are available on request. 14 Again, results not shown but are available on request. 21 substantial negative substitution effects on attendance at single games surrounding doubleheaders. However, regression analysis over sub-periods of the full sample, demonstrate that the regression coefficients are not stable over the full period. Over time both the direct effects and the total effects of doubleheaders on attendance were declining. Table 5 reports the daily regressions over 3 sub-periods of the full sample: the first sub-period when doubleheaders were most frequent (1938-1956), a second sub-period when doubleheaders were less frequent

(1957-1980) and a third sub-period when doubleheaders were infrequent (1981-2009). For each of these sub-periods, we re-estimated models used in the full sample regressions allowing for substitution effects as far as 3 days before and after doubleheaders. 15

During the sub-period from 1938-1956, the regression coefficient on the doubleheader dummy in model 1, .465, is highly significant and indicates that doubleheaders increase attendance by almost 60% on the day of the doubleheader, if one estimates a model without any substitution effects. After controlling for substitution effects out to 3 games, however we find that the coefficient on the doubleheader variable drops to .397 indicating that doubleheaders increase attendance on the day of the doubleheader by approximately 48% and we find the total effect of doubleheaders is to increase attendance by only 15%. While this latter total effects is statistically significant it is dramatically smaller than the 60% total effect estimated in model 1 which includes no substitution effects. One weakness of our method of measuring the substitution effects is that it becomes too cumbersome to use when lags and leads are expanded beyond 4 or 5 days.

15 We have also estimated the total effects of doubleheaders allowing substitution effects as far as 4 days before and after the doubleheaders and found the results are very similar to the results allowing substitution effects of 3 days. We have found our method of estimating the total effects becomes too cumbersome for lags and leads exceeding 4 days. 22

Table 5: Investigating the Total Effect of a Doubleheader Game for Full and Select Samples Model & Parameter of Interest (1) (2) (3) (4) Full Sample DH Rich DH Decline DH Rare (1938-2009) (1938-1956) (1957-1980) (1981-2009) Model (1) Doubleheader 0.3652** 0.4650** 0.2616** 0.0699* {Standard FE: No Lags, No Leads} (0.0197) (0.0238) (0.0232) (0.0319)

Model (2) Total Effect 0.1046** 0.2258** 0.0497 -0.0159 {1 Day Prior, 1 Day After} (0.0296) (0.0466) (0.0422) (0.0599)

Total Effect 0.0350 0.1633** -0.0211 -0.0744 {2 Days Prior, 2 Days After} (0.0419) (0.0561) (0.0678) (0.0849)

Total Effect -0.0114 0.1408* -0.0555 -0.1027 {3 Days Prior, 3 Days After} (0.0495) (0.0575) (0.0786) (0.0990) Notes: Select regression results which are used in the total effect calculations are provide in Table A2. Robust standard errors in parentheses, clustered by home team. * Significant at 5%; ** significant at 1%.

For the second sub-period (1957-1980) when the use of doubleheaders were declining, the coefficient on the doubleheader dummy in model 1 is .262 which again is highly significant and indicates that doubleheaders during this sub-period increased attendance by approximately

30% on the day of the doubleheader ignoring all substitution effects. This is approximately half the impact of the doubleheader variable in the first sub-period. Furthermore, in this second sub- period the total effect of doubleheaders on attendance is insignificantly different from zero once the substitution effects are included.

Lastly during the last sub-period (1981-2009) when doubleheaders have been rare, the coefficient on the doubleheader dummy variable in model 1 falls to .07 indicating that doubleheaders increase attendance on the day of a doubleheader by only 7% ignoring substitution effects. Again for the most recent sub-period we find the total effect of 23 doubleheaders on attendance to be insignificantly different from zero once the substitution effects are considered.16

VI. Empirical Results for Annual MLB Attendance Data

As mentioned earlier Siegfried and Eisenberg (1980a) estimated the total effect of doubleheaders on annual minor league team attendance by regressing annual team attendance on the annual number of doubleheaders, the number of home dates and other controls. They find for the period 1973-1977 that the annual number of doubleheaders does not have a significant effect on annual minor league team attendance. We estimate a similar model using annual MLB data for various sub-periods of our full sample, 1920 to 2009:

