I'm taking a quick break from writing my chapters for Baseball Prospectus 2003. I want to re-visit something I've already hit twice, because I'm a glutton for punishment. I wrote two articles where I took a crack at whether it ever makes sense to walk the 2002 Barry Bonds, first here and then on They've stuck with me because neither time have I come to a complete or correct solution. I'll be the first to admit I'm not an advanced mathematician, that my propeller-beanie work is not ground breaking. Yet here I am again, licking the frozen flagpole. I'm going to offer a detailed walkthrough of one situation, so you can see how I came to those conclusions, and maybe we see where to go from here.

So here's our situation, one of those I identified in the ESPN piece as being a case where you start to consider walking Bonds every time: man on first, two outs. Average pitcher, average defense. Groundball-tastic Benito Santiago's been replaced with an average hitter with an average GB/F ratio. Do you walk Barry?

Here's Barry's 2002 line:

             Avg   G  AB    H 2B 3B HR TBB HBP SO  OBP  SLG
Total       .370 143 403  149 31  2 46 198  9  47 .582 .799

And now, without the intentional walks:

	     Avg   G  AB    H 2B 3B HR  BB HBP SO  OBP  SLG
Total       .370 143 403  149 31  2 46 130  9  47 .529 .799

Two sac flies, by the way. If you figure that Barry got about 4.5 PAs per game, those 68 intentional walks could have composed fifteen full games where he wouldn't have had to swing a bat.

And here's our RRE chart, courtesy of BP's own Michael Wolverton:

      Bases               Outs
                    0       1      2
       empty   0.5111  0.2718  0.1006
         1st   0.8960  0.5358  0.2271
         2nd   1.1422  0.6815  0.3222
     1st 2nd   1.5106  0.9365  0.4501
         3rd   1.4051  0.9445  0.3629
     1st 3rd   1.8379  1.1852  0.5243
     2nd 3rd   1.9564  1.3580  0.6327
 1st 2nd 3rd   2.3324  1.5105  0.7756

If Barry was an average hitter, the RRE in this situation – 2 outs, man on first – is .227. And if you put Barry on intentionally, that jumps to .450, which makes it a bad decision.

Now, in excruciating detail, here are the Barry Outcomes:

  • Walk anyway: 23.9%
  • Barry takes ball on armor: 1.7%
  • Single: 12.9%
  • Double: 5.7%
  • Triple: 0.4%
  • Aloha means goodbye: 8.5%
  • Inning-ending out: 38.4%

Walk or HBP results in runners on 1st and 2nd with 2 outs, which carries a RRE of .450.

Thanks to reader Joshua Buergel, I have better data on runners advancing, which will make the hits section even more complicated.

On a single, the runner advances to second 67% of the time (first and second, .450 RRE), and third 33% of the time (first and third, .524 RRE) On a double, the runner advances to third 60% of the time (.524 RRE), and scores on the double 40% of the time (1 run scored + man on second and new RRE of .322). On a triple, runner scores, Bonds is on 3rd, 1 run scored + new RRE of .363. On a home run, two runs score, new RRE for bases empty with two outs is .100. Out means no runs score, which I'll represent as a 0.

All that remains is the gruesome math, then: event outcome value times probability. In the case of singles, they're further multiplied by the probability of the sub-outcome.

Walks: .450 * .239 = .108
HBP: .450 * .017 = .008
Single with runner to second: .450 * .129 * .67 = .039
Single with runner to third: .524 * .129 * .33 = .022
Double with runner to third: .633 * .057 * .60 = .022
Double with runner scoring: 1 run + .322 * .057 * .40 = .030
Triple: 1 run + .363 * .004 = .005
Home run: 2 runs + .1 * .085 = .178
Ball in play outs: 0 * .384 = 0
Strikeouts: 0 * .086 = 0

Sum that up and we come up with .412, which is our 2-out, 1-man on Barry RRE. We can see what a dangerous hitter Barry was already: the RRE with an average hitter is only .227. But at the same time, the run expectation a team faces after walking Barry–.450–is still significantly higher than facing Barry.

How much better would Barry have to be to make it worth walking him every time in that situation? It's not as much as I thought — if he turned ten of those singles into home runs, it's close enough to make no odds. Now, there's been some work done on whether it ever makes sense to walk a man, with the general consensus being 'no'. But even the Tom Tippett piece was based on throwing Babe Ruth into a lineup of scrubs, and Barry doesn't offer the strikeout rate Ruth did. Still, to win you have to take 27 outs from your opponent, and you can't pick one up walking Barry.

This also uses Barry's straight stat line for this year. We're neglecting, among other things, the fact that he hits half the time in the most severe pitcher's park in the NL. Most importantly, though, there's the real world fact that teams walked Bonds intentionally all year and in those situations he almost never scored.

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