Of all of the statistics that Barry Bonds has piled up in the last few seasons, perhaps the most impressive is the number 120—the number of times he was intentionally walked in 2004. For comparison, the largest number of intentional walks awarded in a season to anyone else was 45 to Willie McCovey in 1969 (at least since the statistic began being tracked in 1955); even Bonds had been intentionally walked at most 68 times in a season prior to 2004 (including 35 intentional walks in his home run record-breaking 2001 season). The reason we find this to be so impressive is that the other stats show Bonds' skills—what happens if a pitcher challenges him—but the number of intentional walks shows just how much he has changed the way that managers approach the game of baseball. In effect, Bonds forced teams to rewrite The Book.

We actually feel that the recent changes to The Book on intentional walks have done us a favor. There isn't a lot in the way of age-old conventional wisdom on this topic (or, more correctly, the conventional wisdom is conflicting), but instead, the fact that managers have been changing their criteria for issuing intentional walks means that there is some openness to some new analysis. So let's have a look.

Before we plow you under with numbers, let's remind ourselves of the reasons a manager might call for an intentional walk. With less than two outs, a man on second or third, and first base open, a walk will set up a double play (and potentially a force on the lead runner). An intentional walk can also let you pick the hitter you pitch to—either to avoid pitching to a very good hitter, or to skip the #8 hitter in an NL lineup to get to the pitcher. Naturally, combining these makes the walk even more attractive—for example, with one out, a man on second, and Bonds at the plate, walking Bonds would set up a potential double play, set up a force at third, and avoid letting Bonds bat.

Of course, each of these arguments has its counter. In the first case, a walk will force your pitcher to throw the ball over the plate to the next batter to avoid a subsequent (unintentional) walk, which may result in a higher probability of the next batter hitting well. If you're walking an outstanding hitter, you're still adding a baserunner (and thus setting up a more dangerous situation), and you are also making it likely that he will come up sooner the next time through the batting order. Likewise by walking the #8 hitter, you're putting a guy on base that probably would have gotten out anyway and missing the chance of having the pitcher lead off the next inning.

For the sake of simplicity, we'll first examine situations in which all batters in a lineup are equal, in order to see if there are any game situations in which a walk is generally beneficial to the pitching team. After that, we'll examine more realistic situations in which we're contemplating walking a better hitter to get to a worse one.

We first turn our attention to situations in which the score, outs, inning, baserunners, etc., call for an intentional walk if the opposing lineup contains nine identical players. Specifically, in what base/out situations would you want to walk the current batter and pitch to an equivalent one? The answers are pretty straightforward. It should be obvious that you would never want to advance the lead runner, which eliminates half of the base states (bases empty, man on first, men on first and second, and bases loaded). As an aside, we note that this isn't exactly the same as first base being open. One could issue a walk with men on first and third and not advance the lead runner; likewise issuing a walk with the bases empty would advance the lead runner (in this case, the batter).

The main situational reasons for walking a batter (i.e., reasons unrelated to avoiding a better hitter) would be to set up a double play or a force on the lead runner. Neither of these reasons makes sense when there are two outs—the double play is impossible, and only the force out at first is needed—so we can probably focus merely on the zero- and one-out states.

Now let's test our intuition against the numbers. You will recall that the Toolshed chapter contains the number of runs a team can expect to score from any base/out state. Since we know the result of a walk—for example, bases empty becomes a man on first—we can fairly easily calculate the change in run expectancy as the result of a walk. Here is the table for all 24 base/out states.