Opening Day

First and foremost, I apologize immensely for the lack of updates lately. I have been very occupied. There will be more updates to come when I finish finals in May. Here is an update I meant to do a while ago.

So, opening day has come and past. It is one of my most favorite times of year, along with the baseball trade deadline. Many fans get excited when opening day comes, eager to see how the offseason acquisitions will pan out. Others look to opening day as a barometer of how well the season will go; to see whether or not players have their heads in the game, and to gauge their team's World Series chances. That got me thinking; what is the combined Opening Day record of all World Series winners?

Before I post the answer, I will post the guesses I collected. My guess is around 45% of World Series winners won their opening day game. My reasoning is that opening day probably has little to no impact on how well a team does during the season. It is, afterall, 162 games long, and things happen. Players get hurt. Players get traded. Certain acquisitions prove to be worthwhile, while others prove to be worthless. (Worthless x 2) (Worthless x 3).

Other guesses: My roommate guessed 54%, on a pure guess, thinking it would be a little higher than fifty, but not by much. His girlfriend guessed 60%.

The combined Opening Day record of World Series Winners is 69-35-1. (Extra points if you can name the one tie), which computes to 65.7%. While it hurts to be the most-wrong on this number, I should still analyze it.

65.7% is higher than each of us expected. This is not that unusually high, however. Assuming that there is a 50-50 chances of winning one's opening day game, then the result should be around 50%. However, given a standard distribution curve, 68% of the results should fall within one standard deviation of either side of the mean. So if we take the mean to be 50%, that means that the majority of the results taken from the sampling should fall inbetween 15.9% and 84.1%. This is a rather large range, so I prefer to take half a standard deviation, since the sample size is rather small. Within half a standard deviation, that means that the results should fall inbetween 33% and 67%. Given this small range, it is perfectly normal for the number of opening day game winners who went on to win the world series to fall in that range.