9.7 Team Talent

9.7.1 Bill James \(\log_{5}\) model

• \(P_{A}\): team A winning percentage
• \(P_{B}\): team B winning percentage

\[P(\text{Team A wins}) = \frac{ \frac{P_{A}}{1-P_{A}} }{ \frac{P_{A}}{1-P_{A}} + \frac{P_{B}}{1-P_{B}}}\]

• weighted average of log odds of winning

9.7.2 Bradley-Terry Model

• \(T_{A}\): team A talent level
• \(T_{B}\): team B talent level

\[P(\text{Team A wins}) = \frac{ \exp(T_{A}) }{ \exp(T_{A}) + \exp(T_{B}) }\]

• similar to softmax formulas
• later: positive correlation

\[\text{more talent} \quad\Rightarrow\quad \text{more wins}\]