In 2019 Liam Hendriks and Kirby Yates had, respectively, the best and fifth best reliever seasons of the 2010s by fWAR. Yates tied for ninth in the NL Cy Young race, while Hendriks wasn’t even listed on an AL ballot. In the entire decade not one time was a relief pitcher a finalist for Cy Young, with the last occurrence of that being Francisco Rodríguez‘s third place finish in 2008. The members of the BBWAA voting for Cy Young each year seem to be averse to listing relievers high on their ballots. Yet, in spite of this seeming trend, I have a postulate. I believe that 2020, assuming the baseball season actually happens here in the Twilight Zone, will be the likeliest in the 21st century for a relief pitcher to win the Cy Young.
Let me explain myself. With the exception of a random Clayton Kershaw or Jake Arrieta becoming the greatest pitcher of all-time for a season, some reliever will always have the most eye popping rate stats in baseball. Yates did this last year, Zack Britton did in 2016, and so on. The reason they don’t get consideration for the
Old Hoss Radbourn Cy Young award is the wide gulf in innings pitched between a top starter and an elite reliever. A short season obviously doesn’t give the starting pitchers time to build large inning advantages over the relief pitchers. Additionally, with this year as more of a sprint than a marathon, starters will have a shorter leash, while relievers are deployed more often, similarly to the postseason, bringing the inning totals closer together.
Of course, saying that all of this will increase the odds of a reliever winning Cy Young is all well and good, but one of my favorite things about baseball is that mathematically, almost any question about it can be answered. In 2019, using an average of ERA- and FIP-, the best qualified starter in MLB was Gerrit Cole, with a 57.5 average. Also in 2019, the MLB leader in IP was Justin Verlander, whose 223.0 scales to 82.2 over a 60 game season. These numbers, 82.2 IP and 57.5 run prevention in comparison to league average (which I will be calling “RP-“), will provide the foundation for determining the worth of an elite starting pitcher in 2020. I would like to be very transparent about the math I’m using in this process. Using a very simple estimator for runs above average, assuming the MLB ERA of 4.338 from the last three seasons, we can calculate how many fewer runs the top starter would allow than a league average starter using this formula:
RAA = (lgERA / 9 * IP) – (lgERA / 9 * IP * (RP- / 100))
So for the theoretical top starter designed earlier, this formula would read:
(4.338 / 9 * 82.6667) – (4.338 / 9 * 82.6667 * (57.5 / 100)) = 16.9343
Value is accumulated above replacement, however, not above average, and runs above replacement increase as innings do. The formula, again a simple, back of the envelope type one, will be:
RAR = RAA + ((0.43 * lgWAR) * lgR/W * (IP / lgIP))
Again, using league averages from the past three seasons and scaling from 162 to 60 games, this can be calculated. The league WAR (lgWAR) in a typical season is 1000, making it 370.37 in the shortened 2020. With 2017-19 as a reference, the entirety of the league (lgIP) will pitch 16070.1 innings. Additionally, the runs per win (lgR/W) in that time span has been 9.2838. Thus, the formula becomes:
16.9343 + ((0.43 * 370.37) * 9.2838 * (82.6667 / 16070.3333)) = 24.5399
So the elite starter’s value is 24.5399 runs. Could a reliever reach this value in 2020? Well, the 2019 relief pitcher with the best RP- was Kirby Yates, with a score of 28.5 (28 ERA-, 29 FIP-). In terms of IP, the leader among relief pitchers was Sam Gaviglio, whose 95.2 scale to 35.1 over 60 games. So this reliever’s RAR calculates out to:
((4.338 / 9 * 35.3333) – (4.338 / 9 * 35.3333 * (28.5 / 100))) + ((0.43 * 370.37) * 9.2838 * (35.3333 / 16070.3333)) = 12.1769 + 3.2508 = 15.4277
Even in a shortened season, the elite starter racks up about 10 more runs over replacement then the relief ace due to a gap of nearly 50 IP. Leaving the 24.5399 number for the starter, how many innings would the reliever have to pitch to close the gap, should the rates remain the same? This is essentially an algebra problem; if x = innings pitched, solve for x.
