If Pittsburgh Were in Game 7 of the World Series Would You Pay \$400 Million to Be There?

Last week, MLB announced their Postseason Ticket Reservation program. This program allows fans to buy the option to later buy a postseason ticket at face value should their team reach the playoffs. You choose the team and game, and then pay \$10 for the Division Series, \$15 for the Championship Series or \$20 for the World Series. If the team you chose gets to that series you have the right to buy a ticket for the chosen game at face value. If not, you get nothing (i.e. your money is not refunded). For the DS you can choose Game One, Two or Three, which are the first, second and third home game for your chosen team, not necessarily the first, second and third game of the series.

So if you choose Game One, you have the right to buy a ticket for the first game of the series (if you have the home team for the series) or the third (if you have the away team for the series). If you choose Game Two you go to Game Two if your team is home and game four if your team is away and the series lasts that long. If you choose Game Three the option is worthless unless your team makes the playoffs, and is home, and the series goes to five games. You get the picture. It works similarly for the CS and WS.

Ok, so should you take part in this program? First, answer these questions: would you like to see a playoff game? Is it worth it to pay above the face value of the ticket to ensure you can go? If so, by how much? That is how much more than face value would you be willing to pay for a given game, assuming that game were to take place. Let’s call that amount, x. Now assuming the probability of the game taking place is p, the the value of the option is:

Value = (1-p)*0 + p*x

Say you are thinking of buying the option to see Game One of the Rangers’ potential ALDS. If they make the playoffs at all this game will happen, and using BPro’s playoff odds they are 82.9% to make the playoffs. So you should buy the option if:

0.829x > 10

x > \$12.06

Would you pay the face value of the ticket plus \$12.06 to see the Rangers play Games One or Three in Arlington of a ALDS? If so, and you have faith in BPro’s playoff odds, you should buy this \$10 option now. Seventeen percent of the time it will be worthless, but 83% of the time you will have something you value at over \$12.06.

We can go through and find the break-even points, the xs, for all of these options. It gets a little more tricky because we have to know the probability that a given team is home or away, advances to the next round, and that a series lasts a certain number of games. Here I did that using BPro’s division and wild card probabilities and a host of simplifying assumptions: all teams have a 50% chance of advancing to the next round; each team has a 50% chance of being home in the Division and Championship Series unless they are a wild card team, in which case it is 0%, or are playing a wild card team, in which case it is 100%; all teams are 50% to be home at the World Series; and the probability of a series lasting a given number of games is based on the breakdowns for all series since 1994.

From these assumptions I calculated that break-even value for each team-series-game combo.

First off, these numbers are only as good as the assumptions behind them. So if you think that the Yankees will be favorites in the ALDS if they get there (which they most likely would be) the break-even values on the Yankees ALCS and World Series option goes down while those for the Twins and Rangers, the Yankees’ likely opponents, should probably be a bit higher. For the Yankees the point is moot as they are the one team that is not part of the program. Also, sorry Baltimore fans, but BPro gives you a zero percent chance of getting to the post-season so your options are worthless.

You have to really value drama if you want to purchase the terminal games for any series. These games are much less likely to happen so their break-even value is much higher than the preceding games. Also because the price of the option increases with each round and the probability of reaching that round decreases the break-even value dramatically increases with each round.

Anyway, for teams like Boston, Tampa Bay, Texas, Atlanta, Cincinnati, St. Louis and San Diego these look like very reasonable numbers, and so their options are probably worth it for fans of these teams.

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Dave Allen's other baseball work can be found at Baseball Analysts.

22 Responses to “If Pittsburgh Were in Game 7 of the World Series Would You Pay \$400 Million to Be There?”

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1. Piccamo says:

While the Pirates in game 7 might have to be worth \$400 MM to someone for it to make sense to reserve it now, at least they have the option. I can’t say as much for us Orioles fans. Despite this, you can still reserve the ability to purchase tickets for the Orioles.

2. MikeS says:

It would have been more efficient if the US mint had simply granted MLB a license to print money.

You know some yahoo in KC is buying WS options that are worthless. This is almost pure profit – the overhead on this scheme must be minimal. Even with the example you gave, both St Louis and Cinncinnati can’t play a 3rd NLDS home game since one has to be the wild card so if some fan in each city is buying options to all possible games one of them has to lose some money.

But to play devil’s advocate with myself, a group of us bought season tickets after the White Sox won in 2005 because we didn’t want to miss it again. We have had a total of 3 playoff games since including the one game playoff with the Twins. The difference is that when I pay my money I know I’m going to get to go to a game.

• TonyC says:

This doesn’t even matter, because even when the fan wins, MLB doesn’t lose. So if St. Louis plays that 3rd NLDS game, instead of selling a ticket to one person for face value, they sell it to another for face value + \$10. Every option sold is free money.

• PhD Brian says:

yes but someone would not buy it if it did not make them happier. Obviously they are stating that they would prefer to pay \$10 every year until their team makes the postseason rather than sit at home while their team plays the postseason. Paying \$10 for an option is way cheaper than buying season tickets. Sitting through hundreds of losing games during off years is more costly than paying \$10 for an option. Both assure you of being there when the team makes the postseason.

This option market would be more efficient if you were allowed to bid on the options. Yankee options would go up in price while Pirate options would go down until they reached an equilibrium value based on the odds of each team making the postseason. Right now I am not sure I would pay \$10 for a Pirate option if I lived near Pittsburgh, but I am certain I would pay a dollar. If the Pirates somehow pulled off the impossible made the postseason and then went to the World Series this season, then being there for those games would be absolutely incredible and probably priceless. Well worth the dollar I spent locking down that right, but at \$10 its not worth it for this team.

