FA - : (FA) FA [3] [4] [5] 1.1 () 25 1:

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(2015), 1939: 133-142 Issue Date 2015-04 URL http://hdl.handle.

1 得点圏打率盗塁併殺を考慮した最適打順決定モデル Titleについて : FA 打者トレード戦略の検討 ( 不確実性の下での数理モデルとその周辺 ) Author(s) 穴太, 克則 ; 高野, 健大 Citation 数理解析研究所講究録 (2015), 1939: Issue Date URL Right Type Departmental Bulletin Paper Textversion publisher Kyoto University

2 FA - : (FA) FA [3] [4] [5] 1.1 () 25 1:

3 \frac{*\ovalbox{\tt\small REJECT}?J\mathscr{X}}{fJ\hslash \mathscr{x}},$ REJECT}^{-}ffi \mathscr{x}}{ \pi b*\re+ae?j }\cdot\frac{\ovalbox{\tt\small REJECT}^{\backslash }\ovalbox{\tt\small REJECT}*\mathfrak{M}\mathscr{X}}{\mathfrak{B}\ovalbox{\tt\small REJECT}\overline{\vec{-}}\ovalbox{\tt\small REJECT}_{f\overline{T}} \mathscr{x}}$ P*\Re}{fJ\mathbb{R}\Re}$ $\frac{a\ovalbox{\tt\small REJECT}\tau_{\backslash }\equiv-nffi\uparrow^{/}\overline{t}\re}{ \pi F*\Re+\S\xi\}J\mathfrak{W}}$ \frac{\not\in fj\mathscr{x}}{fj/ff\mathscr{x}}.$ $\frac{\mathbb{b}\ovalbox{\tt\small REJECT}^{-}-\ovalbox{\tt\small REJECT}_{f\overline{T}}^{-/}\mathscr{X}}{ \pi b*\mathfrak{w}+aefj }\cdot$ $f_{b\ovalbox{\tt\small REJECT}_{\beta}^{-}\equiv{\}f \overline{t}\mathscr{x}}^{f\ovalbox{\tt\small REJECT}\infty rj_{j}\mathscr{x}}$ ( ) $arrow$ $2arrow 17)$ $arrow$ $arrow$ $5arrow 18)$ $6arrow 20)$ $arrow$ $8arrow 23)$ $arrow$ $10arrow 25)$ $arrow$ $arrow$ $10arrow 25)$ $10arrow 25)$ $arrow$ $10arrow 25)$ 1.4 p0 Pr( ) $=$ $= \frac{^{}\backslash }}{}$, ph Pr() $=$ $= \frac{ }{}$ $\alpha$ pb1 $=$Pr( ) $= \frac{h\pi b* }{fj\hslash \mathscr{x}}$. $\frac{\mathfrak{b}\ovalbox{\tt\small $\alpha$ p B2 $=$Pr( 4 $\frac{\mathfrak{w}\pi $ie^{\prime $\frac{\mathfrak{b}\ovalbox{\tt\small REJECT}_{\beta}^{\overline{\equiv}}ffi_{\overline{fT}} \mathscr{x}}{ \pi b*\mathscr{x}+ae?j }\cdot\frac{b\ovalbox{\tt\small REJECT} \mathfrak{n}\iota jj\mathscr{x}}{\mathbb{r}\ovalbox{\tt\smallreject}_{q}^{\rightarrow}=r_{f\overline{t}} \mathscr{x}}$ $= \frac{h\pi bx\mathfrak{w}}{fjr\mathscr{x}}.$ $p_{b_{3}}^{\alpha}=p_{r}$ ( a}\dagger\rightarrow$ [$\mathbb{h}$) $\alpha$ p 1 $=$Pr( ) $\frac{\mathfrak{b}\ovalbox{\tt\small REJECT}^{-}\pi^{-/}\overline{]}}{ \pi F*\mathscr{X}+\oplus fj }\cdot\frac{b\ovalbox{\tt\small REJECT}*\mathfrak{W}\mathfrak{W}}{\mathbb{R}\ovalbox{\tt\small REJECT}_{\overline{\overline{\overline{6}}}}\hslash_{f\overline{T}} \mathscr{x}}$ $= \frac{\phi fj\re}{fjr\mathscr{x}}$ p2 $\alpha=$ Pr( ) $=$ $a_{fjffl\re}^{efj\re}.$ $\frac{\mathfrak{b}\ovalbox{\tt\small REJECT} T^{-}\backslash \overline{-}\re\acute{(t}\mathscr{x}}{ \mathfrak{r}\triangleright R\Re+aefJ\mathfrak{W}}$ p3 $\alpha=$pr( ) $= p4 $\alpha=$ Pr() $= \frac{--\ovalbox{\tt\small REJECT} fj\mathfrak{w}}{fj\mathbb{r}\mathscr{x}}$, p5 Pr() $\alpha=$ $= \frac{\underline{=}\ovalbox{\tt\small REJECT} fj\mathfrak{w}}{fjffl\mathfrak{w}}$ p9 $=$Pr() $= $p_{b}^{\alpha}=p_{b_{1}}^{\alpha}+p_{b_{2}}^{\alpha}+p_{b_{3}}^{\alpha}$

