In Joe Morgan's JoeChat™ yesterday, there was the following exchange:
Ryan (Vermont)
How do you feel things will stand at the end of the day in the AL Central?
Joe Morgan
(11:18 AM)Well, it's not a matter of how they stand at the end of the day today, I think you have to look at the end of the series. The Twins have to win 3 of 4. If they split this series, it will almost be over. It's not going to be easy for the Twins on the road to sweep the Tigers. The Twins, in their ballpark, would have an excellent chance to do so. I just don't see the Twins sweeping the Tigers, so I don't see them winning the division. It's even worse for them if they lose the first game, or lose tomorrow. The Tigers have to win one of the first two games to keep the pressure off themselves. The Twins will face Verlander in the second game. In fact, because they're playing a doubleheader today and in the history of baseball 80% of all doubleheaders have been split.
re-read that last line. "...in the history of baseball, 80% of all doubleheaders have been split."
this is a lie. first of all, from 2002-2008, doubleheaders were split 43.8% of the time. granted, this doesn't cover the same time frame that ol' number-crunching Joe mentioned above. i can't find historical doubleheader data, and don't have the time to comb through 109 year's worth of box scores (ya know, me being a busy working man and all), but here is a little math lesson for you:
for any given team on a long enough time scale, the theoretical probability of sweeping a doubleheader is 25%, winning the first and losing the second is 25%, losing the first and winning the second is 25%, and getting swept is 25%. (unless somehow the team is perenially superior to all other teams in the league, in which case the probability distribution for the yankees would look something like 99%-0.5%-0.5%-0%.) i assure you there is no fallacy in this argument, because we are talking about ALL teams, i.e. the aggregate won-loss percentage is exactly 50% here. so even ignoring the last 7 years (which clearly prove Joe to be a liar), we are talking about a situation that one would expect to see happen 50% of the time (a doubleheader resulting in a split), that Joe claims has actually happened 80% of the time. now again, i don't have historical doubleheader data, so i am going to have to wave my hands a little. since there were 178 doubleheaders in the last 7 years, let's assume there have been 109*178/7 = 2,771 doubleheaders in modern MLB history. (there's actually probably been a lot more, since they were more common back in the day. but keep in mind there used to be only 154 games in the season so this might actually not be too bad an estimate - my gut feeling is that there have been a lot, lot more.) (also, if anything, this underestimate helps Joe, not me, since weirder things - read: 80% of doubleheaders ending in splits - can happen in fewer games.)
so our null hypothesis (i.e. Joe's hypothesis) is thusly: 80% of doubleheaders end in splits. using an n value of 2,771, an x-bar value of .5, and a mu-naught value of .8, i get a z-value of 31.58. (i don't expect you to get this unless you took a statistics class or three. also note that i am taking liberties with conventional symbols, etc.)
31.58. i can't even find an online normal distribution calculator that can give me a precise enough probability of this event actually happening - they all come out to a big, fat, zero.
which is to say this: the probability that over 2,771 doubleheaders, 80% of them would end in a split (when we would expect 50%) is about 0.000000000000000000000001. (give or take a few zeroes.)
there is not a word to describe the reckless, egregious, and sinister claims this man makes week after week on national television and on national internet. he deserves to have his Hall of Fame plaque torn down and melted into computer parts.
