Statistics rule the game of baseball. It’s a game of skill, where the biggest, strongest, fastest guy isn’t always necessarily the best. Experts perform studies, watch reruns of games, and analyze the stats day and night to try to formulate the best factors to look at in a player, team, setting, etc. These stats can help properly evaluate a strategy to see if it really is effective. Every single detail and decision of a player can be factored into statistics. People track every foul ball hit, every time a pitcher throws over to first base to check the runner, every missed ground ball, etc.

The game has been played the same way for the past hundred-so years, with bases at 90 feet apart, and home plate being 60 feet, 6 inches from the pitcher’s mound. Baseball’s heritage and tradition are richer and deeper than those of other sports, with more numbers and more history making the statistics so important to evaluate. Through all the numbers, though, which are the most important to look at? More specifically, does a field’s elevation affect how well a team performs offensively?

Before trying to use the numbers to determine if there is a significant answer to this question, it’s important to decide which batting statistics should be used to investigate the issue.

*wOBA – Weighted On-Base Average*

This uses linear weights to determine exactly how valuable each offensive outcome truly is. We know a single is better than a walk and a triple is better than a double, be we can actually compute the precise values with this statistic.

*BABIP -Batting Average on Balls in Play *

These tend to fall for hits based on three factors. The first is how well the ball was hit, the second is the quality of the defense, and the third is luck. The first one is important, but you don’t want to penalize a hitter for the second two. Luck and defense will eventually even out over a big enough sample, but it can take 500 to 1,500 PA in some cases.

*wRC+ – Weighted Runs Created Plus*

This credits a player for total production rather than on an at bat by at bat basis. It combines the virtues of a weighted statistic like wOBA, with the virtues of counting stats that give players credit for producing at a given level over a great number of plate appearances. It provides a measure of how many runs a player contributed to his team with their bat. It’s also very simple to read. League average is always 100, so the average hitter in 1998 and 2014 would both have a 100 wRC+. Therefore, a player with wRC+ of 110 would be doing 10% better than the league average.

*HR/FB – Home Run per Fly Ball*

This is the ratio of home runs a player hits out of their total number of fly balls (including home runs). While a player’s raw total of home runs will tell you something, their HR/FB ratio can be useful in providing context about how sustainable their power is. According to FanGraphs.com, an average HR/FB rate is about 9.5%, where a good hitter will be around 15-20% and a poor hitter ranges from 1-5%.

*Physics*

When comparing these different statistics across different levels of elevation, physics is the most important factor to consider.

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. The key point here is that if there is no net force acting on an object (if all the external forces cancel each other out) then the object will maintain a constant velocity.

Newton’s second law explains how the velocity of an object changes when it is subjected to an external force. More simply, force (F) equals mass (m) times velocity (a). Newton’s third law, on the other hand, states that for every action, there is an opposite and equal reaction.

When combining all three laws in baseball terms, the force that’s applied when hitting the baseball determines how far the ball will actually go. Then, any ball hit into the air will have the force of atmosphere (pushing against the ball when it comes to distance) and the force of gravity acting on it (pushing the ball down as it goes into the air).

*Elevation*

Therefore, does the different amount of atmospheric pressure at different elevations influence how much force is applied on the ball downward and resisting it to go further? Using wOBA, BABIP, wRC+, and HR/FB, we can compare to see if the ball tends to travel further in thinner air at higher elevations, causing singles to turn into doubles, fly balls into home runs, etc.

Next, to analyze the numbers, let’s establish a base upon which we’ll be using for comparison. The Colorado Rockies’ Coors Field has an elevation of about 5,211 feet above sea level. The next highest field elevation is that of Arizona Diamondbacks’ Chase Field at 1,059 feet above sea level. The average elevation of a major league baseball field is 355.86 feet, excluding Coors Field. Including Coors Field makes the average elevation 517.53 feet. If that’s not enough to understand the difference in field elevation, here’s a bar graph that shows the differences.

*all field elevations were found at BaseballPilgrimages.com

*The Players*

To approach an understanding of differences in elevations, I decided to compare the players from the Colorado Rockies to see how they played at home versus on the road at another field. It’s important to note that more away games are played within their NL West league than out of their league, however I was not able to find the away statistics within their league compared to out of their league, so the numbers might have some skew. Other factors such as not normally playing against a team or in an unfamiliar away field may play in as well.

A rather difficult task that I didn’t think needed much focus was choosing the players which I was going to compare, yet it ended up being one of the hardest parts. I started off wanting to use the 10 players who had the highest plate appearances within the last 10 years to compare. Although, I only wanted to compare players who had a significant number of plate appearances, which I identified as at least 200 to allow for the chances of random error and chance to not have a huge effect on the numbers.

Then, I had to dwindle the number of players to those who have stayed with the Rockies for at least 10 years, and practically all the players had been removed from the “possibly usable” list. After some tweaking and trying to find what was going to work out best, I have chosen 5 players to compare over the last 6 years. I’ve gathered their stats for home vs away games, averaged them, and put each stat in a graph for each player.

* *

**Nolan Arenado**

It’s evident here the difference makes for at home games versus away games over the last six years.

** **

**Charlie Blackmon**

Though the numbers here are closer together, there seems to be a large difference in home run to fly ball ratio at Coors Field compared to other ballparks

**DJ LeMahieu**

Again, the numbers are close together, with a large difference in home run per fly ball hit.

**Carlos Gonzalez**

Differences seem to be pretty consistent across the board for Carlos Gonzalez

**Chris Iannetta**

Chris Iannetta seems to have a significantly different trend of stats when comparing to the other players. He seems to have a better average when it comes to away games, yet he tends to hit more home runs at his home games.

Another thing to note is the different layouts of different major league fields. A fly ball in the Astros’ stadium could be a home run in Fenway Park. Other factors must be taken into consideration as well when comparing home to away games like how sleep/travel could affect a player, an opposing crowd, etc.

It’s possible to further analyze this data in several ways as well. One could look at the same stats for other teams to compare how well they play at their home fields versus away fields to see if there is a significant difference in numbers between them and the Rockies. Also, someone could compare how specific, individual players play at fields of higher altitude compared to that of lower altitude. All in all, there seems to be a consistent trend of the Rockies’ players to hit better in their home field, which has a significantly higher elevation than that of other fields.