By TangoTiger ( tangotigre@aol.com )
There are 24 base-out situations that a batter faces (8 different combinations of men on base, and the 3 outs). Each of those 24 situations has a particular Run Expectancy (RE). For example, at the start of each inning, the average team will score on average 0.56 runs. This is simple enough to figure. If the average team scores 5 runs per 9 inning game, then the average R/I is 5/9 or 0.56. To fill out the rest of the matrix, you need play-by-play data, or a simulator. For example, with the bases loaded and 0 outs, the average team will score 2.4 runs from that point on, to the end of the inning.
Every Plate Appearance (PA) has a start state and end state. That is, before the PA, the batter is facing one of the 24 base-out states, and after the PA is over, there is (possibly) a new base-out state. Since each base-out state has its own RE, the difference in RE (plus any run scored) is the run impact of that batting event that caused that change in state.
For example, with a man on 2B, and 0 outs, the RE for that situation (the start state) is 1.2 runs . If the batter hits a double, the RE for the end state is of course 1.2 runs. As well, a run scored. So, the run impact of this particular batting event is 1.0 runs. If you have a man on 1B with 1 out, the RE is 0.57 runs. A double-play brings us to the end of the inning, and an RE of 0 runs. The double-play in this case is worth -.57 runs.
MOB 1b 2b 3b hr bb k out --- 0.29 0.49 0.68 1.00 0.29 -0.20 -0.20 x-- 0.49 0.97 1.36 1.74 0.43 -0.32 -0.36 -x- 0.72 1.00 1.16 1.60 0.23 -0.39 -0.34 --x 0.72 0.86 1.00 1.51 0.21 -0.48 -0.29 xx- 0.93 1.54 1.94 2.38 0.56 -0.52 -0.48 x-x 0.88 0.93 1.77 2.22 0.38 -0.61 -0.46 -xx 1.17 1.46 1.62 2.07 0.23 -0.70 -0.56 xxx 1.38 2.00 2.40 2.86 1.00 -0.82 -0.68 ROB 0.73 1.14 1.49 1.92 0.42 -0.44 -0.42 avg 0.49 0.79 1.06 1.42 0.35 -0.31 -0.30
A little explanation is in order. The "avg" line matches the standard Linear Weights components that is in the mainstream. It is based on the weighted average of the 8 MOB states. Since the most "popular" state is the no-men-on-base, those numbers are weighted more. The "ROB" is the weighted average of the 7 states with a runner on (everything except the first line). This is useful since most of the time we'll only have player stats with "no one on" or "men on base".
The "out" column is all non-K outs. The "MOB" column is the base that is occupied. "xx-" means runners on 1b and 2b.
If we compare the HR and Triples, we see that the difference with MOB is always around 0.4-something runs. This again makes sense since we expect about 60% of runners from 3B to score. So, the "value of 3b to home plate" is 0.40 runs.
You'll notice also that walks have the least value when no one is on 1B, as again, you would expect. (Note: you will notice that the value of the walk is .29 runs with no one on base, but .21 runs with a man on 3b. They should of course have the same run value, except that there are far more walks with 1 and 2 outs and men on 3b. This chart is weighted by outs as well. If I presented the 24-state chart, you would not see any difference.)
You'll notice that the double is worth far more than the single when we have a runner on 1B. Again, this makes sense, since the most valuable base is the one from 3B to HP, and a single will not be able to score a runner from 1B. The HR is least valuable when you have a runner on 3B because there's already a good chance that that runner will score.
Bonds AB 1B 2B 3B HR BB K other-out --- 272 22 12 2 42 74 51 143 x-- 106 16 9 0 14 30 22 45 -x- 26 2 5 0 4 34 7 8 --x 11 1 0 0 3 8 3 4 xx- 32 5 2 0 3 14 7 15 x-x 11 1 1 0 1 8 3 5 -xx 2 0 1 0 0 4 0 1 xxx 6 0 2 0 2 0 0 2 ALL 466 47 32 2 69 172 93 223 Sosa AB 1B 2B 3B HR BB K other-out --- 298 35 19 3 33 38 89 119 x-- 132 25 10 0 14 14 26 57 -x- 30 3 1 0 4 30 7 15 --x 22 1 1 0 3 16 8 9 xx- 40 7 1 1 3 0 9 19 x-x 19 7 0 0 0 7 5 7 -xx 9 0 0 0 2 6 5 2 xxx 14 5 1 1 2 2 2 3 ALL 564 83 33 5 61 113 151 231 And here are their LWTS in each of the 8 states MOB Bonds Sosa --- 39 24 x-- 31 24 -x- 15 9 --x 4 3 xx- 12 3 x-x 3 3 -xx 2 1 xxx 8 15 TOT +114 +82
Note that the coefficients that I'm using have not been adjusted for the year 2001, nor for parks, both of which would cause some change. So, we see that by looking at the context-specific performance, Bonds is 32 runs better than Sosa. However, if we had simply looked at their overall totals, and applied the overall LWTS coefficients, Bonds would come in at +113 runs and Sosa at +82, virtually the same! What does this mean? This means that neither player gained or lost based on their performance with men on base. In essence, we went through this exercise for nothing.
What is interesting is how Sosa's performance was clearly better with the bases loaded, but Bonds was his better in every other base situation.
Ichiro 28 --- (8) x-- 6 -x- 11 --x 1 xx- 6 x-x 6 -xx 2 xxx 5His context-specific performance is +28 runs. It's a good performance, but nowhere near an MVP-type year. If we just looked at his overall numbers, and applied the overall Linear Weights, he would have come in at +18. Therefore, we can say that his phenomenal performance with runners on base was worth +10 runs more than expected.
Even Boone doesn't do so good. Well, +34 runs for a 2B is pretty good, but again, nowhere near MVP status. Looking at his overall numbers and overall LWTS would have given him +36, so Boone's performance with men on base was a little below his norm.
Boone 34 --- 16 x-- 6 -x- (1) --x 3 xx- 9 x-x 0 -xx 0 xxx 2So, how about A-Rod and Giambi?
A-Rod 52 --- 20 x-- 13 -x- 6 --x 2 xx- 4 x-x 6 -xx 3 xxx (2)That's more like it. +52 for a SS is an excellent performance. His performance with men on base was slighly below his norm, as his overall LWTS shows +55. Ah, but Jason Giambi. +79 if you just looked at his overall numbers, but when you see how incredible he was with men on base, he comes in at +88.
Giambi 88 --- 20 x-- 32 -x- 7 --x 2 xx- 11 x-x 2 -xx 2 xxx 12Ok, so +88 runs for a 1B or +52 for a SS? I estimate that positional adjustment between a SS and 1B is about 20-25 runs. It's alot easier to find a good hitting 1B than a good hitting SS. But there's a 36 run gap there. Unless A-Rod defense is far better for his position than Giambi's... As best as I can tell, each of their defenses is slighly above average for their positions.
Giambi looks like the best player of the four.