Mike Matheny is too slow to replace starting pitchers

A boxing match has raged on for nine or ten rounds. Punches fly. Punches land. One of the competitors is worn down, on the ropes. Forget landing a clean hit, the man can barely stay upright.

Now imagine him exiting the ring as a new fighter takes his place. Fresh. Agile. Dominant. The tides have suddenly turned. Our new boxer, who the opposition is just now seeing for the first time, escapes trouble and closes out a victory.

You know where I'm going with this.

I think everybody can agree on one thing: Mike Matheny, like every manager at some point, has made the mistake of watching a game slip away at the hands of a fatigued or struggling starting pitcher. I acknowledge that I write with the luxury of hindsight, but how many times must an event occur before we quit chalking it up as an isolated incident? At what point do the dots connect to form a concrete pattern? This is Matheny's sixth year on the job.

Apologies, I've been meaning to get that off my chest.

So we've arrived at this problem that we're all too familiar with. Rather than discuss a potential solution of note (spontaneous coughing fit ensues), we're going to take a step back by trying to answer these two questions:

1. Just how costly has Mike Matheny's "slower hook" with starters been for the Cardinals?
2. How does Matheny compare in this regard to the 29 other managers in Major League Baseball?

To begin, I needed a way to measure a manager's trust in his starter as the game progressed. I looked at every plate appearance that occurred during a starter's third time–and only his third time–through the order in addition to being classified as a "high leverage" situation. (Any game event with a leverage index above 2.0) If that seems like a hyperspecific filter, just keep in mind that there were numerous variables I needed to account for.

• In many instances, the second time through the order is simply too early for a manager to go to his bullpen without expanded rosters.
• Stats from the fourth time through the order become too unstable to use for two reasons: 1) The sample size drastically shrinks; 2) Starters lasting that deep into a game are likely the beneficiary of "survivor's bias". (Not only is this a more talented group to begin with–how often do you see a terrible pitcher toss a complete game?–, but they have also been pitching exceptionally well on that particular day.)
• Managers are more willing to push the envelope with their starters in low leverage, blowout games. Is it worth burning a reliever for tomorrow to keep one or two runs off the scoreboard in the seventh inning of a 9-0 landslide?

Technical note: From this point on, I will use SP wOBA to denote a starting pitcher's wOBA in the aforementioned third time, high leverage situations. The same applies with any other starting pitcher stats used in this article.

With the game on the line and the advantage shifting from the starting pitcher to the batter, righting the ship with your starter is rarely the sabermetrically sound decision. However, like seemingly everything in baseball, context is key. A manager with an excellent rotation and an awful bullpen should, in theory, have a "slower hook" than the average club.

Returning to our original question about how costly Matheny's hook has been, we need to determine how the Cardinals would have performed with a reliever on the mound as opposed to the game's starter. To do this, I simply calculated the difference between SP wOBA and RP wOBA (relief pitcher wOBA in all situations). If you're wondering why SP wOBA doesn't entail all situations while RP wOBA does, remember that we're comparing what a starting pitcher did do to what we would expect a reliever to do in that exact same situation. I gave some consideration to using only a team's three or four best relievers for RP wOBA, but seldom do managers trot out their elite hurlers in the fifth or sixth inning, even if advanced metrics say they should. The whole idea behind this methodology is to simulate what would happen if a real human manager, not a robot, pulled his starter and made a call to the bullpen.

Got all that? Let's jump into the results.

There it is. Quite literally nobody in all of Major League Baseball has been burned by a slow hook as badly as the Cardinals.

There is one factor that the above table does not address. While the Braves and Cubs have virtually identical net wOBAs, the Braves have allowed their starters to face 45 more hitters in the described circumstances. Put another way: a mistake becomes more costly the more times you make it.

To compute raw run values I turned to wRAA, which measures total offensive value. (wOBA works on a per-plate-appearance basis, not crediting managers who make fewer mistakes to begin with.) From there I could find the win value of a manager's starting pitcher hook by using the 2017 cost of a win: 10.057 runs.

In just 98 particular plate appearances the Cardinals have lost 1.13 wins by sticking with their starting pitcher. And that's before taking into account that these are high leverage situations with an even more dramatic swing in win probability than the average moment.

How much does Matheny's bullpen management in all situations cost the Cardinals? What about his suboptimal lineup construction? Based on the data, it's safe to assume that better management alone could have easily made up the one-win margin between St. Louis and San Francisco for the second wild card last year. If the Cardinals fall just short of the postseason again this season, couldn't the same thing be said? By definition, an employee should be able to justify their salary through their positive contribution to the company.

Dear St. Louis Cardinals,

In what world is negative value considered a positive contribution?

Yours truly,

Tyler