4 135 $\alpha$ $\beta$ $= \frac{ }{+ }$. $=$ $=$ $=$ 1.5 $P=(P_{ij})=p(j i)$, $i,$ $j=1$, 2, $\cdots$ $ $, 25 $P=3021\{\begin{array}{llll}A_{0} B_{0} H_{0} O_{0}O_{1} A_{1} B_{1} H_{1}O_{2} O_{2} A_{2} F_{2}O_{3} O_{3} O_{3} 1\end{array}\}.$ $A_{1}$ $1\cross 25$ $u0$ $u_{0}=$ $[1$ $0$... $0]$ $n$ $u_{n}$ $u_{n}=$ $[0$ 1... $0]$ $n$ 2( 1 ) $P_{n+1}$ $n+1$ $u_{n+1}(=u_{n}p_{n+1})$ n l $1 2 25$ $U_{0}=020:1\{\begin{array}{llll}1 0 \cdots 00 \vdots O 0 \end{array}\}$

5 136 ( ) ( ) $U_{n}$ $n$ ( ) ( ) $U_{n+1}$ $(i$ $=$ $U_{n}(j$ PO $+U_{n}(j-3$ Un(j l )Pl Un(j 2 )P2 $P$ 3 $+Un$ ( $j$ 4 ) $P$ 4. (1.1) $PO,$ $P1,$ $P2,$ $P3,$ $P4$ $0$ $P=P0+P1+P2+P3+P4$ $P$ (1.1) 1 1 $0$ ( ) 1 () 1 2 $0$ $ $ $u_{0}p0= [1 0 0]P0= [ A ].$ 1 $ $ $u_{0}p1= [1 0 0]P1= [ B ].$ 1 $U_{1}$ $U_{1}=20201\{\begin{array}{l}u_{0}P0u_{0}P1O\end{array}\}$ $0$ (1 $0$ $arrow 2$ $0$ ) $[A]PO=u_{0}P0\cdot PO.$ 1 (1 $0$ $arrow 2$ $arrow 2$ $0$ ) $[A]P1=u_{0}P0\cdot P1$ $[B]PO=u_{0}P1\cdot PO.$ 2 (1 $0$ $arrow 2$ $arrow 2$ 1 ) $[A]P2=u_{0}P0\cdot P2$ $[B]P1=u_{0}P1\cdot P1.$

6 $(U_{2} (0$ $))$ $0$ $0$ $(0$ $=$ $(0$ Ul $)PO=u_{0}P0P0=[C].$ 2 ( $U_{2}(1$ $0$ $0$ (1 ) $=$ $U_{1}(0$ Pl Ul (1 )PO $= u_{0}p0p1+u_{0}p1po$ $= [D].$ 3 $(U_{2} (2$ $))$, $0$ (2 ) $=$ $U_{1}(0$ P2 U1 (1 )Pl $=$ $u_{0}p0p2+u_{0}$plpl $= [E]$ $U_{2}=03220:1\{\begin{array}{l}CDE0\vdots 0\end{array}\}$ $(n+1)$ $j$ 5 1. $n$ $=j$ $(n+1)$ $0$ $arrow U_{n}(j$ PO. 2. $n$ $=j-1$ $(n+1)$ 1 $arrow U_{n}(j-1$. Pl. 3. $n$ $=j-2$ $(n+1)$ 2 $arrow U_{n}(j-2$ P2. 4. $n$ $=j-3$ $(n+1)$ 3 $arrow U_{n}(j-3$ P3. 5. $n$ $=j-4$ $(n+1)$ 4 $arrow U_{n}(j-4$ P4. $1\sim 5$ $U_{n+1}$ $(j$ $=$ $U_{n}(j$ P0 $+U_{n}(j-3$ P3 Un $(j-1$ $)P1+U_{n}(j-2$ $)P2$ Un $(j-4$ P $i$ (STEPI) $(i=1, \cdots, 9)$ $P^{i}$ $P^{i}=P0^{i}+P1^{i}+P2^{i}+P3^{i}+P4^{i}.$