(3) ln(total attendit,12 )  # Double it ,3  # Home Dates it ,4   Season Win % it ,   i t it ,

where total attendit, denotes the total attendance for team i in year t , # Doubleit, denotes the total number of single-priced doubleheaders for team i in year t , #Home Datesit, denotes the total number of home dates for team i in year t , Season Win%it, denotes the winning percentage for team i in year t , i is a team specific year invariant effect for team i , t is a year effect common to all teams, and it, is the remaining disturbance term capturing all remaining factors.

The estimates for model (3) are shown in Table 6 and indicate that the team season winning percentage has a positive and statistically significant effect on annual team attendance in all sub-samples of 1920-2009. The number of home dates also has a positive effect on annual

16 An abbreviated table of such regression point-estimates is available in the appendix, see Table A2. Comprehensive tables are available on request. 24

team attendance in all sub-samples, although in the post-1956 samples its effects are statistically

insignificant. Similar to Siegfried and Eisenberg’s (1980a, 1980b) finding for minor league

baseball, for all sub-periods in our annual sample we find no evidence that the number of

doubleheaders has a positive effect on annual attendance.

Table 6: Effect of the Number of Single Priced Doubleheaders on Total Season Attendance

Dep. Var: (1) (2) (3) (4) (5) (6) (7) ln (Total Attend) Sample 1920-2009 1938-2009 1920-1956 1920-1937 1938-1956 1957-1980 1981-2009

# Doubleheaders -0.0115 -0.0187** 0.0040 0.0182 -0.0045 -0.0346* -0.0303 (0.0065) (0.0068) (0.0081) (0.0098) (0.0098) (0.0136) (0.0197)

# Home Dates 0.0195** 0.0128* 0.0226** 0.0324** 0.0207** 0.0015 0.0020 (0.0063) (0.0057) (0.0067) (0.0091) (0.0062) (0.0143) (0.0082)

Season Win % 0.0250** 0.0236** 0.0260** 0.0304** 0.0226** 0.0290** 0.0233** (0.0020) (0.0022) (0.0022) (0.0029) (0.0034) (0.0024) (0.0021)

Year Dummies Y Y Y Y Y Y Y

Team Dummies Y Y Y Y Y Y Y

Observations 1,922 1,634 592 288 304 518 812

R-squared 0.878 0.832 0.876 0.856 0.887 0.745 0.689 Notes: Robust standard errors in parentheses, clustered by home team. * Significant at 5%; ** significant at 1%.

It is worth noting that in the annual regressions for the period from 1938-1956, the

doubleheader variable actually has a negative coefficient. Although this coefficient is not

statistically significant, in the daily regression over this period we found the doubleheader

variable to be small but positive and significant. One explanation for this difference is that the

annual regressions allow for the possibility that the substitution effects may extend beyond 3 or 4

days.

25

VII. Conclusion

Using MLB daily attendance data from 1938 to 2009 as well annual MLB data from 1920 to 2009 we find only weak evidence that doubleheaders ever had a positive effect on season attendance. While it is undoubtedly true that doubleheaders have increased attendance on the day of the doubleheaders this appears to have been mostly offset by reduced attendance at single games surrounding doubleheaders. If our analysis is correct that doubleheaders mainly redistribute annual attendance without substantially increasing total annual attendance, it appears that doubleheaders have at most a small marginal benefit. Given that there are positive marginal costs of holding doubleheaders (increased utilities, additional wear and tear on players and stadia) the widespread use of doubleheaders prior to 1970 is a mystery. We put forth the possibility that doubleheaders were a mistake.

26

Appendix

 Data

In estimating equation (1), we used a collection of individual regular season game logs sorted by home team from retrosheet.org.17 The following edits were made to the 1920 to 2009 sample. First, we dropped all attendance values which exceeded 100,000; as a result 4 observations were dropped. Next, we dropped all games played in the month of March; as a result 45 observations were dropped. Lastly, we dropped all triple header games; as a result 1 observation was dropped.

