As an answer to AlexW's question in the game thread today (August 15th) I've figured out how to determine whether it's worth it to buy tickets for the final Boston series of the season. This study is highly subjective, so feel free to quibble with my assumptions/valuations.
Let's start with the framework for the analysis:
- You're attending, or at least paying for, all three games in the series
- You have to commit to the trip today, before the O's play any more games
- For this analysis let's just call any post-season: "playoffs" (WC counts as in)
- Let's assume Camden Depot has it exactly correct and it will take 87 wins to get an AL wild card. So if the O's enter the series with 87 or more wins, they're already in. If they enter with fewer than 84, they're already out. Anything in between means the series will decide their fate (ie. DRAMA!)
From this framework we can look at the 4 possible outcomes of the trip and the net value you'll get from them.
The Orioles could be...
- out of contention by the time you get there. Return: -$1,000
- in contention entering the series, but don't make it. Return: $0
- in contention entering the series, and DO make it. Return: $10,000
- already in the playoffs and just mopping up. Return: $5,000
So if they've been eliminated before you get there, you're taking a loss because it's a wasted trip and you bought the tickets, etc... But if they're already in, you still gain, because you get to be there enjoying it and thinking playoffs.
Alternatively, if the O's playoff fate is still undetermined going into the series (ie. DRAMA!!) but they fall short, then the drama pays off the loss and the sad so you break even, but if they make it then the drama amplifies the joy of the win and you get a big return.
Knowing that you know you better than I know you, I'd assume you might think the numbers should be different, in which case let me know and I can re-do them.
So now all that's said, we get to the crux of the analysis. By weighting the various outcomes by their probability of happening, we can get to an Expected value (EV) of the trip with this formula:
EV = (Prob. Already In * $5,000) + (Prob. Already Out * -$1,000) + (Prob. Dramatic Loss * $0) + (Prob. Dramatic Win * $10,000)
With me so far? So now obviously all of those probabilities are based on what the O's "true talent" is and therefore how they can expect to do over the next 43 games, plus the following three if it's undecided. Here I've made up a table of the Expected Value (EV) based on different true talent levels. (A true talent level of .500 means they will have a 50% chance of winning each remaining game, not that they will win 50% of their remaining games)
Scen. Win % AlrIn DramW DramL AlrOut EV
Low 0.400 2.6% 3.8% 8.9% 84.8% $(405.66)
Pythag 0.466 14.5% 12.5% 17.2% 55.7% $1,151.66
Even 0.500 27.1% 17.0% 17.8% 38.0% $2,237.13
Current 0.543 48.3% 18.7% 13.8% 19.1% $3,422.93
High 0.600 76.4% 12.6% 5.9% 5.1% $4,143.47
BkEvn 0.410 3.5% 7.6% 7.5% 81.4% $14.12
How to read this:
- If you think the O's true talent level is equal to how they've played so far (.543 win%), weighting up those returns gets you an expected value of $3,422.93; with nearly a 50% chance getting $5,000 and only a 19.1% of taking the big loss. Meaning you should DEFINITELY GO!
- But if you think the O's are actually a true talent .400 team, then you're more than likely to get there with them already eliminated, so don't go.
If you think these outcome values are correct (relative to one another, not absolute, btw), and you believe the Orioles will play at a .410 true talent level over the remaining schedule. Then book that ticket. If you think they'll be worse than that, then don't.
It's worth noting that even at their current Pythag (.466) you're firmly in the black and should go.