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The Mirage of "Productive Outs"

Willie Bloomquist grounds out. No idea whether this was a productive out or not.
Willie Bloomquist grounds out. No idea whether this was a productive out or not.

"There is no such thing as a productive out. Outs are sacred, as you only have 27 of them - therefore never give them up."
- - Billy Beane

If you've listened to any D-backs broadcast over the past couple of weeks, you have probably heard a great deal of talk about "productive outs" - and, in particular, the Diamondbacks failures in this situation. There's no doubt the team are bad in this area: through Tuesday's game the team was dead-last in the National League, in terms of both number of productive outs and the percentage of chances for such (PO%), which they converted. But how much does this matter?

Let's dig a little deeper and see how important they are.

It seems to have been part of the managerial mantra for ever. In 2004, for example, Detroit Tigers hitting coach Bruce Fields firmly stated, "That's how games are won and lost -- productive outs, advancing baserunners and getting guys in from third with less than two out." Or, as Joe Posnanski said, "You ever see a big league dugout after someone moves a runner to third on a routine ground ball to the right side? It's like Mardi Gras. High fives! Hugs! Confetti! Charles Lindbergh didn't get the welcome that a baseball player gets for hitting a timely dribbler to second base."

Initially, it seems they may be significant. After all, the most successful 2012 team in the category of PO% are the Dodgers, currently running away at the top of the National League West. But is that really a tribute to the virtues of advancing runners? Because rounding out the top five in the category are the Pirates (averaging less than three runs per game), Giants, Rockies, the Cubs. Hardly what you'd call a parade of offensive win. Conversely, the leaders in the other two divisions, the Reds and Nationals, are currently ranked 13th and 14th in PO%, and seem to be managing quite well, despite bypassing the middle stanza of "get 'em on, get 'em over, get 'em in."

Even more damningly, if we look back at the larger sample size provided last year, we see that the Diamondbacks, who rolled to the NL West title, were ranked... 15th in the National League for both productive outs and PO%. So, last year's team did perfectly well, while being almost as wretched in advancing runners as this year's model. We certainly didn't hear many complaints then about this aspect of the Arizona game. Indeed, all three 2011 division winners, the Phillies, Brewers and Diamondbacks, came in at below the league-average of 188 productive outs. So if any direct correlation exists between this stat and success, it's hard to see.

"There is simply no evidence to support the notion that making productive outs is a legitimate, repeatable skill. Nor is their any reason to believe that they are the key to winning games. The productive out is to baseball what a lab fee is to a college term bill: sure it's there, but those big numbers at the top still trump everything else."
-- Anthony Passaretti, Baseball Prospectus

Most productive outs are not a crucial part of a run scoring. The majority either advance a runner who gets stranded anyway, or advance a runner who would score later anyway, on a base hit. To me, that's a huge flaw in the definition of the term: you shouldn't call an out "productive" unless it is key to a player crossing home-plate. For instance, leas-off double, ground-out that advances the runner, sacrifice fly - those are productive outs. But make it a lead-off single, followed by a ground-out that advances the runner then a sacrifice fly, and if the next guy pops out, those first two outs should not be described as productive.They're just outs. And outs are bad, m'kay?

Obviously, you can point to specific cases - and Mark Grace usually does - where a failure to advance runners costs a team significantly. But, in general, the difference between an out and a productive out is an awful lot less than the difference between an out and a non-out. Beane was right, in that there is almost no such thing as a "productive out" - if you define "productive" as "increases the number of runs a team is likely to score in an inning." Advancing any men on base 90 feet is nearly always outweighed by giving up one-third of your outs.

This can be seen if you look at Run Expectancy Matrixes, which show, for any given situation, e.g. men on the corners, one out, how many runs a team is likely to score thereafter. Here's the one for 2011:

Runners 0 Outs 1 Out 2 Outs
Bases empty 0.481 0.258 0.097
Man on third
1.312 0.899 0.355
Man on second
1.063 0.649 0.314
Second and third
1.894 1.290 0.572
Man on first
0.850 0.503 0.217
First and third
1.681 1.143 0.475
First and second
1.432 0.894 0.434
Bases loaded
2.264 1.534 0.692

For example, with a man on first, and no outs, a team is expected to score 0.850 runs. An "unproductive out", e.g. a strikeout, pop-up or fielder's choice where the lead-runner is erased, makes it a man on first and one out, where the run expectation is 0.503. But even the "productive out" such as a sacrifice bunt, where we have a runner on second with one out, reduces run expectation significantly to 0.649. That's the case for outs in all scenarios except second and third, or bases-loaded - calling the rest "productive" is incorrect. They're just "less unproductive", and that takes away a lot of the sting. Who cares if Arizona are terrible at making less unproductive outs?

But how much has their failing here cost us this season? Cyril Morong crunched the numbers and figured out the value of a productive out in runs, and also has the breakdown of productive out scenarios - for instance, most are with a man on first. Putting those two together, we can work out that an average productive out is worth 0.166 runs over an unproductive one. Now, in 206 opportunities this year, the D-backs have made 46 productive outs. If we had done so at a league average rate (31%) we would have 63.86. Assume those extra 17.86 outs are each worth 0.166 runs, Arizona would this year have scored an extra... 2.96 runs.

Or, in round numbers, with unproductive outs at an insane, likely unsustainable level (we're at 22%; no NL team has been below 25% since we entered the league), they have cost the D-backs less than three runs. About one run every 16 games or so. That's what Passaretti's quote above means. Sure, advancing runners is better than not advancing them - all else being equal. But all else rarely is, and PO% has such a trivial effect on actual offensive numbers, it isn't realistically worth any degree of concern. Much like batting order, it appears to be one of those aspects of the game, that pundits and fans tend to think is a lot more significant than it actually is.

One slight caveat to this. In 2003, Buster Olney disclosed that of the post-season sets since 1969, "in 62.3% of those 130 series, the team with the advantage in Productive Outs has prevailed." That might be because playoff games are likely between similarly-matched teams, e.g. last year, all but the Phillies had 90-97 wins, so little things like advancing runners can make a difference. However, note it was not PO% which Olney used, just the raw number of PO. Dan Agonistes suggested this "simply reflects the fact that winning teams get more runners on base, have more productive out opportunities, and therefore usually end up making more productive outs:"

Overall, as Clay Davenport put it, "If you get enough hits and homers, it doesn’t matter how often someone moves from second to third on a grounder." Worth remembering, the next time your blood-pressure rises after a K with a runner in scoring position.

"What gets me nowadays is this thing they call the productive out. A guy hits a ground ball to second base and they give him a pat on the back. I spent my entire career hitting ground balls to second and there's a reason I went into TV"
-- Joe Garagiola