# Should I Stay or Should I Go

By Billy Fryer in R

September 8, 2022

# Introduction

# Four Factors

### Factors 1 and 2: Distances to Target Base

### Factor 3: Base Running Speed

### Factor 4: Game Information

### Factors for Future Consideration

# How Safe or Out Data was Obtained

# Modeling

# Applications

# Run Expectancy

### Applying Run Expectancies

# Final Takeaways

# Reference

Marchi, M., Albert, J., & Baumer, B. S. (2019). Chapter 5: Value of Plays Using Run Expectancy. In Analyzing Baseball Data with R (Second, pp. 111–136). essay, Taylor & Francis Group, LLC.

# Appendix A: Modeling Expanded

# Appendix B: Converting Advance 2 Bases Probabilities to Run Expectancy

To calculate the change in run expectancy, the following formula is used:

**[RE(Success) x Pr(Success) + RS(Success)] + RE(Failure) x (1-Pr(Success)) + RS(Success)] - [RE(No Attempt) + RS(No Attempt)]**

Where: **RE()** is the run expectancy of a given game state, **Pr(Success)** is the probability of advancing 2 bases as given by the model and **RS()** represents the number of runs scored on the play.

**RE(No Attempt)**) is the run expectancy given the runner stops at the intermediate base. This helps determine if the reward of the risk is worth more than staying put. Let’s work out an example together - the Go Example. As stated previously, our game state before the play is “100” because the only runner on was on first base and we assume that there was 1 out. From the model, the probability that the runner would be safe at 3rd base is 88%. Now let’s look at the possible outcomes. If the runner decides to try and advance 2 bases, this means our possible game states after the throw are “101, 1 out” if the runner is safe or “100, 2 outs” if the runner is thrown out. If the runner decides not to attempt to take third, the games state will be “110, 1 out”. Regarless of situation, no runs are scored. If the information is plugged into the formula, it looks like this.

**[RE(101, 1 out) x (0.88) + 0 + RE(100, 2 outs) x (1-0.88) = 0] - [RE(110, 1 out) + 0]**

The run expectancy table is used to evaluate the last three missing pieces of information. The formula then reduces to:

**[(1.119 x 0.88) + (0.165 x 0.12)] - 0.860 = 0.14452**

**[RE(101, 2 outs) x (0.88) + RE(3 outs) x (1-0.88)] - RE(101, 2 outs)**

Because when there are 3 outs the team switches from offense to defense, the run expectancy when there are 3 outs is always 0.

**[(0.482 x 0.88) + 0] - 0.394 = 0.03016**

Although the value is still positive, it is much closer to 0. This means that the risk is very high but still worth taking.