On Bullpen Usage

Today’s sermon is based on a verse from the Book of AAR: “It sure seems like we do better against the pen than we do against the starters.” I’m going to get to that question, but not until tomorrow at best. As a preliminary, I’m going to look at the history of bullpen use. We all know that starters don’t work as many innings as they used to. But look at the following graph, which gives the percentage of innings by starters by team since 1904:

You probably shouldn’t need a graph to show this. You can see it in win totals. Cy Young won 511, Walter Johnson won 417, Warren Spahn won 363, Randy johnson won 303, and Justin Verlander is going to retire with maybe 270. But the graph doesn’t require on knowing much baseball history.

But what about bullpens. I’m going to create a team-level statistic that I call Starter Strength. The definition of starter strength is:

Since the goal of defensive baseball is to prevent runs, the goal of allocating innings to starters and relievers is (with a few exceptions I’ll discuss in a moment) to try and keep this ratio close to 1. If the bullpen is giving up more runs per inning than the starters, it would behoove you to keep starters in longer. Similarly, if bullpens are stingier than starters, they ought to get more innings.

What are the wrinkles to this seemingly obvious truism? Well, first of all you are sometimes in blowouts, either favorably or unfavorably. In such instances, you can tolerate bad bullpen performance because it is so rarely contributing to wins and losses. In those cases, you tolerate a high Starter Strength. On the other hand, late close games are characterized by high leverage: runs in these instances contribute (or detract from) wins a lot more than the average run does. In those cases, you would like Starter Strength to be low, holding the number of runs equal. So let’s see what happens when we graph Starter Strength over time:

In this chart, the teams above 1.0 have weak bullpens and the teams below 1.0 have weak starting staffs. But note that since 1940 the median team has been within shouting distance of 1.0, suggesting that teams roughly know what they’re doing, at least on average. Note also that from about 2015, the ratio had gotten low: starters were, on average more reliable than bullpens, but this moved up in the last 10 years back up to 1.0 on average.

For those of you uninterested in longterm trends, here are the same two graphs since 2015:

A few things to note here: first, the wide dispersion in 2020 comes from the short season. Secondly, I said you should use your bullpen when starters aren’t as strong, but in the last 5 years starter usage has actually increased slightly even though bullpens have been stronger than starters. The main reason for this, I think, is rule changes, in particular the three batter rule which eliminated the LOOGY. This rule affects only bullpens, and they have gotten worse, an effect that is independent of their share of total innings.

Does any of it matter, though? I ran a statistical analysis in which I tried to explain win percentage as a function of total runs allowed (normalized for overall MLB runs per game in the given season), the starter strength (defined above) and the share of total innings from starters. As you’d expect, runs allowed is super important. Having better starters is helpful as well, and managers adjust the share of innings thrown by starters such that there is essentially no added effect. That doesn’t mean that the fraction of time your starters start doesn’t matter… only that managers and general managers, on average, optimize it.

Tomorrow, I’ll try and answer AAR’s question: do the Braves do better against bullpen arms than starting arms. If so, do they do so better than other teams do?

The Game

A warm muggy night in St. Louis, with rain that led to a delay in the top of the 4th. Isn’t every summer night a warm muggy night in St. Louis? And the threat of rain of course reminded me, as it always does, of Game 0 in 1982. But the rules have changed now…. leads don’t get washed out any more.

The Cardinals were wearing their City Connect uniforms which calls their city “The Lou.” I’m not sure how they wrestled that definite article away from Louisville, and if they’d called themselves “A Lou,” it would remind people that Matty Alou played for the Cardinals for a couple of years late in his career. (I just looked Felipe up: he’s 91. Way to hang in there, Felipe. I saved my allowance to buy your autobiography in 1967. I think the only other sports autobiography I ever bought was Ball Four. I confess that Felipe Alou‘s deep Christian faith was less inspiring to me that Jim Bouton‘s faith in mischief. But Felipe is still alive and today happens to be the 7th anniversary of Bouton’s demise. He who laughs last….)

It was announced today that Shohei Ohtani will be skipping the ASG. But Sale still plans to go. Dumb.

Up to the rain delay there were only three hits combined from both teams and only one threat. A leadoff double for the Cardinals was quickly stranded by Chris Sale… that’s what he does.

At this point it’s 10:30 and the field is completely flooded. In other sports news, I will be participating in the Senior Championships tomorrow at my golf club and I have an early tee time. I am hoping to finish in the top 10 in my age group this year, and the fact that there are only 9 people in my age group entered gives me a pretty good chance, but I need to get my rest.

St. Louis. They wash out a Phil Niekro start in 1982 and a Chris Sale start tonight. Horrible place.

They say now that the game is resuming at 11:45 EDT. Not for me, I’m afraid. I’ll try and post an update tomorrow morning in this space.

I awoke at 1:40, secure in the knowledge that everyone in my age group was prostate-awakened at 1:40, to discover that we had lost 2-1 and that Roger Staubach’s backup took the loss. I will probably not use my next 4 awakenings to elaborate on this. Get ’em tomorrow.