Monday, May 1, 2017

The unrealised potential of bobbleheads, 2017 edition

TLDR: "the MLB could have sold an additional 95,000 tickets in 2016 and [...] the value of the tickets would be at least $3 million."

"In summary, [...] the MLB could have sold an additional 113,000 tickets for the 2017 season worth an estimated $4 million."

In a previous post, I asserted that Major League Baseball (MLB) could gain from efficiently offering promotional giveaways at select games. I had built a simple model and predicted that the 30 teams of the MLB could have sold an additional 95,000 tickets in 2016 and suggested that the value of the tickets would be at least $3 million.

Now, I want to extend the analysis to the current season to again see how the MLB may benefit from selecting which games to feature a promo. I begin by taking the following steps:
  1. Scraping each team's website for information on their 2017 promotional schedule.
  2. Parsing through the text to identify the dates with promos such as (not exhaustive):
    • replica World Series rings,
    • collectible coins,
    • collectible pins, and, everybody's favourite;
    • bobbleheads.
  3. Merging these promo dates with the 2017 MLB regular season schedule.
  4. Predicting attendance with and without promotions.
  5. Choosing the best candidates for promo games and comparing against the actual promo games.
After collecting and combining each team's promo schedule, I parsed the text for "major promotions" which I defined as having a re-sale value of approximately $10 or more. In total I identified 231 promos for the 2017 MLB season, which is "in the ballpark" of the 232 promos I used with the 2016 data.

I want to make use of the same model for predicted attendance that I developed with the 2016 MLB regular season. I limit the data to the name of the opponents and the date of each match to pick the best promo game dates. This is to imitate the same information a baseball club has when they organize and release their promotional schedule - often months before the game! Thus, using the 2016 attendance data, I run the following model and predict the attendance in 2017:

ln(attendance) = f(promo, opening day, opponent skill, division, interleague, day of week, month, home team fixed effects)

where opening day indicates the game was played on the season's opening day, opponent skill is the number of predicted wins for the opponent from Baseball Prospectus as of February, 2017. Division and interleague are indicators the game was between teams of the same division and different leagues, respectively. The day of week, month, and home team fixed effects are sets of dummies indicating the day, month and home team.

I take the model described above and predict the attendance of each 2017 MLB game with and without a promo. When choosing the best candidates for a promo game, my objective function is to maximize profit. Due to the concept of dynamic ticket pricing, profit maximization means that each MLB club will increase the price of tickets for a particular game as the demand for the game increases. Here is a great explanation of dynamic ticket pricing (check out the example). I am looking for games that are predicted to have relatively high attendance (compared to other games in the same stadium) and yet are also predicted to have enough tickets available if a promotional giveaway is scheduled. I balanced the two effects as follows:

Ranki,t = (xnp,i,t - µnp,t) / (snp,t) + (deltap,i,t - µp,t) / (sp,t)

where xnp,i,t is the predicted attendance of game i and team t if the game does NOT feature a promo (maxed at stadium capacity), µnp,t is the mean predicted non-promo attendance of team t and snp,t is the standard deviation. Similarly, deltap,i,t represents the predicted increase attendance of game i and team t if the game DOES feature a promo (still maxed at stadium capacity). In other words, deltap,i,t is the predicted promo attendance minus the predicted non-promo attendance: µp,t and sp,t are the mean and standard deviation of this difference. respectively.

After having the model choose the best games, I calculate the number of additional tickets sold for the season for each team. As a crude measure, I use the Forbes Business of Baseball Valuation Lists for the average ticket price of each team to calculate the foregone revenue of each team which I have plotted below:

I have added a 95% confidence interval around the average estimated foregone revenue. This was calculated by randomly redrawing the coefficient values for the regression and re-predicting the effect of a promo. Note that the confidence interval is not necessarily symmetrical due to the fact that I bound the predicted attendance to be no greater than capacity. Additionally, some of the intervals are not shown because they are too narrow.

The St. Louis Cardinals appear at the top of the list of losers, a trend we saw in the 2016 version of the analysis. The $1.4 million foregone revenue is a consequence of two effects: (a) the Cardinals offer the most promotional giveaways in a season of all 30 MLB teams at 22, and; (b) the model reassigns nearly 75% of the promo games.

On the other extreme, the San Francisco Giants consistently have sellout crowds at their park and average an attendance that is greater than their capacity (thanks to standing room only tickets). The model never suggests altering their promo schedule, although some economists may suggest canceling their promo schedule and/or raising ticket prices in general.

In summary, I demonstrated that the MLB could have sold an additional 113,000 tickets for the 2017 season worth an estimated $4 million. Using the lower bound value from the simulation, the minimum foregone revenue of the MLB is in the range of 2.3 million.

The full table of results is below. Columns B and C are the mean estimates from the simulation described above which explains why there is an average of 170.4 reassigned promos. Feel free to offer any questions or comments.

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