Linear Program

The Player Rating Formula and the ensuing Runner, Pitcher, and Catcher ratings allow us to generate a model that will deliver a binary decision making tool that considers both the quality of the base runner and the quality of the pitcher/catcher tandem. With each Runner rating associated to a player's name, we can show how each individual player compares based on their data from the 2015 season. To capture the essence of a stolen base, we offset the Runner rating by the summed average Pitcher and Catcher ratings, therefore creating an offense/defense equality. Additionally, to further expand our tool, we developed the equation for both Pitcher and Catcher ratings one standard deviation superior and one standard deviation inferior than the league average. Consider this the 'above average' pitchers/catchers and the 'below average' pitchers/catchers.

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The output Xi represents the difference between the offensive and combined defensive ratings. When Xi is positive, the tool will output a 1. When Xi is negative, the tool will output a 0. Further details on the binary output are provided under the Discussions tab.

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With the output of a 0 or 1, we now have a simple tool that offers more clarity on whether or not to attempt a stolen base.

After we generated the output data for all three Pitcher and Catcher percentiles (-Sigma, Average, +Sigma), we show that the base runners fall within four tiers. The tiers are divided based on the standard deviation data provided under Player Rating Formula.

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The primary function of our binary output is to synthesize the situational Runner, Pitcher, and Catcher ratings into a more easily understandable form. Instead of calculating the probability of success for a stolen base attempt, which would necessarily factor in a considerable number of external inputs that contribute to the event of a stolen base, we focus on comparing the average quality of the runner against the average quality of the pitcher/catcher duo. The value lies in comparing the ability of the runner based on statistical data against the ability of the pitcher/catcher duo. When the linear program outputs a 1, this translates to the average effort from the runner will beat the average effort from the pitcher/catcher duo. When the program outputs a 0, this translates to the average effort from the pitcher/catcher duo will be stronger than the average attempt from the runner. To be clear, the binary output does not comment on the probability of success, and the output of a 1 does not indicate that the base runner will successfully steal second base. Similarly, an output of 0 does not indicate that the base runner will be thrown out if he attempts a steal. For example, a below average base runner could attempt a steal against an above average pitcher/catcher duo, and because of a poor pitch or a poor throw, which would be atypical but possible, the runner could be successful. By focusing on the average effort, we can thus provide a subtle recommendation that provides the manager with a tool for deciding whether or not to attempt a stolen base. Furthermore, when the output is 1, we consider the expected value of the stolen base attempt to be positive, and that over the long run the accumulation of positive expected value stolen base attempts will provide a significant advantage for the team.

By working with one standard deviation above and below the average defensive rating, we hope to capture a more comprehensive view of the league, offering managers the ability to tailor the output to their needs. Stolen base prevention is not consistent across the league, and therefore by differentiating our model into three tiers we offer another level of information for the manager. Lastly, our goal is to provide an elementary decision making tool, rooted in the organic statistics of the game, that will offer an ability to view a particular situation with simplified data available.

To demonstrate the utility of our decision making tool, we outline three base running scenarios where our binary output can be effective.

Yadier Molina vs. Dee Gordon
As an above average catcher, and with one of the strongest abilities to prevent the stolen base, Yadier Molina is a force behind the plate. As a manager, with Dee Gordon on first base and Molina catching, a tough decision arises. Based on the data, Dee Gordon's rating surpasses the above average defensive rating, but by a fairly small margin. With this in mind, the manager understands that the best from Gordon will beat the best from Molina. However, if Gordon were to get a poor jump or suffer any other minor setback during his stolen base attempt, there is little margin for error. Therefore, the binary output would recommend sending Gordon, yet the slim margin educates the manager that in situations of more risk, a cautious approach might be best.

Yadier Molina vs. Paul Goldschmidt
The change in this scenario from the first lies in the quality of base runner. Although Goldschmidt runs well for a first basemen, his ability to steal bases falls far short of Dee Gordon. Naturally, as Molina possess a strong capability of throwing out base runners, a manager will be more wary of sending Goldschmidt against him. Our decision tool outputs a zero for Goldschmidt against above average defensive ratings, which indicates that the best from a catcher could likely throw him out at second. This isn't to say a manager will never send Goldschmidt, as situational factors come into play throughout the season, but in aggregate Goldschmidt will rarely run against the better catchers in the league. The risks remain too high, and the expected value of a Goldschmidt steal attempt against a Molina quality catcher is fairly low.

Nick Hundley vs. Paul Goldschmidt
The change in this scenario from the second lies in the quality of catcher. Although Goldschmidt wouldn't typically run against an above average catcher, for which our decision tool outputs a zero, when the catcher is below average the manager will likely send Goldschmidt as often as possible. Against below average catchers, Goldschmidt receives a one from our tool, indicating that Goldschmidt's best will likely beat the best from Hundley. Thus, in the many scenarios where Goldschmidt faces a below average catcher, the manager has considerable incentive to attempt a steal, and the expected value of such an attempt is high.