We are approaching the one-month mark of the 2021 season, which seems like a good time to examine how our statistics are measuring batter and pitcher contributions so far.

Today, we’ll talk about our composite batter metric, Deserved Runs Created Plus (DRC+), and our composite pitcher metric, Deserved Run Average (DRA). We’ll discuss some of the changes we’ve made, hopefully do a better job of explaining how they work, and finally look at some notable 2021 examples of these statistics in action.

__Improvements__

__Improvements__

As you can see from our new Leaderboards and Player Cards, we are providing more ways than ever to see how our statistics break down the players that interest you.

But a key part of our ability to do this is the updates we have made to these metrics themselves. With respect to DRC and DRA, the primary highlights are these:

- DRC and DRA have now been unified under the same code base. Their models were already quite similar, and it made little sense to continue to calculate them separately. At the end of the process, we still put hitters on the DRC scale and pitchers on the DRA / cFIP scales, because those outputs are easier to understand. But all of these statistics now consider the same underlying information as appropriate.

- You may have noticed that both DRC and DRA were available almost right away after the 2021 season started, rather than the one-month delay that had become commonplace. The reason is that the underlying model structure has been converted from lme4 (penalized optimization) to Stan (fully Bayesian inference). Stan is more robust, does a much better job with uncertainty, and will allow us to announce some exciting new features soon.

- DRC and DRA values also now explicitly incorporate our prior knowledge about typical league-wide rates for various batting components in recent seasons. This allows us to intelligently shrink outliers early on while crediting performances more likely to stick over the long haul.

__Skepticism and Proportionality__

__Skepticism and Proportionality__

As we’ve discussed before, a defining feature of all our modeled statistics, but especially DRC and DRA, is **skepticism**: the belief that all player performances should be somewhat discounted, and that some should be discounted more than others. This skepticism manifests itself as shrinkage, the pulling of outlier performances toward the grand mean of the baseball population for that statistic. Factors which influence the amount of shrinkage include sample size (smaller samples being less trustworthy), quality of competition (inferior opponents justify more skepticism), and the parks in which players have played, among other factors.

Statistical skepticism is not a new idea. The general idea is similar to reversion a/k/a regression to the mean: the idea that in most systems, participants generally trend toward the midpoint of all performances. Before modeling tools became broadly accessible, analysts could enforce anticipated regression to the mean by adding a number of league-average plays to actual performances to create an updated “expected” value.

However, ideally we would do better than this. Shrinking one event is fine, but if you take away plate appearances from one batting event, you need to find somewhere else to put them. Some events are more likely than others, and the way you redistribute those events matters. In other words, if you want to shrink a player’s strikeout rate, fine, but if you take away strikeouts, where do they go? And if you award more strikeouts, where do they come from? Do these revised strikeout numbers affect home runs, singles, or walks? Or all three? You need to *redistribute *those shrunken values appropriately, or you are going to create new problems in the course of addressing an existing one. Some methods seem to implicitly assume that shrunken events all become outs, but that is not a reasonable assumption.

Let’s illustrate this with some percentages. Baseball batting events are often described as “multinomial,” because there are multiple potential outcomes when a hitter steps into the box, and we can count the total number of events in each category. But here it is more helpful to think in terms of proportions. For the 2021 season through the end of last week, here is how various batting events have stacked up, by percentage:

**Table 1: 2021 Batting Events by Percentage**

BIP_Out |
SO |
BB |
HBP |
IROE |
Single |
Double |
Triple |
HR |

42.6% | 25.0% | 9.2% | 1.3% | 0.8% | 13.4% | 4.0% | 0.4% | 3.2% |

These proportions are fairly stable from year to year, the narratives you might hear notwithstanding. Over time some changes do happen (for example, there have been more strikeouts and fewer outs on balls in play in recent years), but this distribution generally describes pretty much any modern baseball season, and it has once again assumed its typical shape only a few weeks into April.

What these percentages illustrate is that there is no free lunch. If you are going to shrink one batting event toward the mean, you have to redistribute the confiscated or inserted events among the other batting events, preferably in a principled way. We’ll call this the issue of **proportionality**. (We could also call it *reversion over the simplex*, but that is not very catchy). It bears some resemblance to the traditional focus on Batting Average on Balls in Play (BABIP), but proportionality, as we are applying it, properly expands the analysis to include all significant batting events, not just ones where contact has occurred.

Proper redistribution is tricky, because there are at least two other factors in play: (1) other batting events *also *need to be adjusted for quality of opponent, park, platoon matchups, and other factors; (2) these other batting events *are* *also *being shrunk toward the overall mean. It is, in the abstract at least, a dizzying collection of adjustments to make.

