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  • March 9, 2010

    Probabilistic Model of Steals, Combined Parameters

    Monday I introduced the idea of a Probabilistic Model of Steals. In that post, I looked at how the stage of the game, represented by the inning, changed the probability of attempting a steal, and the success rate on those attempts. Subsequent posts examined outs and the score difference. This posts looks at what happens when all three parameters are combined.

    To review, I’m only concerned with the pure steal situation, only a runner on first. I define score difference from the point of view of the offensive player (Offensive score – defensive score). In looking at the data, a lead of seven runs in either direction seemed to be the point where teams really stopped running, so any lead of seven runs or greater is either placed in the 7 or -7 bin. I also put all extra innings in the 10 bin for that category, since each extra inning starts the same, with the score tied. The following table shows the probability of attempting a steal based all three parameters. Only combinations with at least 1500 steal situations are displayed:

    Inning Outs Score Difference Situations SB Attempts Steals Prob. of an Attempt SB Pct.
    1 0 0 14212 2416 1672 0.170 0.692
    9 2 0 1680 248 183 0.148 0.738
    8 2 2 1672 243 167 0.145 0.687
    8 2 0 1935 279 194 0.144 0.695
    3 2 -1 2639 376 253 0.142 0.673
    9 1 0 1761 248 176 0.141 0.710
    7 2 1 1958 273 189 0.139 0.692
    7 2 2 1714 239 177 0.139 0.741
    1 1 0 13735 1913 1295 0.139 0.677
    7 1 2 1727 231 156 0.134 0.675
    8 1 2 1648 220 154 0.133 0.700
    10 2 0 2197 290 204 0.132 0.703
    2 2 2 1715 225 146 0.131 0.649
    8 2 1 1752 229 161 0.131 0.703
    8 1 1 1722 223 149 0.130 0.668
    3 2 0 4677 609 426 0.130 0.700
    4 2 2 1878 239 158 0.127 0.661
    5 2 1 2478 312 202 0.126 0.647
    8 1 0 2039 254 175 0.125 0.689
    7 1 1 2003 248 140 0.124 0.565
    7 2 0 2135 260 175 0.122 0.673
    3 2 1 3194 386 274 0.121 0.710
    5 1 2 1839 223 143 0.121 0.641
    3 1 0 4910 589 374 0.120 0.635
    10 1 0 2552 305 216 0.120 0.708
    6 2 1 2262 264 173 0.117 0.655
    3 1 1 2960 347 217 0.117 0.625
    5 2 2 1911 223 150 0.117 0.673
    5 2 0 2784 326 227 0.117 0.696
    6 2 2 1796 208 143 0.116 0.688
    3 1 2 1907 220 145 0.115 0.659
    5 1 1 2417 272 173 0.113 0.636
    3 0 1 2385 270 182 0.113 0.674
    6 2 0 2350 263 186 0.112 0.707
    5 2 -1 2346 260 175 0.111 0.673
    6 1 2 1752 194 118 0.111 0.608
    7 2 -1 2099 227 172 0.108 0.758
    4 1 2 1791 193 115 0.108 0.596
    8 2 -1 1960 210 158 0.107 0.752
    1 1 1 1734 183 122 0.106 0.667
    6 1 1 2305 242 142 0.105 0.587
    3 1 -1 2759 291 197 0.105 0.677
    4 2 1 2722 284 187 0.104 0.658
    5 1 0 2953 307 170 0.104 0.554
    5 0 1 2022 211 131 0.104 0.621
    3 2 -2 1617 167 123 0.103 0.737
    5 0 2 1563 161 104 0.103 0.646
    7 0 2 1505 154 100 0.102 0.649
    2 2 1 2973 302 203 0.102 0.672
    7 1 0 2241 227 132 0.101 0.581
    1 2 0 12013 1219 871 0.101 0.715
    6 2 -1 2179 220 147 0.101 0.668
    8 0 1 1612 156 105 0.097 0.673
    6 1 0 2471 238 140 0.096 0.588
    8 0 2 1504 145 87 0.096 0.600
    9 1 -1 1662 158 116 0.095 0.734
    3 2 2 2066 196 136 0.095 0.694
    4 1 0 3624 338 196 0.093 0.580
    4 1 1 2794 259 151 0.093 0.583
    4 2 0 3477 325 219 0.093 0.674
    7 1 -1 2099 194 126 0.092 0.649
    9 2 -1 1810 165 141 0.091 0.855
    4 2 -1 2504 222 147 0.089 0.662