After these simple corrections, the data set contained 151,323 observations. From this total, there are 127,008 observations for single games, 12,158 observations for the first game associated with a doubleheader and 12,157 observations for the second game associated with a doubleheader. Conditional on attendance being positive, there are 115,249 observations for single games, 1,328 observations for the first game associated with a doubleheader and 9,905 observations for the second game associated with a doubleheader. Conditional on attendance being zero, there are 0 observations for single games, 8,467 observations for the first game associated with a doubleheader and 0 observations for the second game associated with a doubleheader. Conditional on attendance being missing, there are 11,759 observations for single games, 2,363 observations for the first game associated with a doubleheader and 2,252 observations for the second game associated with a doubleheader.

As mentioned in the data section, the way in which attendance was recorded can be categorized into the aforementioned three groups. However, there are a number of exceptions. Table A1 outlines and accounts for all the ways the attendance figures associated with doubleheader games were recorded in the Retrosheet game logs. Most observations for doubleheader games appear in pairs where the first observation corresponds to all outcomes during the first game and the second observation corresponds to all outcomes during the second game.18 In Table A1, such observations are referred to as paired observations. For example, there are 8,459 observations where attendance equals 0 for the first game and equals some positive value for the second game of a doubleheader. The few remaining doubleheader games do not appear in pairs and represent either just the first game with no corresponding second game

17 The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at www.retrosheet.org. 18 Approximately 64 doubleheader games were recorded in pairs but the second game associated with a doubleheader came first followed by the first game. These observations were rearranged manually. 27 or just the second game with no corresponding first game. These games are called non-paired observations in Table A1.

For most of the data, the total attendance associated with a doubleheader game is recorded by the second game. This would include the following:

 8,459 observations where attendance equals 0 for the first game and equals some positive value for the second game.

 537 observations (out of 1,195) where attendance for the first game is positive and equals the attendance for the second game. We assumed that such observations redundantly entered the total attendance of a single-priced doubleheader; as such, these games remained as doubleheaders.

 248 observations where attendance equals missing for the first game and equals some positive value for the second game.

However before dropping the first games associated with these observations we re-coded the start time – the night game dummy variable – so the second game matched the start time of the first game. This start-time correction imposed 651 real changes (20 of which set equal to missing) for the 8,459 observations where attendance equals 0 for the first game and equals some positive value for the second game. It imposed 22 real changes for the 537 observations (out of 1,195) where attendance for the first game is positive and equals the attendance for the second game. Lastly, it imposed 5 real changes (1 equal to missing) for the 248 observations where attendance equals missing for the first game and equals some positive value for the second game. After these changes, the observations corresponding to the first games of a doubleheader were dropped. Thus, 8,459 observations were deleted from the first sub-sample, 537 from the second and 248 from the third.

For a portion of the remaining observations, we have the following sub-samples:

 130 observations where attendance for the first game is positive and the attendance for the second game is missing. Such observations were re-coded as a second game of a doubleheader.

 6 observations for the split-stadium doubleheader games between the New York Yankees and New York Mets in 2000, 2003 and 2008. Press releases from MLB.com suggested that these were all separate-priced doubleheader games. Thus, these observations were re-coded as single games. 28

For the last remaining sub-samples, we have the following:

 658 observations (out of 1,195) where attendance for the first game is positive, the attendance for the second game is positive, and both values were not equal. We assumed such observations represented a doubleheader game where fans were charged separate admissions for each game; as such, these games were re-coded as single games. Thus, 658 real changes were made.

 1 observation where attendance for the first game is zero and there are no recorded second games associated with these particular doubleheaders. These observations were dropped; thus, 1 real change was made.

 7 observations where attendance for the first game was zero and the attendance for the second game was missing. These observations were dropped; thus, 7 real changes were made.

