It seems to happen every year — a good hitter gets especially hot in the playoffs and people start talking about how he should get the “Barry Bonds Treatment,” i.e., walking the batter almost every time he is up. It is generally a bad idea to give a free pass to any hitter that often, but if any current player deserves that treatment, it is Albert Pujols. A comparison of Pujols and Bonds as hitters is not quite as interesting as it sounds. Pujols’ highest single-season wRC+ is 185 in 2003; in 1993, Bonds’ wRC+ was 193 and that was only his sixth-best season. What more is interesting is the thought that teams should walk Pujols almost every time he is up. If you are reading FanGraphs, I hope that you know that walking even a Hall-of-Famer-if-he-retires-three-years-ago hitter like Pujols every time is bad strategy. However, Pujols is obviously good enough that opposing managers are justified in giving him a free pass in certain situations. How common are those situations?

Just to make it clear: for the duration of this post I will be following the analysis of intentional walks found in Chapter 10 of The Book. I am going to try to avoid regurgitating too many of the specific analytical details — if you want those or a more in-depth analysis as to the logic behind all of this, I recommend you read that chapter (and if you are interested in questions like these, you will love the whole book, anyway).

I should also make clear that there are many different variations of base/out/game situations, as well as lineup situations, all of which make a difference. I am not going to get to them all, for obvious reasons of space and sanity. Also, although the analysis is meant to be for “intentional walks,” I think that for a hitter with strike zone judgment like Pujols, many “intentional unintentional walks” can be included here, as well. So by “free passes” and the like you can include many of those.

In general, intentional walks are overused. As The Book explains in detail, almost every intentional walk will increases run expectancy. There is one general exception to this rule — runners on second and third, two outs, and an elite hitter like Pujols (who is mentioned specifically!) at the plate. However, that is just a general analysis of run expectancy without taking into account the game situation (inning and relative score) and the quality of the hitters behind the elite hitter. The chapter on walks eventually gets to a chart of base/out/inning/score situations and when a walk is advisable. Each state has a specific ratio associated with it — this is the ratio of the potential walkee’s expected wOBA to that of the hitter(s) behind him. Depending on how many outs into the inning the game is at, the ratio is the elite hitter’s expected wOBA divided by a weighted average of the expected wOBA of the two, three, or four hitters following him (i.e., how many batters are expected to hit on average after the intentional walk). If the ratio is equal to higher to the ratio on the chart, the intentional walk is advisable.

The theory behind all of this can be found in the relevant book chapter. How do we apply it to Pujols’ case? First, we need the expected wOBA for Pujols and the hitters following him. There are a number of different possibilities (particularly given the Cardinals’ manager) for the lineup sequence following Pujols, but I will consider just a couple based on recent games. The first is a post-Pujols order of Lance Berkman, Matt Holliday, David Freese, and Yadier Molina. The second, which might be used against left-handed starters, is Freese, Holliday, Berkman, and Molina. I realize that for the games in Texas, Allen Craig might come into play here as the DH, but am trying to limit my possibilities — in those cases, he will probably be hitting lower than fifth, anyway, and so the changed impact (making a walk less advisable) will not be that great given the weight assigned to that spot.

We also need projected current “true talent” wOBAs for the players. I got these by using Oliver‘s final 2011 update. However, we want to go deeper, as it will matter whether there is a right- or left-handed starter on the mound, so based on the Oliver forecasts, I estimated each relevant hitter’s platoon skill (hopefully you are beginning to see why I limited the variations). Finally, to be more accurate, The Book advises removing the walks from both the numerator and denominator of the wOBA calculations for the player who might be walked then multiplying by 1.12, since in each situation, an intentional walk and unintentional walk have the same game impact.

I won’t run through all the other hitter’s various projections for you, but to get a sense of how incredible Pujols is (if you don’t already know): Oliver has him projected for a .443 wOBA, with the walk-modification recommended, I get a .457 wOBA for him. For platoon skill, I get .449 versus right-handed pitchers, and .480 versus left-handed pitchers. Yikes.