3. RonDom says:

Bought a game two for the NLDS with the Dodgers (and Braves)

And reserved a game two for the Dodgers in the world series

4. das411 says:

…but does this take into account the fact that the Pirates have never lost a deciding World Series Game 7??

• philosofool says:

Good point. Let’s change the value of that option to \$320M. I’m in!

5. CesarV says:

Nice exercise but it lacks a level or two of analysis. First of all, the price paid for the option can’t be greater than the expected prize of the scalped ticket minus the option prize (why pay 400 million for something worth \$100.00?). This would negate the value of purchasing an option. Second, the buyer should wait for the last minute to buy the option, since apparently there is no time decay in this specific instrument. This will assure the buyer better odds of the options being in the money come postseason.
Cool article though, and good to know you can get this sort of option.

• Dave Allen says:

Cesar,

Good points. If you think that the cost of a scalped ticket is going to be low than there is no reason purchasing the option. And also as you say waiting longer is better to buy the option is better. The only problem there is if you wait to long there might not be any options left available for the tean/series/game you want. I don’t know whether these things will sell out but you could see it happening for the more popular teams.

• PhD Brian says:

A scalped ticket has a surety of value not figured into these options. You know the game will happen. Whereas, option prices more the more uncertainty it has. (I teach options at the college level) His bizarre expected values are more the result of the options not being fairly priced. I doubt many have purchased Pirate options at \$10 for that is clearly to high a price for most people to pay, but a Dodger fan has a much better chance his option will pay so those have probably sold rather well. If this market was allowed to fluctuate in price (like a stock) every franchise would probably sell a similar number of options but teams with a high degree of postseason success would sell for much higher prices and teams with low odds would go for much less than \$10. The expected value of every option would be roughly the same (adjusted slightly for team popularity).

6. wayne says:

In some cases, the pre-reservation options are even worth even less than this analysis indicates. The reason is that it will still be possible to buy tickets for a somewhat reasonable price (relatively speaking) after the playoff teams are determined.

For example, pick an extreme case. Even in the unlikely event the Pirates play in Game 1 of the NLCS, you could presumably still buy a ticket from someone right outside the gate before the game for juuuust a bit less than \$20 million above face value. Heck, there are probably people in, say, Tampa who would sell a ticket to Game 5 of the ALDS for less than \$250 above face value depending on how good the tickets are (not picking on Rays fans here; thresholds for many realistic playoff teams probably aren’t very different for games like that).

Essentially, if the anticipated price of a ticket purchased after the game is scheduled is less than the price on this chart plus face value, the value of the pre-reservation is zero.

7. Jason B says:

Neat article…one thing, though. You state the value of the option as:

Value = (1-p)*0 + p*x

The [(1-p)*0] part of the equation would reduce to 0, no? Which would reduce the equation to Value = p*x? Is a parenthesis misplaced or something?

• Dave Allen says:

I think you are miss reading the parentheses, as you say the first term (1-p)*0 is just zero, which leaves just the second term p*x.

8. jw says:

Can I sell my reservation to a third party? If so we could have a thriving derivative market going here. There would be many interesting hedging strategies, since the different teams are directly competing against their divisional rivals for playoff spots (hedging Yankees options with Rays options, etc). Kind of makes me want to break out my quantitative analysis books and MATLAB and find a way to make money off of it (or just write a Community Reserach post or something).

• Brian says:

I’m about 99% sure I’ve seen this done for the NFL. Some website get Superbowl tickets, and sold them off as options for each NFC team (or AFC team. I forget how they did it). And the pricing was very different by team.

9. Arbitrageur says:

I think that everyone in here is actually thinking about this wrong. This is actually a great way to make a lot of money for MLB and for the smarter members of society. If I bought the maximum 2 tickets through the World Series for games that are guaranteed to happen (Home Game 1) should that team make the playoffs for every NL team that has a reasonable statistical chance (Cardinals, Reds, Braves, Phillies, Mets, Dodgers, Rockies, Padres). I am quite likely that I will end up with at least 2 playoff teams using BP odds, and it is likely that I have 3-4 teams. All of this for only a premium of \$720. World Series tickets the last few years have gone for about \$400/ticket over face (at 2 per round, that is \$800 profit/face). Champ. Series have gone for about \$200 premium over face (@ 2 tickets is \$400 profit) and Divisional Series has only been about \$100 premium (@ 2 per is \$200).

That means that for each DS I stand to make \$200 per series (and can have up to 4), \$400 per series for CS and \$800 for the WS. I put in \$630, so basically I am betting that at least 2 of my teams will make the playoffs, and that one of the two will win one series. Anything else over that is just gravy, and remember that doesn’t even take into account markets where ticket price premiums would be greater ( NY Mets).

The reason that this works and that it is valuable is that all option prices are the same for every MLB team, even though everyone in the world knows that these teams that were cherry-picked are very likely to be playoff participants in some order. So yeah, some guy in Pittsburgh might get ripped off. But I am going to make money.

• Arbitrageur says:

Sorry should read that I put in \$720 not \$630..

• PhD Brian says:

This why bidding on these options should exist. Then your opportunity for arbitrage goes away.

10. BB says:

There’s no option to reserve tickets for the Yankees.

11. Coby DuBose says:

This almost feels like MLB is promoting gambling. Actually, that’s exactly what they’re doing.

12. Haris says:

If I didn’t know better I would have said this came from the minds of Jeffrey Skilling and Ken Lay. After all they are the pioneers/thieves who tried to trade weather futures

13. pete10j says:

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