Applied multi-level model on panel data in MLB promotion marketing

The answer is likely to be bobblehead giveaways.

Since 1999, promotional departments of MLB teams have been using these little men to squeeze extra attendance as fans love it.

However, there’re so many factors, both on the field and off, affecting an individual’s decision whether or not to have an MLB game.

In addition to promotions, fans also consider the timing, weather, the winning percentage of the games, and whether or not the game is a marquee game [1].

Therefore, sometimes baseball marketers fail to understand the true effect of the bobblehead promotion on attendance.

Our analysis aims to answer one central question: offering bobblehead giveaways can increase how much sales, by how much amount and how this result varies among MLB teams.

Understanding this can help us to make a sophisticated recommendation for promotional baseball department when it comes to bobblehead promotion.

Our report contains the following parts:II — Data CharacteristicsIII — Model Selection & InterpretationIV — Recommendation & ConclusionV — AppendixII — Data CharacteristicsThe dataset provides attendance information for all MLB teams for 2012 season.

Each row illustrates attributes of one game, which can be divided into 4 buckets: Time (Month, Date, Day of Week, Day/Night), Weather (Temperature, Sky), teams (home_team, opponent) and promotion (Cap, Shirt, Fireworks, Bobblehead).

All of these variables can have more or less effect on the attendance of the game.

Table 1: Dependent and Independent variables of the datasetWhat we really care about is the effect of bobblehead on attendance.

We want to know how offering bobblehead affected the attendance and whether the effect varied by teams or by the time when it was offered, other conditions remain equal.

This is the panel data, which includes both cross-sectional and time series data.

In this case, the dataset provides observations of bobblehead promotion at different times of the season and across different teams.

Therefore, the effect of bobblehead might vary not only by time but also among teams.

Let’s confirm it through our visualization.

You can understand more about panel data here.

a) Home_team on attendanceFigure 1: Avg.

attendance varies among MLB teamsThere’re rich teams and not-so-rich teams in MLB.

There’s a difference between the popularity between the big-market teams like New York Yankees, LA Dodgers, Philadelphia Phillies, San Francisco Giant,… and the small-market teams like Tampa Bay Ray’s, Oakland Athletics, Seattle Mariners,… Those big-market teams usually have higher revenues, more budget, more star-players, thus attracting more attendance than small-market teams.

In this market, the brand name was a crucial factor in determining the amount of attendance of each game.

“The problem we’re trying to solve is that there are rich teams and there are poor teams.

Then there’s fifty feet of crap, and then there’s us.

It’s an unfair game.

”— Billy Beane, General Manager of Oakland A, 2002.

b) Bobblehead on attendanceFrom Figure 2 we observe that:● Some teams had a clear difference in term of attendance between the game with bobblehead and game without bobblehead such as San Francisco Giant, Philadelphia Phillies.

● Some teams didn’t experience clear effect or didn’t have enough data to have a clear effect such as Boston Red Sox, San Diego Padres, Colorado Rockie, Minnesota Twins.

● The majority of teams saw an increase in the attendance: Houston Astro, Seattle Marine, Cincinnati Reds, Toronto Blue Jay etc.

Figure 2: Attendance difference between games with bobbleheads and without bobblehead / The number of games with and without bobbleheads among teams.

However, was the increase the consequence of the bobblehead promotion? Not really.

From the following figure, you can see that a significant portion of bobblehead was offered on Saturday and Sunday, which were usually the most crowded days of the week.

It’s possible that people will go to the games because on the weekend even without the bobblehead.

So we’re motivated to determine the true increase in attendance as the consequence of bobblehead.

Also, was there any difference in term of an increase in attendance by bobblehead in weekdays and weekend?Figure 3: Bobblehead offering and attendance by days of weekc) Other type of promotions on attendanceShirt, cap, firework (on the same graph): figure 4 shows that promotion of cap and shirt had slightly effect on the attendance.

Fireworks seemed to have the biggest effect on attendance among these three.

On average, games that have fireworks had 34,400 attendance while games without fireworks only attracted 30,600 fans.

Figure 4: Variation in attendance by Cap, Shirt and Fireworksd) Seasonal effectExcept for some teams (Boston Red Sox, San Francisco Giant, Philadelphia Phillies, Milwaukee Brewers, St.

Louis Cardinal) where the attendance was stable across months, other teams seemed to have some seasonal effect with the highest attendance on June and July and going down in April, August, and September.

e) Weather (temperature, sky) on attendanceFrom the graph above, we don’t see a clear relationship between temperature and game attendance.

Also, sky condition seemed to be a significant factor.

Fans tend to go to the ballparks on the days when there was a cloudy or clear sky.

They don’t want to go out on rainy days or when there was dome.

f) InferenceThis visualization provides us the hint on what should be included in our model as the independent variables.

For most of the variables, we see a correlation between them and attendance.

Therefore, we will incorporate home_team, month, weekday, weather (except temperature) in our modeling step.

III — Model SelectionAggregationAn aggregation approach helps us find out the average effect of bobblehead on attendance across team and time.

Using the linear regression model, we examine the relationship between whether a bobblehead promotion was offered in a game and the attendance for that game.

We have the coefficient of bobblehead is 4494, meaning that offering bobblehead would increase the attendance of a baseball game by 4494, on average.

The problem of the aggregation approach is that it fails to demonstrate the heterogeneity between MLB teams regarding the impact of bobblehead promotion.

In the next sections, we will use 2 other approaches that help us identify this variation.


GroupingThere are 2 central questions of grouping approach:● Was the timing of bobblehead promotion an important factor?.As mentioned above, a significant portion of bobblehead was offered on the weekend.