I am going to deal primarily with situations where the starter is in an pitching well enough to stay in under normal circumstances (I realize that has been rare in this season’s playoffs, but bear with me), as dealing with various pitcher chances complicates things much further. In any case, I am primarily concerned with the “Bonds issue,” i.e., whether Pujols should be pitched around even in situations where one normally would not do so with “merely good” hitters. Let’s begin with a right-handed pitcher on the mound and Berkman-Holliday-Freese-Molina behind Pujols. The switch-hitting Berkman destroys right-handed pitching (.409 expected wOBA), but it is interesting that even after regressing Holliday’s observed “reverse” platoon split, he still projects to hit righties just as well as Berkman (.410 expected wOBA, I will not get into how I would change Tony La Russa’s likely batting orders). Freese (.339) and Molina (.331) aren’t bad, either. Given the ratio of Pujols’ .449 to the appropriate weighted averages of the others’, in what situations is a walk acceptable with a right-handed pitcher on the mound? Not many, given how Berkman and Holliday mash righties. A few of the situations:

– bottom of the eighth, one out, runners on second and third, score tied or the Cardinals ahead
– top of the ninth, one out, runners on second and third, score tied or the Cardinals ahead
– bottom of the ninth, none out, runner on second, score tied
– bottom of the ninth, none out, runners on first and third, score tied
– bottom of the ninth, none out, runners on second and third, score tied or Rangers up by one
– bottom of the ninth, one out, runner on third, score tied
– bottom of the ninth, one out, runners on first and third, score tied
– bottom of the ninth, one out, runners on second and third, score tied or Rangers up by one
– bottom of the ninth, two outs, runner on second OR third, score tied

I think that is actually the complete list, or close to it. Relatively speaking it is not a very long list, when you consider all of the possible game states. Given that that all of them are in the eighth or ninth inning, if the Rangers have a left reliever handy for Berkman and a righty available for the rest of the hitters, a free pass for Pujols becomes an even less advisable alternative.

What about if the Cardinals go with the same order against a left-handed pitcher? Then things are opened up a bit, given Pujols expected .480 wOBA against southpaws and Berkman’s big split (although his projection against lefties isn’t horrible — .347). The possibilitie really expand if the Rangers fall behind early. For example, if the Rangers get down by four or five runs early, and Pujols comes up, with one or two outs, runners on, and first base open, they could justify an intentional walk to Pujols, assuming a lefty is still set to face the middle of the Cardinals order. And, of course, the later one gets into the game, the more situations might call for such a walk.

That is worth watching for, but the Rangers would probably go to their strong bullpen pretty early if they start getting rocked in the opening innings. More importantly, La Russa has been hitting David Freese cleanup against lefties (yes, Holliday would make more sense, but I’m trying to keep it both realistic and simple for the sake of space). So what situations allow for walking Pujols given a Pujols-Freese-Holliday-Berkman-Molina sequence and a southpaw on the mound to face all of them?

Actually, it’s about the same as for the Pujols-Berkman-Holiday-Freese-Molina sequence. With Berkman hitting fourth, the ratios of Pujols’ expected wOBA versus lefties to the weighted average of the others (depending on the number of outs when Pujols comes to the plate) is 1.28 with no outs, 1.25 with one out, and 1.34 with two outs. With Freese and Berkman switching spots, the ratios are 1.28, 1.23, and 1.28. Basically, with either lineup, other than late-game situations when the Rangers are likely to be into their bullpen, the Cardinals need to be blowing the game open for a walk to Pujols to be a good strategy. Even then, there usually needs to be one or two outs, at least one runner on, and first base open. Listing the situations would not only be laborious, but might give the false impression that there such situations are somewhat common. Given the specific games states involved, they are actually rare.

Despite a 2011 that was poor by his standards, Albert Pujols is still probably the best hitter in baseball (Joey Votto, Jose Bautista, Miguel Cabrera, and Adrian Gonzalez fans might protest, but that’s a pretty select group). If any current hitter should get intentionally walked in an unusual situation, it would be him. However, intentional walks almost always increase the run expectancy of the team at-bat, and given that the Cardinals have other excellent hitters, the situations in which a free pass even to Albert Pujols is a good idea are quite rare. This is particularly true prior to the late innings, when the Rangers will have the option to play match ups with Pujols and the hitters behind him. The Rangers should tread carefully, but they don’t need to give in to the “Bonds treatment” buzz.