 2,115 observations where attendance for both the first and second game was missing. These observations were dropped; thus, 2,115 real changes were made.

In this newly constructed data set, there are a total of 137,704 observations. Of this total, there are 128,330 observations for single games and 9,374 observations for doubleheader games. The gain of 1,322 observations for single games is accounted for by the changes made to the 658 observations (out of 1,195) where attendance for the first game is positive, the attendance for the second game is positive, and both values were not equal. Recall, these observations were re- coded as single games and thus would represent a net-gain of 2 658 observations. In addition, the 6 split-stadium games between the New York teams were re-coded as single games.

To account for the loss of 2,783 doubleheaders, recall our initial sample contained 151,323 observations, 12,157 of which were for the second game associated with a doubleheader. Of this 12,157 total, 9,905 corresponded to the second game of a doubleheader conditional on attendance being positive. Also, we had 0 observations for the second game associated with a doubleheader conditional on attendance being zero and 2,252 observations where attendance was missing. Further, after all the changes, the attendance levels associated with the second game of a doubleheader are always positive. This creates the loss of 2,783 observations, 2,252 of which are explained by the loss associated with no longer having missing attendance figures for the second game of a doubleheader. The remaining 531 can be explained by the loss of 658 observations, the gain of 130 observations and the loss of 3 observations. The loss of 658 comes from the observations where attendance for the first game was positive, the attendance for the second game was positive, and both values were not equal. Recall these were re-coded as single games. The gain of 130 comes from the 130 observations where attendance for the first game 29 was positive and the attendance for the second game was missing. Recall these observations were re-coded as second games of a doubleheader. Lastly, the loss of 3 comes from the second games of the split-stadium doubleheader games between the New York Yankees and New York Mets. Recall, these observations were re-coded as regular games.

For the regression analysis, we restricted the data from 1938 to 2009 due to the high frequency of missing observations on attendance from 1920 to 1937. Specifically from 1920 until 1937, the smallest proportion of missing values on attendance was about 35% (1924) and the largest was 77% (1934). Thus, dropping all observations prior to 1938 resulted in a loss of 17,381 observations. As a result, the total number of observations declined from 137,704 to 120,323.

For the sample sizes in our regression results, the reported total of 119,174 observations in the basic regression of log attendance on Doubleheader is explained by subtracting the 1,149 missing observations on attendance from 120,323. For all remaining models, the reported total of 118,477 observations is explained by subtracting the 728 missing observations on the dummy variable for night games from 119,174 and then adding the 31 observations where night games and attendance are both missing in order to avoid double-counting.

Table A1: How the Retrosheet data record Attendance and Doubleheader Games (Data 1920 – 2009)

First Game Attendance Second Game Attendance Number of Observations

I. Paired Observations

1st Game = 0 2nd Game > 0 8,459 1st Game > 0 2nd Game > 0 1,195 1st Game > 0 2nd Game = 0 0 1st Game = 0 2nd Game = 0 0

1st Game = missing 2nd Game > 0 248 1st Game > 0 2nd Game = missing 130 1st Game = missing 2nd Game = missing 2,115

1st Game = 0 2nd Game = missing 7 1st Game = missing 2nd Game = 0 0

II. Non-paired Observations

Solo 2nd Game > 0 3 Solo 2nd Game = 0 0 Solo 2nd Game = missing 0 30

Solo 1st Game > 0 3 Solo 1st Game = 0 1 Solo 1st Game = missing 0

 Select Regression Estimates

Table A2 provides a select list of regression estimates used to estimate the total effect of a doubleheader. The total effect estimates are shown in Table 5.

