The following table shows the amount of runs, on average, a team is expected to

Question

The following table shows the amount of runs, on average, a team is expected to score given how many outs there are and how many players are on base. For example, if there are no outs and a player is on first base and another player is on third base, the team is expected to score 1.940 runs for the remainder of the inning.

Suppose that there are one out with runners on first and second. What is the expected number of future runs scored in the inning?

future runs

Suppose that the batter strikes out. What is the new expected number of runs scored in the inning?

future runs

The value that the batter has contributed is defined by the following equation.

VALUE = Expected Runs in new state Expected Runs in initial state.

What is this batter's value?

Notice that if the batter's value is negative, then the batter has actually made is less likely that the team will score future runs in the inning and if the batter's value is positive, then the batter has made it more likely that the team will score future runs in the inning. How did the batter affect the expected future runs scored in the inning?

The batter made it less likely that the team will score future runs in the inning.The batter made it more likely that the team will score future runs in the inning.    

In this situation, we now have two outs and runners still on first and second. Suppose that the next batter gets walked and the bases are now loaded. What is the new expected number of future runs scored in the inning?

future runs

What is this batter's value?

How did the second batter affect the expected future runs scored in the inning?

The second batter made it less likely that the team will score future runs in the inning.

The second batter made it more likely that the team will score future runs in the inning.   

Distribution of Runs Scored in Remainder of Inning Situation Probability of
Scoring Runs Expectation Bases
Occupied Outs % of
Situations 0 Runs 1 Run 2 Runs >2 Runs Runs None 0 24.3% 0.747 0.136 0.068 0.049 0.461 1 17.3% 0.855 0.085 0.039 0.021 0.243 2 13.7% 0.933 0.042 0.018 0.007 0.102 1 0 6.4% 0.604 0.166 0.127 0.103 0.813 1 7.6% 0.734 0.124 0.092 0.050 0.498 2 7.8% 0.886 0.045 0.048 0.021 0.219 2 0 1.1% 0.381 0.344 0.129 0.146 1.194 1 2.4% 0.610 0.224 0.104 0.062 0.671 2 2.9% 0.788 0.158 0.038 0.016 0.297 3 0 0.2% 0.120 0.640 0.110 0.130 1.390 1 0.7% 0.307 0.529 0.104 0.060 0.980 2 1.2% 0.738 0.208 0.030 0.024 0.355 1, 2 0 1.4% 0.395 0.220 0.131 0.254 1.471 1 2.6% 0.571 0.163 0.119 0.147 0.939 2 3.3% 0.791 0.100 0.061 0.048 0.403 1, 3 0 0.4% 0.130 0.410 0.180 0.280 1.940 1 1.1% 0.367 0.400 0.105 0.128 1.115 2 1.6% 0.717 0.167 0.045 0.071 0.532 2, 3 0 0.3% 0.180 0.250 0.260 0.310 1.960 1 0.7% 0.270 0.240 0.280 0.210 1.560 2 0.8% 0.668 0.095 0.170 0.067 0.687 Full 0 0.3% 0.180 0.260 0.210 0.350 2.220 1 0.8% 0.303 0.242 0.172 0.283 1.642 2 1.0% 0.671 0.092 0.102 0.135 0.823

Explanation / Answer

on (1,2) bases one runner is out

so for (1,2) leave 0 and1 look for 2 (as 1 runner is out)

the numbers of runs scored in future=0.403

2) when batter(1,2) is striked out only 3 is left

at inning or when 0 is out the expected no of scores =1.390

3) batter value= 1.390 -0.403 = 0.987

batter value is positive . therefore, the batter made it more likely that the team will score future runs in the innings

4) now the next batter(1,3) gets walked and the bases are reloaded(means there are zero outs)

for bases (1,3) the expected number of future scored innings = 1.940

the value of batter(1,3) =1.940- 1.390 =0.55

the the value of batter is positive , the batter made it more likely that team will score in future innings.

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