Our analysis for the Player Rating Formula focused on the 2015 season. To develop the formula, we initially created three separate ratings: Runner rating, Pitcher rating, and Catcher rating.

**Runner Rating**

The Runner rating measures the base runner's ability to successfully steal second base, weighing success rate with attempt rate, as detailed below. The weights are vital, as success rate must be balanced with the boldness of the base runner, that is how frequently does the runner attempt to steal when they have the opportunity. This system of weighing both rates allows the Runner rating to distinguish between the runner with a Success rate of 75% in 40 attempts (30 SB) and a runner with a Success rate of 90% in 20 attempts (18 SB). While one player might have a lower success rate, they actually attempt more stolen bases and therefore could arguably be a more valuable base stealer.

**Pitcher Rating**

The Pitcher rating measures the pitcher's ability to successfully prevent base runners on first base from stealing second, weighing successful prevention rate with the frequency of stolen base attempts against the pitcher with a base runner on first base. Again, the weights are crucial, as prevention rate must be balanced with the total stolen base attempts against the pitcher as this overall volume can be a strong indication of futility on behalf of the pitcher. Pitchers excellent at preventing stolen bases might have few attempts against them, an element of stolen base prevention that must be considered.

**Catcher Rating**

The Catcher rating inherently follows a similar mold to the Pitcher rating, capturing the catcher's ability to prevent the base runner from stealing second base. However, due to the relatively small amount of catchers in the MLB, we lacked sufficient data to generate a catcher Attempt rating, and therefore we simply doubled the catcher Success rating when calculating the total Catcher rating.

The output from our Runner rating calculations provided data on the most successful stolen base leaders from the 2015 MLB season. Listed below are the top base runners. For context, relevant base running data has been provided.

We compiled the average pitcher and average catcher ratings into a 'defensive rating,' which is 135.800. To enhance our model we also develop the analysis for one standard deviation (64.989) above and below the average. Thus, we have an above average pitcher/catcher rating of 199.789, and a below average rating of 71.810. These three ratings are used when showing the different tiers of runners.

To further demonstrate the validity of the Runner rating, and to emphasize the importance of weighing both the Success rate and the Attempt rate, three comparisons between base runners are provided below.

**Comparison 1:**

The first comparison demonstrates the two essential factors of our Runner rating: Success rate and overall volume. As shown, Billy Hamilton during the 2015 season stole one fewer base than Dee Gordon, but with a considerably higher Success Rate. Therefore, the overall Runner rating for Billy Hamilton reflects the difference in Success rate, placing him higher than Dee Gordon. Similarly, Dee Gordon stole bases at roughly the same Success rate as Starling Marte during the 2015 season, yet with nearly double the volume. Therefore, the overall Runner rating for Dee Gordon reflects the difference in overall volume, placing him higher than Starling Marte. Finally, as seen with Billy Hamilton and Starling Marte, when a player dominates another, that is steals bases with a higher Success rate and with greater overall volume, their Runner Rating reflects the difference on an even greater scale.

**Comparison 2:**

The second comparison demonstrates the impact that opportunities to steal a base, that is the number of times during the season a player is on first base, has on the Runner rating. As shown, both Jacoby Ellsbury and Ender Inciarte have similar Success rates and overall volume. Yet, when the base runner's attempt rate is taken into consideration, Jacoby Ellsbury clearly shows that he managed to produce the same statistics as Ender Inciarte despite fewer opportunities. Therefore, Jacoby Ellsbury receives a slightly higher Runner rating, built on the inherent projection that if he were to have the same opportunities as Ender Inciarte, he would have had slightly higher stolen base production.

**Comparison 3:**

The third comparison provides an additional example of how Success rate and overall volume impact the Runner Rating. Jarrod Dyson, clearly one of the more prolific base stealers during the 2015 season, had the highest Success rate among qualified players. Though his overall volume is surpassed by numerous other players, his sheer ability to steal bases in limited opportunities and with great success is reflected in his Runner rating. Jason Heyward, another player with an excellent Success rate, slots in below Dyson both due to the slightly lower Success rate and the more opportunities. Finally, as a reflection of how a drastically lower Success rate can impact a player's Runner rating, Anthony Gose drops twenty-four spots in the list due to his relatively poor Success rate despite stealing the same volume.