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As I stepped out of the car, the intense 100˚ F heat and high humidity washed over me. On June 4th, 2011, the Cardinals were scheduled to play against the Cubs at Busch Stadium in St. Louis. It was the first baseball game I had ever been to and although I was never much of a sports fan, I couldn’t wait to watch the game. As I walked into the giant brick stadium, I marveled at all of the World Series pennants that hung on the wall. Thousands of people poured in as we pushed our way through the crowd. The freshly manicured field, gorgeous downtown St. Louis skyline, and a setting sun met our eyes as we took our seats.   It was a very fun and exciting game to watch, and the Cardinals would go on to win 5-4. Something that I didn’t know, or perhaps even thought about, was how much math was going on as this game unfolded. A staggering amount of data was being recorded each minute of the game. Even I was among the data recorded; a single attendee that was a part of 43,195 people that attended that evening.1 And it wasn’t just that game, but every game that had been occurring up this point over the last 100 years.  The statistics behind baseball is astonishing. There is a vast amount of data that has been recorded, with entire societies and classes dedicated to researching and learning more about the science behind it. Teams now use much of the analyses to figure out how much value to assign players, where to place them in a lineup, and spot weaknesses in other teams. It got me thinking: If I were to start a team today, what would be the best way to find out whom to put on my team? Statistics would lead the way.   \subsubsection{What \paragraph{What  Makes a Great Hitter?} There are a number of factors that go in to choosing the great members that make up an excellent team. Knowing when and, more importantly, when not to swing is key. 2. A batter’s likelihood of hitting a ball can be measured by dividing the number of times at bat by the number of times they are officially at bat. It’s known as the Batting Average 3  $AVG = Hits/# of At Bats$  So I go to various universities and find a number of candidates who have incredible averages. But let’s say we have a bunch of them who have a small standard deviation between them, say .375 ± .1. How do I know which ones to choose? Well, in order to win in baseball, at least on the offensive side, we need to score as many runs as possible. So the player who can get the most number of bases with the least number of at bats would be more valuable. This statistic is known as the Slugging Percentage. 
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The problem with SLG is that it only measures official at bats. So any sacrifice balls or walks are not recorded. This means that it’s leaving out a bunch of potential runs that the batter is earning. So, we can add these factors into our formula. Adding walks, hit by pitch, and sacrifice flies, we can get a better representation of how well they will perform. It’s known as the on-base percentage.  $OBP = Hits + Walks + Hit by Pitch / # of At Bats + Walks + Hit by Pitch + Sacrifice Flies$  Given this information, I now know what to look for in my offense and how to make the tough decision of who to choose from in a sample of excellent batters. Next up, I’ll need some pitchers who can keep the other team from scoring.  \subsubsection{What \paragraph{What  Makes a Great Pitcher?} A great pitcher can change an entire game single-handedly. They control the strikes and walks that occur. But once the batter makes contact with the ball, the rest of the defense is left up to the players in the field. We’re going to focus primarily on the pitcher, however. If the rest of the defense is playing at league average, we can use a metric known as the Fielding Independent Pitching.  FIP = 13 * Home runs + 3 * walks – 2* strikeouts / innings pitched + C  The constant C is to make the figure look more like the scale used for Earned Run Average (ERA). The ERA is another formula used to show how many runs a pitcher lets allows in a given game.