Was there any difference in effect on attendance if the bobblehead is offered on the weekday?● Was the size of the city an important factor?.We all know that MLB attendance varied by cities since each city has a different living standard, fan base and the number of substitutes.

All these heterogeneities will affect the way bobblehead impacts attendance.

To simplify, we only based on city population as the first heterogeneity factor since it indicates how big fan base is.

To answer the first question, we split our dataset into 2 groups: games that happen on weekdays and games that happen on the weekend.

After that, we apply linear regression for each subset of the data.

The results show that there was a difference between the effect of bobblehead offered on weekend and the effect of bobblehead offered on the weekday.

On average, bobblehead on weekday lifted game attendance by 6,628 (24.

7% on average) while bobblehead on weekend increased 2,938 attendance only (8.

9% on average).

This can be explained by the fact that on weekend, many fans go to watch baseball no matter whether there are bobblehead giveaways; while on weekdays, they need more incentive to attend the game.

Regarding the second question, we acquired a new dataset about city population and based on that, we split the dataset into 2 groups: 1 group with the home team comes from small city (meaning that the population is less than 1 million) and the other group comes from big city (meaning that the population is bigger than 1 million).

There are 9 teams basing in big cities and 21 teams in small cities.

Again, linear regression result shows that there was a difference between the effect of bobblehead for teams from the big city and the effect of bobblehead for teams from small cities.

On average, bobblehead in the big city increases attendance by 7,638 (24.

2%), while bobblehead in the small city increases attendance by 2,485 only (8.


Though differing in town population, the average attendance might not vary that much between the teams when there is no bobblehead (31.

5K vs 29.

2K on average).

When bobblehead is offered, attendance in big cities was improved much more significant than in small cities.

It might be the case that big cities have a bigger fan base and there are more incremental fans attracted to the bobblehead giveaway than in small cities.

Using the grouping approach give us more insights about the diversity in baseball when it comes to bobblehead promotion.

However, there’s still some level of aggregation in this approach, which might clear out helpful information that we can offer to baseball marketers.

We want to find an approach that can demonstrate the heterogeneity at the team level, and multi-level model is our next attempt.


Multi-level modelWhile the aggregate model provides a fixed intercept and fixed slope of bobblehead across all games in the season, the multi-level model[2] assume that the effect will vary across teams, as we treat it as the first level in this case.

There is still a fixed effect of slope and intercept, which are 3997 and 32004, respectively.

This can be interpreted that there’s an average increase of 3997 in game attendance by teams.

(Note that this fixed slope is slightly different from the slope in aggregate approach (4494) because the slope in aggregate approach is the average increase by games).

The varying slopes and intercepts as the result of the multi-level model are shown via the following graph.

Here, the random effect of intercept demonstrates the different level of attendance among MLB teams.

Also, the random effects of bobblehead are the deviation of each team from the fixed effect.

Therefore, we can come up with the final average effect for each team by adding the fixed effect to the random effects.

Here is our final result:Figure 8: The verying final average effects of bobblehead on MLT teams● LA Dodgers enjoyed the biggest positive effect of bobblehead on attendance (on average offering bobblehead increased an additional 13,766 attendance), followed by Toronto Blue Jay (~8,838), and Atlanta Braves (6,678).

● On the other hand, San Francisco Giants was the only team to bear the negative effect of bobblehead on attendance (on average, offering bobblehead decrease 1023 attendance to their games).

Also, Chicago White Sox, Washington Nationals, New York Mets and Chicago Cubs were the teams that see a slight increase in ticket sold with a bobblehead giveaway.

● 13/30 teams such as San Diego Padres, Colorado Rockies, Minnesota Twins, Boston Red Sox, Detroit Tigers didn’t see a clear effect of a bobblehead (with the random effect ~ 0) because we don’t have enough observation with bobblehead (the minimum is 3 observations) from these teams.

● The random effects in intercepts simply illustrate the discrepancy in the average level of attendance for each team.

IV — Recommendation & ConclusionBobblehead promotion was proved to be effective in increasing baseball attendance.

Promotional department of MLB teams can expect to increase the attendance by an average of 4428 per game.

However, since there is a huge heterogeneity between teams due to many factors, this effect of bobblehead also varied all the way from about 13,700 down to a negative number among teams.

Los Angeles Dodgers was the team seeing the biggest impact of bobblehead while San Francisco Giant slightly suffered from the promotion.

The analysis also gives us some insights about when and where a bobblehead giveaway campaign should be implemented.

While the majority of games that have bobblehead were on the weekend, our analysis shows that the impact of bobblehead on the weekend was inferior to on a weekday.

Bobblehead on weekend increased the attendance by 8.

9% while the number for a weekday was 24.


Also, teams in big cities should strongly consider offering bobblehead promotion more than teams from small cities because they have a much bigger fan base and therefore they can attract more fan to go to the ballparks with the bobblehead.

For further research, we suggest that a bigger data sample with more observation of bobblehead promotion implemented should be used to have a more significant result.

In the above analysis, there 13/30 teams we cannot infer the final effect of bobblehead since we only have 0–2 observations with bobblehead offered for each team.

We suggest that at least 3 observations should be gathered.

Reference:1, The Effects of Promotions on Attendance at Major League Baseball Games, Amanda Schoenrock, 20092, Understand Panel Data Regression, Madhav Mishra3, Simple explanation of Multi-level modelAbout the author: I am an MBA student at the University of California, Davis.

I have a passion for Marketing Analytics, Modeling, Machine Learning, and Data Science.

This article belongs to my independent study under my MBA program.

A big thank to my classmate, Jamie Ho for his contribution to this project.

If you have any comment, feedback or questions, feel free to reach me at mapnguyen@ucdavis.

edu or connect me on LinkedIn.

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