Fortunately, DRA, DRA-, cFIP, and DRC+ do this dynamically so you don’t have to. They accomplish this by expecting each batting event, across the league, to roughly conform to its typical end-of-season distribution. This helps distinguish enduring performances from temporary ones, even early in the season. But we also give the models some room to adapt if a particular season starts to show a different and persistent trend.

Generally speaking, the batting events that tend to be most “deserved,” which is to say, they have the widest expected distributions among players, are, in decreasing order:

Event |
Player Type |

Triples | Batter |

Home Runs | Batter |

Hit-by-Pitch | Batter |

Walks | Batter |

Hit-by-Pitch | Pitcher |

It’s almost as if batters have more control over their plate outcomes than pitchers do.

By contrast, the batting events that tend to be least “deserved,” in further decreasing order, are:

Event |
Position |

Infield Reach on Error | Pitcher |

Doubles | Batter |

Singles | Batter |

Singles | Pitcher |

Doubles | Pitcher |

Putting this all together, our deserved metrics: (1) resist crediting players for contributions that, in part, are better attributed to other players; (2) apply shrinkage on a component-by-component basis; and (3) automatically distribute shrunken PAs toward other expected batting events, while still working to account for overall circumstances.

Let’s see how these principles have manifested so far during the 2021 season.

**Hitter Performances**

We focus on comparisons of “actual” versus “deserved” performances. We use OPS and RA9 as our guideposts for “actual” results for hitters and then pitchers, respectively. There are alternatives, but they tend to say similar things to OPS and ERA. We included only players with at least the 75th percentile number of plate appearances for hitters (as of this writing, 72 PA) and the 75th percentile of batters faced for pitchers (as of this writing, 15.7 IP). All statistics should be complete through last week’s games.

For the first time (publicly), we will also reference the “deserved” component values for each batting event. That means we will be discussing deserved strikeout rate (dSOR), deserved walk rate (dBBR), deserved home run rate (dHRR), and so on, next to their actual equivalents..

We’ll begin with hitters.

*Ronald Acuña Jr.*

*Ronald Acuña Jr.*

One hitter on whom OPS (1.224) and DRC+ (148) essentially agree is Ronald Acuña: both rank him as essentially the best hitter in baseball so far this season.

**Table 2: Ronald Acuña Jr.**

Category |
Actual |
Deserved |

Strikeouts | 14% | 18% |

Walks | 14% | 12% |

Home Runs | 8% | 5% |

Singles | 14% | 14% |

Doubles | 7% | 5% |

Why does DRC+ agree with OPS? Because Acuña’s strikeout and walk rates are excellent, and both also are likely to reflect real skill (walks slightly more so than strikeouts). The strikeout rate gets shrunk upward, the walk rate gets shrunk downward a bit, but neither category requires a massive reallocation. The deserved home run rate does take a haircut, because it is an extreme outlier this early. Many of the larger disagreements between OPS and DRC in April stem from the fact that OPS takes April home runs at face value and DRC does not.

But this doesn’t really hurt Acuña, because he is average to above-average at everything, and none of his event totals is otherwise an extreme outlier. The net result is that Acuna adds positive value in virtually every possible way at the plate, and aside from some softening around the edges, DRC sees nothing not to like.

*Freddie Freeman*

*Freddie Freeman*

Next, let’s choose an example of where DRC+ (130) is much more impressed than OPS. OPS thinks Acuña’s teammate Freddie Freeman is merely very good (.825). We’ll skip the table this time, as a narrative explanation should work just as well.

In terms of actual results, Freeman has a very low (13%) raw strikeout rate and an extraordinarily high (21%) raw walk rate. OPS thinks that is nice and all, but he has also hit only 8 singles (8.4% of his PAs) and 2 doubles (2.1%) so he doesn’t yet have much to show in that respect. With OPS and virtually every other batting metric, no results equals no credit.

But DRC sees something very different. Even after shrinkage, Freeman’s deserved strikeout rate remains remarkably low (15%) and the deserved walk rate remains very high (14%). But it also expects that his singles and doubles rates will shrink considerably toward league means, for three reasons: (1) the league means are much higher than his current values; (2) there is much less variance around singles and doubles than strikeouts and walks; (3) we have to put all those missing strikeouts *somewhere*, and once again, Freeman has a lot of positive places to put them.

Taken together, for the time being this adds up to a substantial deserved increase in singles (up to 13.7%) and doubles (raised to 3.8%). Because Freeman gets credit for the allocation we *expect him to have* with this level of plate discipline, DRC views Freeman as secretly having a bit of a monster season, and presumably his actual results should start showing up.