Table A2: Select Regression Estimates for Various Sub-samples (1) (2) (3) (4) (5) (6) DH Rich Sample (1938-1956) FE 1P, 1A 2P, 2A 3P, 3A 4P,4A 5P, 5A Doubleheader 0.4650** 0.4146** 0.4022** 0.3974** 0.3962** 0.3938** (0.0238) (0.0273) (0.0287) (0.0288) (0.0295) (0.0295) 1 Day Prior -0.1853** -0.1853** -0.1853** -0.1851** -0.1848** (0.0216) (0.0220) (0.0219) (0.0218) (0.0218) 1 Day After -0.1792** -0.1771** -0.1770** -0.1766** -0.1765** (0.0359) (0.0358) (0.0354) (0.0351) (0.0351) 2 Days Prior -0.0488* -0.0490* -0.0486* -0.0472* (0.0203) (0.0203) (0.0202) (0.0202) 2 Days After -0.0904** -0.0884** -0.0878** -0.0850** (0.0241) (0.0236) (0.0234) (0.0237) 3 Days Prior -0.0276 -0.0269 -0.0255 (0.0272) (0.0274) (0.0276) 3 Days After -0.0456* -0.0442* -0.0416 (0.0203) (0.0196) (0.0200) 4 Days Prior -0.0095 -0.0083 (0.0241) (0.0239) 4 Days After -0.0210 -0.0182 (0.0281) (0.0279) 5 Days Prior -0.0406 (0.0224) 5 Days After -0.0538* (0.0223)

DH Decline Sample (1957-1980) Doubleheader 0.2616** 0.2390** 0.2298** 0.2262** 0.2246** 0.2259** (0.0232) (0.0239) (0.0258) (0.0264) (0.0266) (0.0266) 1 Day Prior -0.1557** -0.1567** -0.1576** -0.1575** -0.1577** (0.0260) (0.0269) (0.0272) (0.0272) (0.0271) 1 Day After -0.1500** -0.1529** -0.1535** -0.1535** -0.1536** (0.0216) (0.0218) (0.0220) (0.0219) (0.0219) 2 Days Prior -0.0296 -0.0309 -0.0310 -0.0315 (0.0388) (0.0390) (0.0390) (0.0389) 2 Days After -0.1041** -0.1051** -0.1053** -0.1052** 31

(0.0205) (0.0207) (0.0208) (0.0207) 3 Days Prior -0.0519* -0.0518* -0.0524* (0.0243) (0.0243) (0.0241) 3 Days After -0.0432 -0.0433 -0.0424 (0.0226) (0.0226) (0.0226) 4 Days Prior -0.0392 -0.0394 (0.0257) (0.0256) 4 Days After -0.0184 -0.0178 (0.0236) (0.0235) 5 Days Prior 0.0578* (0.0249) 5 Days After 0.0029 (0.0187)

DH Rare Sample (1981-2009) Doubleheader 0.0699* 0.0672* 0.0653 0.0644 0.0638 0.0635 (0.0319) (0.0326) (0.0331) (0.0334) (0.0336) (0.0338) 1 Day Prior -0.0897* -0.0888* -0.0885* -0.0881* -0.0875* (0.0418) (0.0413) (0.0412) (0.0409) (0.0405) 1 Day After -0.0540* -0.0531* -0.0530* -0.0523* -0.0522* (0.0226) (0.0221) (0.0220) (0.0216) (0.0215) 2 Days Prior -0.0675 -0.0658 -0.0654 -0.0655 (0.0445) (0.0434) (0.0432) (0.0432) 2 Days After -0.0571 -0.0562 -0.0562 -0.0558 (0.0305) (0.0300) (0.0299) (0.0297) 3 Days Prior -0.0648 -0.0631 -0.0619 (0.0425) (0.0414) (0.0409) 3 Days After -0.0298 -0.0287 -0.0288 (0.0248) (0.0245) (0.0243) 4 Days Prior -0.0507 -0.0497 (0.0505) (0.0502) 4 Days After -0.0347 -0.0346 (0.0224) (0.0222) 5 Days Prior -0.0734 (0.0504) 5 Days After -0.0035 (0.0311) Notes: All regressions include dummy variables for game characteristics – night game, opening day and holiday game dummy variables – as well as dummy variables for the day of week, month of year, team and year. Robust standard errors in parentheses, clustered by home team. * Significant at 5%; ** significant at 1%.

32

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