    5 1 -1 2382 210 124 0.088 0.590
    3 1 -2 1708 149 99 0.087 0.664
    5 0 0 2567 224 137 0.087 0.612
    6 1 -1 2322 202 124 0.087 0.614
    5 2 -2 1805 156 108 0.086 0.692
    2 1 1 2786 233 127 0.084 0.545
    2 2 0 6841 575 378 0.084 0.657
    1 2 1 2720 229 159 0.084 0.694
    3 0 0 4504 376 227 0.083 0.604
    4 1 -1 2735 227 143 0.083 0.630
    6 0 1 1963 162 101 0.083 0.623
    3 0 -1 2489 204 132 0.082 0.647
    8 1 -1 1960 158 111 0.081 0.703
    5 0 -1 2131 173 106 0.081 0.613
    2 0 1 2195 178 98 0.081 0.551
    6 0 0 2267 181 106 0.080 0.586
    7 0 1 1782 143 89 0.080 0.622
    4 0 0 3498 276 173 0.079 0.627
    2 1 0 7574 588 324 0.078 0.551
    2 1 -1 2785 212 115 0.076 0.542
    6 0 2 1608 121 83 0.075 0.686
    2 2 -1 2519 183 125 0.073 0.683
    4 1 -2 1948 140 93 0.072 0.664
    6 0 -1 2120 147 94 0.069 0.639
    6 2 -2 1773 122 92 0.069 0.754
    7 0 0 1945 134 81 0.069 0.604
    4 0 -1 2538 167 117 0.066 0.701
    8 0 0 1858 123 78 0.066 0.634
    9 0 -1 1523 99 71 0.065 0.717
    6 1 -2 1931 126 96 0.065 0.762
    5 0 -2 1636 105 69 0.064 0.657
    4 2 -2 1749 110 70 0.063 0.636
    10 0 0 2578 162 110 0.063 0.679
    9 0 0 1640 101 72 0.062 0.713
    5 1 -2 1915 115 77 0.060 0.670
    4 0 1 2348 137 87 0.058 0.635
    2 0 -1 2512 142 79 0.057 0.556
    2 0 0 6983 390 231 0.056 0.592
    7 0 -1 1806 100 55 0.055 0.550
    2 1 -2 1505 82 50 0.054 0.610
    4 0 -2 1739 94 58 0.054 0.617
    7 1 -2 1779 93 73 0.052 0.785
    7 2 -2 1743 87 71 0.050 0.816
    8 0 -1 1681 75 54 0.045 0.720
    6 0 -2 1704 76 54 0.045 0.711
    8 2 -2 1687 74 67 0.044 0.905
    8 1 -2 1731 74 56 0.043 0.757
    9 1 -2 1698 65 65 0.038 1.000
    7 0 -2 1593 48 37 0.030 0.771
    8 0 -2 1514 44 34 0.029 0.773
    9 2 -2 1642 20 20 0.012 1.000

    I’m not surprised that the mostly likely situation for attempting a steal is with the lead-off man on and the score tied in the first inning. That’s pretty much what lead-off men are designed to do, get on base and steal if they have the opportunity. Most of the other high steal attempt situations are late in the game with two outs and the score fairly close, but not trailing. In fact, in the top 34 rows, the only trailing situation in is in the third inning, with two out trailing by one. My guess is these are situations in which the lead-off man reached the second time around, and it’s worth him getting in scoring position for the big guns. The low attempt situations mostly come late in the game with teams trailing by at least two runs.

    What impresses me here is that managers really do know how to use the stolen base. They tend to run when one run is important, or early on when their best thief reaches base. Looking at the list, there are very few situations in which I’d ask, “Why are you running often there?” The consensus manager, if you will, has a pretty good grasp of when to run.

    The next installment examines which players run often, and which players cling to first.

    As always, I’m interested in your feedback. The next installment will combine inning, outs and score difference into a complete model. You can follow the series here.

    Please consider supporting this work with a donation to the Baseball Musings Pledge Drive.

    The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at 20 Sunset Rd., Newark, DE 19711.

    Posted by David Pinto at 8:31 pm | Base Running, Defense, Probabilistic Model of Steals | Permalink | No Comments

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