((4.338 / 9 * x) – (4.338 / 9 * x * (28.5 / 100))) + ((0.43 * 370.37) * 9.2838 * (x / 16070.3333)) > 24.5399
(4.338/9)x – (123.633/900)x + (1478.52963258/16070.3333)x > 24.5399
0.43663366943x > 24.5399
x > 56.2025
The reliever, despite having far superior rate stats, would need to pitch 21 more innings than the scaled leader for a 60 game schedule. This number is attainable, perhaps, by multi-inning pitchers coming out of the bullpen. Pitchers who aren’t restricted to the closer role, like the titular Drew Pomeranz, Tampa Bay’s Nick Anderson, and Seth Lugo of the incredible spin rate stand out, as does Jesús Luzardo should the A’s decide to use him as a relief pitcher. It is, however, highly unlikely.
But I’m, just for fun, going to ratchet things up a notch; in the short season, starters could post some utterly obscene rate numbers. The best ERA- among qualified starters in the 21st century belongs to Pedro Martinez from 2000, with a mark of 35. Randy Johnson the following year had the best FIP-, with 47. This best possible starter, by rates, has an RP- of 41. Keeping the 82.6667 IP from earlier, this monstrous starter (Tyler Glasnow is going to best those marks this year, by the way) the RAR would read out as:
((4.338 / 9 * 82.6667) – (4.338 / 9 * 82.6667 * (41 / 100))) + ((0.43 * 370.37) * 9.2838 * (82.6667 / 16070.3333)) = 23.5088 + 7.6056 = 31.1144
Using the rates from 2019 Yates like earlier, a reliever would have to pitch 71.1 innings (x > 71.2597) to reach the value of
Glasnow the hypothetical über elite starter. This number is absolutely unobtainable for a relief pitcher in 2020—save for maybe a Ross Stripling type swingman—as even starting pitchers will have trouble reaching that in about a dozen starts.
Sometimes, however, relievers randomly have incredible seasons. It’s possible that that could happen in 2020. Using the same time frame as with starters, the best ERA- in relief is 13 (2016 Britton) and the best FIP- 19 (2003 Eric Gagne). This averages to a RP- of 16. By this point the math is established enough that I’ll just give the answer, assuming the 35.1 IP from earlier. This level of run prevention for that amount of innings is worth 17.5565 RAR. To get to the the value of the 2019 leading starter, the reliever would have to pitch 49.2 innings, or 62.2 innings to get to the starting pitcher with best-of-the-century numbers. Even the lower of those two numbers extrapolates to 134 innings in a full season, which is, as I said earlier, possibly but very improbable.
I am very disappointed. I titled this article before working out all the calculations, thinking that Drew Pomeranz (or Nick Anderson) could have a Cy Young chance in a short season. So far, the math has not borne out what I wanted to see. My hopes appear dashed, so as a last ditch effort, I’m going to figure out what the relationship between volume and quality is in RAR. Put simply, I’m going to see how much better than a starter a reliever has to be to make up for the difference in innings.
The blue line represents a starting pitcher with the assumed 82.2 IP, while the red line is a reliever with 35.1. In this case, the independent (x) variable was RP-, while the dependent (y) is RAR. The y-value (RAR) of the relief pitcher at x=0 (RP-=0) is 20.2814. The first real x-value for the starter where y<20.2814 is 68.5. As the slope of the starter line is -0.3985 and of the reliever line is -0.1703, the value of the starting pitcher decreases about two and one-third times faster than that of the relief counterpart, meaning the reliever could have their RP- increase 7 points for every 3 in the starter while still having more value.
Yet this, as was mentioned, is only true if the RP- of the starter begins at 68.5, compared to 0 for the reliever. The last instance of a league-leading starter having a RP- over 68.5 was in 2016 (Corey Kluber, 74). Using the best RP- for a reliever in the 21st century, which was 16, and the 7:3 ratio, this still wouldn’t be good enough to make the relief pitcher more valuable than the starting counterpart.
In a final way of looking at this, I’ll put a graph of value where the x-variable is innings pitched, instead of RP-, using the RP- values of 57.5 and 28.5 from previously in this article.
Again, blue is starter, red is reliever, and the y-value is RAR. I consider the potential maximum for a relief pitcher this year to be 50 IP, and at that point y=21.8317. The starter crosses that mark at 73.2 IP, which a normal season would equate to 199 IP. It’s almost guaranteed to an elite starter will reach that amount, and getting a reliever to 50 IP is unlikely. Even 40 IP is pushing it, and at that point the starter would only need 59 IP. Anyway I can think of to slice it, the arm out of the bullpen falls short of the one taking the mound in the first inning. I’m sorry Pomeranz.