7 138 (STEP2) $U_{0}$ $1 2 25$ $U_{0}= 2001\{\begin{array}{llll}1 0 \cdots 00 \vdots O 0 \end{array}\}\cdot$ $U_{0}$ 1() $0$ 1 (STEP3) $U_{1}$ $U_{0}$ (1.1) $U_{1}$ $(j$ $U_{1}$ (1 ) $U_{1}(21$ $=U_{0}(j$ POl Uo $(j-1$ Pll Uo $(j-2$ P21 $+U_{0}(j-3$ P31 Uo $(j-4$ P41 $U_{1}=[U_{1} (1$ $), \cdots, U_{1}(21$ $)]^{T}$ (STEP4) $U_{1}$ (1.1) $(j$ (1 ) $U_{2}(21$ $=U_{0}(j$ P02 Uo $(j-1$ P12 Uo $(j-2$ P22 $+U_{0}$ $(j-3$ P32 Uo $(i-4$ P42 $U_{2}=[U_{2} (1$ $), \cdots, U_{2}(21$ $)]^{T}$ (STEP5) $U_{2},$ $U_{3},$ $\cdots$ $r$ 2 $U_{n}$ 25 $R(25)=[x_{0}, x_{1}, \cdots, x_{20}]^{t}$ $r\ovalbox{\tt\small REJECT}$ $r=0\cdot x_{0}+1\cdot x_{1}+2\cdot x_{2}+\cdots+20\cdot x_{20}.$ (STEP6) $r_{1}$ 1 1 $R$ $R=r_{1}+r_{2}+\cdots+r_{9}.$ $R$ ! $=362880$ 1 1

$$\rangle 14$ $5$ : $14$ DeNA $6$ :$

8 139 $1$ : 14 : $2$ 14 $3$ : 14 $4$ : $\rangle 14$ $5$ : $14$ DeNA $6$ : 14

9 140 $7$ : 14 $8$ : 14 $9$ : 14 $10$ : 14 $11$ : 14 $12$ : 14

10 $13$ : $14$: $15$ : $16$ : 2 FA $\mathbb{e}[obo_{fa_{1}}]=fa$ 1 $\mathbb{e}[obo_{fa_{2}}]=fa$ 2 FA 1 FA FA 1. 8 (a) 3 (b) 2. FA 1, FA 2 (a) $3 \gamma$ (b) 3. FA 1, FA $\mathbb{e}[obo_{fa_{1}}],$ $\mathbb{e}[obo_{fa_{2}}]$ FA FA MLB MLB

11 142 FA 17: FA ( ) References [1] (2012), : [2] How to choose Fkee Agent batters? -Introduction to Baseball financial engineering-, SIT OR [3], (2002), [4] :(2001), OR [5] (2000), $[6 $ K. Ano, Modified Optimal Batting Order based on Markov Chain, (2000), The 8th Bellman Continuum on Computation, optimization and Control, 2000, Taiwan. [7] K. Ano, Modified Offensive Earned-Run Average with steal effect for baseball, (2001), Applied Mathematics and Computations.Vol.120, pp s. [8] 1997 $2$ Nanzan Management Review, Vol.14, No.1 & pp [9] Vol. l114, pp [10] 1998 Vol.1068, pp

FA $1$ $$ 1, $$2 : $2$ : Takehiro Takano $$ 1, Katsunori Ano2 $*1$ : Graduate School of Engineering and Science, Shibaura Ins

FA $*1$ $*$ 1, $*$2 : $*2$ : Takehiro Takano $*$ 1, Katsunori Ano*2 $*1$ : Graduate School of Engineering and Science, Shibaura Ins Title マルコフ連鎖に基づく最適打順モデルによる FA 打者獲得戦略 ( 不確実不確定性の下での数理意思決定モデルとその周辺 ) Author(s) 高野, 健大 ; 穴太, 克則 Citation 数理解析研究所講究録 (2016), 1990: 89-96 Issue Date 2016-04 URL http://hdl.handle.net/2433/224603 Right Type