Wednesday, August 1, 2018

Does the San Diego Padres' Five-Win promo pass the test?

TLDR: While there are umpteen-million gimmicks and promotions offered to get consumers out to the ball park, the San Diego Padres recently came up with a new one: the Five-Win Pass where fans get tickets to every Padres game until the fan sees five wins.

How many games might a fan expect to see with a Five-Win Pass? What does a fan stand to gain from a Five-Win Pass? And is the Five-Win Pass even worth it? 

In one word: Probably*

There are umpteen-million gimmicks and promotions offered to get consumers out to the ball park; some good, some bad, some just plain weird (see free compostfree thongs, and the time one "lucky" fan won a funeral package). Despite a seemingly never-ending supply of ideas, it appears the San Diego Padres recently came up with a brand new promotion that deserves attention: the Five-Win Pass.

The Padres announced that starting 27 July 2018, for $99, fans could purchase a Five-Win Pass that guarantees them entrance to every Padres home game until the fan sees five wins (or 30 September, whichever comes first). With the 42-63 Padres all-but-out of playoff contention (essentially a 0% chance), the team appears to have switched its focus to maximizing home-game revenue, even if that means encouraging their fans to potentially cheer against their own players.

Regardless of how you feel about this approach, the obvious economic question (and you are reading a sports economics blog) for fans now becomes, 'Is the promotion worth $99?'

To answer that question, we must first answer, 'How many home games will it take for the Padres to win their fifth game?' With a rather elegant formula (see below: I saved the best for last), we can find the expected number of games it will require for a team with a .400 win percentage to get the fifth and final win. Below is a graphical depiction of the cumulative probability (in classic San Diego Padre colours).

What we see is that at about the same probability as a coin flip, it will take at least 12 games for the Padres to reach their fifth win, which is not exactly World-Series-contending baseball. Note that while the probability of five wins in less than five games is exactly zero, the probability of the Padres winning five of their remaining 30 home games this season is less than 100%! (This is a consequence of probability: although it does get pretty (imperceptibly) close to 100%).

The second question we must answer is, 'What does one gain by purchasing the Five-Win Pass?' To answer this I have to assume that each individual is trying to maximize the number of baseball games they attend, and that attending a game resulting in a loss is as desirable as attending a game resulting in a win. I also assume, albeit haphazardly, that the probability the Padres win any game is exactly equal to their .400 win percentage.

With the assumptions above in mind, I calculate the expected savings per game by purchasing the Five-Win Pass. Since the seats promised to Five-Win Pass holders regularly sell for approximately $18.50, we can calculate the savings by multiplying $18.50 by the number of games the promo lasts for and subtracting out the original cost of $99. However, this would assume that the Five-Win Pass holder attends all the games, including a 10-game home stand on consecutive days. If we look at behaviour of season-ticket holders, we know that season-ticket holders usually do not attend all 81 home games a season.

Below is a graph of the possible per game savings the Five-Win Pass could offer. It depends on, (a) how quickly the fan see the Padres reach their fifth win, and; (b) how many games a Five-Win Pass holder intends to attend. The shaded area marks the bounds of the maximum and minimum savings, while the thick line within the range marks the probability-weighted expected savings.

Moral of the story: the more games you attend, the more you will save per game. It is interesting that there exists an area where individuals would be strictly better off by purchasing individual tickets than the Five-Win Pass, but there is no area where fans would be strictly better off by purchasing the Five-Win Pass rather than individual tickets. Instead, if Five-Win Pass holders attend ~50% of games, they will only be somewhat more likely better off purchasing the Five-Win Pass.

Furthermore, there exists many bizarre scenarios wherein a Five-Win Pass holder misses a few losses and, not being able to realize the full value of their Five-Win Pass, become 'disappointed' while watching Padres win. I can only imagine an entire section of the stadium booing a walk-off home run!

So, is the Five-Win Pass worth the $99 price tag? In one word: Probably*

* If (a) the probability the team wins any one game is constant, (b) you value a home loss the same as a home win, and; (c) at the very least, attend more games than not.

Stay tuned for the next edition of Sport and Economics (in that order) as I will attempt to answer the question, 'Was the Five-Day Pass worth it for the Padres?' and I will look to quantify the potential success of the promotion.

PS. Here is the formula to calculate the probability the Padres (or any team for that matter) achieves their fifth win in i games (i ≥ 5):

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