Prerequisites
- - Variables and expressions from prior lessons.
- - Basic understanding of baseball metrics.
- - Comfort with substitution and arithmetic.
Why This Matters
Baseball decision systems are mostly input-output stories in disguise. Velocity goes in, whiff probability comes out. Rest days go in, projected stamina comes out. Plate appearances go in, expected runs come out. Function notation gives a reliable language for these stories so analysts can explain where numbers come from and why they differ across players. Without explicit function structure, teams confuse observed stats with modeled values and struggle to debug disagreements across tools. Strong function notation prevents that by making each mapping explicit and traceable.
Lesson Opener
Suppose w(v) represents expected whiff probability from fastball velocity. The expression w(97) is not just a math exercise; it is a baseball question asking for model output at a specific velocity context. If one analyst reports w(97)=0.31 and another reports 0.27, the difference might come from model definition, calibration data, or hidden inputs. Function notation helps isolate those sources by forcing clear argument definitions and output meaning. In this lesson, students turn baseball narratives into function notation, evaluate functions at concrete inputs, and communicate interpretations as full baseball sentences rather than symbol-only fragments.
Learning Objectives
- - Write correct function notation from baseball stories.
- - Evaluate and compare function values at multiple inputs.
- - Explain function outputs for coaching decisions.
Roadmap
- Translate baseball relationships into function signatures.
- Evaluate function outputs at concrete inputs.
- Interpret values in tactical baseball language.
- Differentiate function rules from isolated raw observations.