Playoff Tickets Options Pricing

April 8, 2008 12:13 PM

SportsMathFilter: How do I correctly price playoff ticket options?

I buy 1/4 of a the season tickets from a season ticket holder for a NBA team in Los Angeles. That team is not the Lakers (don't laugh). For the 2008-2009 season, I want to buy an option on playoff tickets. How would I correctly determine a fair price for these options?

I imagine I would take into account the likelihood of them going to the playoffs but have no idea what other variables I would consider or the formula would look like.

I do know the formula will be different depending on how many games and which rounds of the playoffs, so feel free to assume either (1) all home games for the first round or (2) all home games through to the finals.

I am lousy at math, so if you provide a very complex formula, I would greatly appreciate an English explanation alongside explaining the logic.

posted by charlesv to Sports, Hobbies, & Recreation (11 answers total)

How does this option work? Is it nonrefundable? If you buy the option, and the team doesn't make the playoffs, do you get your money back?
posted by Dec One at 12:23 PM on April 8, 2008

What is the strike price, i.e. at what price does the option give you the right to buy the playoff tickets? What would you estimate the market price of the tickets would be if the team does make it to round n of the playoffs? What would you estimate are the chances of the team making it to round n of the playoffs?
posted by ssg at 1:01 PM on April 8, 2008

More details are needed here on how the option works.

I'm taking this as you pay money up front, so that if the team makes the playoffs, you can then purchase tickets for more money on top of purchasing the options. Is this correct? And how will it be determined which games you get to choose?
posted by gauchodaspampas at 1:05 PM on April 8, 2008

Without any more detailed information about how the options work, here is a simple formula you can use. Let p be the probability that the team makes it to the playoffs and plays that game (10% chance is .1, 50% chance is .5) and v be the value of the option if the team makes the playoffs (ie, how much you would save using the option to get a ticket rather than a scalper).

The price you should pay in order to break even is just p times v. So, if the option for game one of the finals will be worth $400 if they play it, and your team has a 10% chance of making it to the playoffs, you shouldn't pay any more than $40 for the option. Think of it like gambling, if you bet $100 on black and 50% of the time it pays you $200, you're expected to break even (which is why Vegas has green numbers so that there is less than a 50% chance of hitting black).
posted by burnmp3s at 1:20 PM on April 8, 2008

Response by poster: Dec One:
The money would be nonrefundable.

ssg:
Assume the tickets would be $95 each to the season ticket holder but say $250 each on the open market. The option would give me the right to buy them at $95. I do not know the chances of the team making it to the playoffs, and don't even know how to calculate that.

gauchodaspampas:
Correct. I pay the money up front in exchange for the rights to purchase the tickets for more money on top of the options. As for which games, let's assume that for each round it will be half of the home games. Which games exactly determined at random by picking numbers out of a hat.
posted by charlesv at 1:23 PM on April 8, 2008

You need to be able to estimate the chance that the team will make it to the nth round of the playoffs in order to calculate a value for the options (as burnmp3s does). Clearly, options for the best team in the league should be worth more than those for the worst team in the league, so you need some estimate of probability to value the options. I know nothing about basketball, so I can't help you there.

Also, you might want to consider the value of the options to you, instead of just on the open market. Would you pay the $250 market price for playoff tickets? If you wouldn't, then you need to decide on a price you would pay in order to calculate the value of the option to you.
posted by ssg at 2:03 PM on April 8, 2008

Are you sure you understand the rules correctly? I ask because this sounds like an illegal game of chance. You pay money up front; if the team wins enough to get into the playoffs, you get something tangible (the ability to purchase tickets at below-market prices); if the team doesn't do as well, you lose the money you put up? That's gambling, and usually not allowed in the U.S.
posted by Dec One at 2:09 PM on April 8, 2008

Best answer: I would price this as a series of 16 cash-or-nothing binary (or digital) call options (there's a maximum of 16 home games in the NBA playoffs), but I'll use some simplifying assumptions here.

Suppose the non-Lakers team does make the playoffs and the season-ticket holder buys the playoff tickets. He can then sell these for a price in the future, presumably above the face-value that he paid for them. We'll call this (Market - Face).

For purposes of making this easier, in each playoff game the non-Lakers team plays they have a 50% probability of winning (and, consequently, they also have a 50% probability of making it to the next round of the playoffs). So the probabilities associated with the number of games in a 7 game series are
4: 12.5% (2 home games)
5: 25% (2.5 home games)
6: 31.25% (3 home games)
7: 31.25% (3.5 home games)
The expected number of home games is 2.90625

So a simple estimate of the value of holding a strip of playoff tickets, if they make the playoffs, is:
(1st Rd Market Price - Face)*2.90625 games +
.5*(2nd Rd Mkt Price - Face)*2.90625 +
.5*.5*(Conference Finals Mkt Price - Face)*2.90625 +
.5*.5*.5*(NBA finals Mkt Price - Face)*2.90625

Call this whole mess "Z"

And, of course, you need an estimate of the probability they actually do make the playoffs. Call this "p".
The 2009 NBA playoffs are around 1 year away, so if you were to price this option today you would want discount it at the 1 year risk free rate (it's abnormally low right now - around 1.75%).

So I'd call it:
option value = p*Z/(1.0175)
posted by milkrate at 2:13 PM on April 8, 2008 [2 favorites]

Response by poster: Thanks, milkrate & burnmp3s. That is what I was looking for.

Now, as far as my team's chance of making it to the playoffs in 2009...I'd rather not think about it. I wish they hadn't traded Sam Cassell.
posted by charlesv at 3:49 PM on April 8, 2008

Note that there's a number of moving parts that I glossed over with the 50% assumption, but taking them into account will make it a much richer, more interesting problem. Like if you think a team has a 75% chance of winning a single game, it means they have a 92% chance of winning the series and the expected number of home games in a 7 game series drops to about 2.6.

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posted by milkrate at 4:39 PM on April 8, 2008

I remember reading about a place on the web that does something like this. I think it was called ticket reserve or something like that, but if you can find it, they may have some options on Lakers tickets, which you could maybe use as a guide.
posted by Todd Lokken at 7:42 PM on April 9, 2008