# Home Field Advantage

/I woke up one morning a few months ago to find a text from my older son that had a link to an article about how the previous night was the first time in Major League history that all 15 HOME teams won their game. My first reaction was "really?" Baseball is well over 100 years old and in all that time the home team had not won every game of a scheduled day? Then I realized that they were not talking about every home team winning, they were talking about all 15 home teams winning on a single day. There have only been 15 home teams (i.e. 30 teams in the league) for a couple of decades. The article referenced that going back to 1914 something like this had not occurred. So, I took this to mean that on a night in which EVERY team was playing that all the home teams had not won their game. This still seemed surprising until I gave it a bit more thought.

Assuming for a moment that the probability of any team winning any game is 1/2. That is, either team is as likely to win the game as the other, the probability that all 15 home teams win their game is 0.5 raised to the 15th power. This number is not as small as you might think and works out to be 1 in 32,768. That doesn't sound absurdly rare, so how come this has never happened before? For that, we need to realize that in a 162 game season, all 30 teams probably play on only about 125 of the days. Many teams have off on a Monday or a Thursday. There are rainouts. So, this means that in any given season there are only 125 chances for this event to occur. So, over 100 seasons, there are only 12500 chances for something that should occur 1 in 32768. So, what is the probability that it would occur exactly 1 time? 26.05%. This is less than half the probability that it would not occur at all over that time (68.29%). So, it is more likely than not by a better than 2 to 1 margin that this even would never have happened by now.

Of course, over the past 100 years there were for most of that time far less than 30 teams. They also used to play less than 162 games per year and played more double headers. So, getting an exact probability is a bit more complex than what I presented here. I also made a HUGE leap by assuming that each game had an equal probability of the visitor or home team winning. Fortunately, I was able to retrieve from one source (Yahoo! Sports) the odds of each team winning before the game started.

Interesting enough, on this particular night, the home team was favored to win EVERY game. Thus, it is probably not a huge surprise that all the home teams won. But, being the favorite is hardly a guarantee of winning. As it turns out, all the home teams were favorites the next night too. But on Wednesday night, 4 of the home teams lost. In baseball, more than any other major sport, the odds change greatly from one night to the next even if the same two teams are playing because of the starting pitchers. So, just because the home teams all won on Tuesday and those same teams played again on Wednesday, does NOT mean that the odds of each team winning was similar from one night to the next.

In order to calculate the probability that all 15 home teams won on Tuesday, we need to multiply the 15 probabilities together and look at this number. When this is done, we get 0.00041. This translates to 1 in 2441. That is not a typo. This is more than 10 times more likely than the baseline number I showed before. On this particular night, the home teams were heavy favorites. The Mets were a better than 2 to 1 favorite to beat the Rockies. The lowest it got for the home team was 53%. As I took these numbers from Yahoo! Sports, there is a possibility that they represent betting lines (and not true odds) and this some sort of vig is built into them. Even if this were the case, the probability on this particular night was clearly far greater than on an average night.

Schedules in baseball are relatively random. Yes, teams play other teams in their division a set number of times, etc... But there is not a lot of rhyme or reason to when a team is home vs. away. The real oddity of the night might be that all of the home teams were the favorites. As in any sports, teams tend to perform better at home. But, asI stated earlier, the impact of the starting pitcher on a team's probability to win is greater than you would find for a single player in other sport from game to game (barring injury). Zack Greinke was pitching for the Dodgers. He happened to be pitching at home. Had he been the visiting pitcher, the Dodgers would likely still have been favored.

So, it took some random events lining up combined with some less than random events happening in the expected probabilities for this once in a century event to occur. How is this relevant to casino gambling. It is all about understanding probabilities. When you first began reading this article and read that all 15 home teams had won for the first time, were you surprised? Were you more or less surprised by the end of the article? Players have a tendency to personalize the odds of events occurring. If you haven't hit a Royal, you might think it is as rare as hitting a million dollar jackpot on a slot. If you've hit 3 Royals in the past month and then go 3 months without one, you may think you've gone cold. In reality, you're probably right in the range known as 'expected'.