Q: What are the chances of the Red Sox making the World Series?
A: Slim, but measurable and in numeric terms.
There was a particularly revealing stat given last night during Fox's (NYSE: FOX) coverage of the ALDS matchup between the New York Yankees and the Boston Red Sox: In the 25 postseason best-of-seven series where a team was down 3-0, none of them came back to win the series. But down three games to none, and down to their last half inning, the Boston Red Sox made a remarkable comeback last night -- scoring a run in the bottom of the ninth off of Yankees postseason superhero Mariano Rivera to tie the game, and then winning it in the bottom of the 11th on David Ortiz's dramatic two-run home run.
I also had an epiphany:
Watching Yankees first baseman Tony Clark bobble that ground ball in the bottom of the ninth, I had a vision of Red Sox first baseman Bill Buckner in the 1986 World Series. At that point, I just knew that the Red Sox would not only win the game but also come back and win the series. While it wasn't Tony Clark's bobble that cost the Yankees the game in the end, I couldn't help but think how ironic it would be if that play reversed the Red Sox "curse," or even put a reverse curse on the Yankees where they never win again.
Fat chance. But in today's exercise, we are going to study probability forecasting by calculating the chances of the Red Sox winning the last three games and making the World Series.
The probability of an event occurring is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 being a mathematical certainty. Thus, 0.6 means that an event has a 60% chance of occurring, and 0.4 indicates a 40% chance of success.
We start with a base model and adjust the probabilities based on other factors. In this case, we'll assume in our base model that all else being equal, the home team will win 60% of the time. The Red Sox play Game 5 tonight at home, with Games 6 and 7 being played in New York.
| Win Probability |
|
|
Base
|
| Game 5 |
0.6 |
| Game 6 |
0.4 |
| Game 7 |
0.4 |
Other factors affecting the model include the probability that Red Sox star Pedro Martinez will pitch tonight, as well as the momentum and confidence gained from last night's win. For fun, we also assume that if the Red Sox win tonight, that momentum will carry into Game 6. However, the effect is canceled out in Game 7 simply because the Yankees are the Yankees and will also have the clear pitching advantage.
In simple terms, the probability of the Red Sox winning all three games is equal to the probability of a Game 5 victory * Game 6 victory * Game 7 victory. Thus:
| Win Probability |
|
|
|
Base
|
Adjusted
|
| Game 5 |
0.60 |
0.7 |
| Game 6 |
0.40 |
0.45 |
| Game 7 |
0.40 |
0.4 |
| Combined |
0.096 |
0.126
|
Using the adjusted probabilities, the probability of the Red Sox winning all three games and making the World Series = (0.7)(0.45)(0.4) = 0.126, or 12.6%. Slim, but better than the historical average of zero.
Forecasting and calculating probabilities is essential to calculating expected values and thus stock valuation. As we'll discuss next time in an exercise covering expected value, this is true for any company in any industry, from Google (Nasdaq: GOOG), eBay (Nasdaq: EBAY), and Electronic Arts (Nasdaq: ERTS) to Home Depot (NYSE: HD) and Wal-Mart (NYSE: WMT). And as you've probably figured out by now, many of the factors going into the forecasts are very subjective -- part of the reason stock prices are so volatile.
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Fool contributor Jeff Hwang is a Florida Marlins fan and maintains no fanatical affiliation with either baseball team mentioned in the above exercise. Jeff owns shares of both eBay and Electronic Arts.
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