**Pitching Performances**

We can make similar comparisons on the pitching side. We’ll look at the relative ranks of two pitchers by RA9 versus DRA.

*Corbin Burnes*

*Corbin Burnes*

For an example of where RA9 (1.84) and DRA (1.22) basically agree, let’s start with somebody who has been getting a lot of attention this year: Corbin Burnes. He ranks as the best pitcher in baseball by DRA and cFIP, minimum of 20 IP, although RA9 puts him 10th.

Here is some actual versus deserved component data on Burnes:

**Table 3: Corbin Burnes**

Category |
Actual |
Deserved |

Strikeouts | 45% | 37% |

Walks | 0% | 4% |

Home Runs | 1% | 2% |

Singles | 9% | 12% |

Doubles | 4% | 3% |

To understand why Burnes is still ranked so highly by DRA, we apply a similar proportionality analysis as we did above for DRC. Here, Burnes’s staggering strikeout rate has been shrunk from 45% to 36% and his 0% (!) walk rate is shrunk upward to 4%.

Regardless, Burnes is seen by DRA as deservedly keeping 41% of his plate appearances from putting the ball in play. Per our chart above, the average plate appearance keeps 34% of balls out of play (25% average strikeout rate plus 9% average walk rate). Burnes thus starts out with a substantial advantage over other pitchers, and since the majority of the remaining 60% of plate appearances will end up being an out, that doesn’t leave much room for hits to do damage. Even with the substantial shrinkage that always gets applied to singles, doubles, and home runs for pitchers, he ends up with a better-than-average allocation of all three, and it nets out to a superior DRA.

[On a related note, the proportionality concept helps explain why True Closers often get away with high walk rates. If nobody can put the ball in play, then the primary concern is just not walking runs in. On occasion of course, a few balls do get put into play, and then it can get ugly.]

*J.A. Happ*

*J.A. Happ*

We’ll conclude with an example of DRA being far more pessimistic. At the time of writing, RA9 ranks J.A. Happ (1.69) very highly, whereas DRA ranks him much lower (6.34). What makes DRA so skeptical about Happ? Again, it is proportionality.

Happ is the mirror image of Burnes, except that his results do not seem to have caught up to his process. We’ll again choose narrative over a table. Happ has a 16% strikeout rate (shrunk up to a 19% dSOR) and a 10% walk rate (shrunk down to 8% dBBR). Even with DRA giving him that benefit of the doubt, DRA thus expects, by the law of total probability, that Happ will allow the remaining 74% of his plate appearances to put the ball in play, versus the MLB average of 66%.

That is a tough way to make a living in major league baseball. Will most of those balls in play become outs? Yes. But a proportionately larger share of them are now also expected to become some mixture of singles, doubles, triples, and home runs, because there is only so much any pitcher can do once the ball has been put into play. Pitching to contact is essentially pitching to runs, and DRA expects Happ to pitch into many more runs than have shown up so far.

__Conclusion__

__Conclusion__

The big question on your mind probably is, “when will we see these deserved components?” The answer, we hope, is “soon.” We continue to roll out features on our Player Cards and deserved components are on that list to be added. The idea is similar to the “deserved runs” concept that are currently on the new Player Cards, but we suspect deserved components will end up being much more popular because they are rates rather than counts.

In the meantime, we hope this makes the overall approach of DRA and DRC more clear, and perhaps gives you further ideas how to use skepticism and proportionality to better value batter and pitcher contributions.

#### Thank you for reading

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What I'm curious is the balance between the plate appearance outcomes and the various adjustments made. As in I would think that the ratios of BB, K, 1B etc. in relation to the expected (i.e what this article is largely about) accounts for the lions share of DRA, and the adjustments due to batter, umpire, ballpark etc. are smaller. But I'm just wondering to what degree? Like given a certain distribution of PA events for a pitcher compared to the league, the next walk issued would have a certain value of some kind, let's say "1", right? The value would also be affected by who was walked, where and so on.

So, how different would it be if the pitcher in question walked Mike Trout with the worst framing catcher behind the plate, and with an umpire with a very tight zone. Versus if it was, say, Dee Strange-Gordon with Yasmani Grandal catching and a very generous ump?

I understand that you probably can't answer that specific scenario, and I'm sure I'm misrepresenting the workings of DRA, but basically what I'm curious is how much the adjustments for personel involved, environment, location etc. can impact the "raw" PA outcomes. Just a general idea of scale would be nice, like are we talking 1%, 10%, 20% between the "best" and "worst" walk that a pitcher could issue?