Waiting for a save that might never come

It almost feels wrong to pick on one manager, but the rules of writing compel me to open with an illustrative example. It was Friday, October 11, 2013 and the Dodgers were playing the Cardinals in the first game of the NLCS. Both teams scored two runs in the third inning and then failed to score again in the next six innings. By rule, a game like that goes on until one team outscores their opponent in any one given inning. This one took 13 innings to reveal a winner, but the innings of interest for the moment are innings nine through twelve.

Across these four innings the Dodgers used four relief pitchers. None of them were Kenley Jansen, the Dodgers closer. Jansen didn't pitch until there were men on base in the 13th inning because Don Mattingly was holding him back for a save situation and by the time he brought him in, it was too late. On the road, in a tie game, in the 9th inning or later, managers don't use their closers with terrifying regularity. Dusty Baker did it a lot. Jim Leyland did it three times over the course of a week in August and lost all three games. Nearly every manager in the league abides by this rule during the regular season. In the playoffs, some are willing to bend the rule. Mattingly didn't and he lost.

Most regular readers likely know that "saves" are a silly statistic and that modern closer usage is quite ridiculous. Managers cater their decisions to the notion that it requires a special pitcher to handle the final three outs of a game if the team is leading by three runs or fewer. If you read that out loud and think about it, you'll go insane. The assumptions contained in the closer mythology include that: the ninth inning is inherently different from the others, the highest leverage situation is always the ninth, that a three run lead is different from a four run lead no matter the opponent, and that your closer will only perform well in save situations.

The save and closers as concepts are worth destroying, but that's likely going to require generational replacement among baseball's on field generals. A more achievable intermediate goal should be to get managers to use their closers in tie games on the road in the 9th inning or later. It has to stop.

Now lest you think this is another "new-school" versus "old-school" debate concocted to drive page views and call other people mean names, I assure you that I've had this debate with other well respected sabermetrically inclined writers. Managers are thinking about saves and how "closing" a game is different, but some stat-savvy people have made a case that the strategy is reasonably sound. Let's consider it.

First, let's make a few assumptions and caveats clear. In the following situation I will assume that a team's closer is actually their best reliever and therefore is expected to give up the fewest runs on average, but this isn't always true. Also, the part of the order that is due up is relevant to which reliever a manager selects. It might make sense to save your best reliever for the other team's best hitters while using a lesser reliever to get 7-8-9. I'm also going to make the assumption that the closer is well-rested enough that the manager would have been willing to bring him in in a "true save situation" in the ninth inning.

The situation we'll consider is the ninth inning of a tie game. The same logic applies for every subsequent inning and the transgression becomes worse as the innings continue. The longer you wait to bring in your closer the worse it gets because you're invariably bringing in lesser and lesser relievers.

You're the road team, heading into the bottom of the ninth inning with the score tied and your starter is out of the game. Do you go to your best reliever or do you save him for the half inning after you score to take the lead? To answer this question, let's turn to win probability and a handy calculator available at The Hardball Times.

Entering the bottom half of the ninth, the visiting team's win probability is something in the neighborhood of 37%. The exact numbers vary depending on the run environment, but the calculator gives 37.4% and the real situation from last Friday stood at 37.2% according to FanGraphs. In this situation, a single run allowed will cost the visiting team a 37% drop in win expectancy and we assume that the closer gives them the highest odds of not allowing a run. If the visiting team escapes the inning, the team has a 50% chance of winning the game. If they don't, they have a 0% chance.

Now let's consider the circumstances if the visiting team scores one run in the top half of the next inning. With a one run lead, the visiting team has a win probability of 82%. If the visiting team allows a run with a one run lead, their win probability drops 32 percentages points to 50%. The actual change in win probability of allowing a single run is relatively close, but favors using the closer in the tie game. This is where the reasonable argument comes into play. The cost of allowing a run is about the same in both situations, but that misses a key point.

We can't just think about the changes in win probability, we have to think about the overall payoffs. If you allow a run in a tie game, you lose. You cannot un-lose the game. If you allow a run with a one run lead, you keep playing. The payoff of allowing a run in a tie game is 0%, but with a one run lead it's 50%.

You want to bring your closer into the game when allowing a run is costliest because on average they will allow the fewest runs. And this entire proof is predicated on only scoring one run. If you team scores two runs or more, the difference grows even more.

When you find yourself in a tie game on the road, you should go to your closer because one of three things could happen if you manage to escape the ninth inning:

1) You could fail to score in the top of the 10th inning, meaning that the situation will repeat

2) You could score a single run in the top of the 10th inning, meaning you're better off using your better pitcher in the tie and your worse pitcher with the lead (as discussed above)

3) You could score more than one run in the top of the 10th inning, meaning that the cost of one run in the bottom half is even lower than in scenario #2

In #2 and #3, the best strategy is always to use your closer in the tie assuming there isn't a match-up opportunity you are trying to exploit. In #1, you're indifferent between the two strategies in theory, but there is a possibility that you will allow a run in the ninth inning and never get there.

Managers need to go with their best pitcher in tie games on the road in the ninth inning or later, but they almost never do. There really isn't any sort of logic to doing so except that managers like to use their closers in save situations. It's a suboptimal strategy. If you save your closer, you're increasing the odds you allow a run in the ninth inning and decreasing the odds you allow a run in the 10th inning despite the fact that you know with absolute certainty that the run in the ninth is more costly.

We complain a lot about managers and their tactical choices, but we know in the end that most of their job is outside the lines. That said, there's no reason for major league front offices to allow managers to employ a strategy like this that is always wrong. This isn't like bunting, which is occasionally a good strategy and requires judgment. Managers hold their closers back for saves that might never come and it bites them quite often. It got Mattingly on Friday, it got Baker and Leyland with regularity, and plenty of others over the course of the season.

The conventional wisdom is that you don't go to your closer in a tie game on the road. This isn't sabermetrics versus old-school wisdom. This is simple logic and the conventional wisdom is wrong.

. . .

All statistics courtesy of FanGraphs and The Hardball Times.

Neil Weinberg is a Staff Writer at Beyond The Box Score, contributor to Gammons Daily, and can also be found writing enthusiastically about the Detroit Tigers at New English D. You can follow and interact with him on Twitter at @NeilWeinberg44.

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