MASTER NOTES: Moving the Decimals

On the August 11 edition of the BaseballHQ Radio podcast, Todd Zola and I got into an energetic discussion of how easy it is to gain points in the ratio categories even this late in the season. His position was that it can be done, and it’s easier than you might think. My position was that that it’s not easy, because after 20 weeks, the ratio categories have established some pretty huge denominators.

Todd is smarter than me, and his university level math is miles ahead of my elementary skills. So the difference of opinion worried me.

I checked it out. As it turns out, we’re both right.

Let's look at a league where a fantasy team gets 50 innings per week, pretty normal for 5x5 leagues that count strikeouts because there’s more focus on starters.

After six 50-inning weeks, the team has 300 innings, and if you don’t understand why, your math is even more elementary than mine. And perhaps you should consider another hobby.

Anyway, let’s say the team has allowed 140 Earned Runs (ER), a 4.20 ERA. The owner calculates that nothing much will change and his projected ERA (pERA) won’t change. This owner wants to bring his pERA down to 3.95 because historically in this league, that will get the points he needs in the category.

He still has 1,000 future innings to work with. To finish at his 3.95 target, he needs a 3.88 ERA during those thousand innings.

Of course, a 3.88 ERA is already something of a big ask for a team whose staff so far has been one-third of a run worse than that. But the owner has multiple pathways. He might have a fine starter whose ERA to-date has been hammered by one bad start, and who can be counted on—as much as any pitcher can be counted on—to get back to form. If the owner has a surplus in another category, he can trade for a solid ERA performer. He might have a top starter coming back from the DL to replace an iffy replacement.

And in the latter two cases, he gets an “addition-by-subtraction” benefit just by getting rid of the bad innings of his worst pitcher. Dropping a starter projected to 140 innings and 4.80 ERA lowers the team pERA to 4.13, a seven-point improvement. Adding a 3.50 starter in his place cuts the pERA further, to 4.06.

In short, he has options.

But if he starts the process seven weeks later, those options have shrunk. At the All-Star break, he has only 650 innings left and because of the Curse of the Oversize Denominator (also the title of the worst Hardy Boys mystery ever), he needs a 3.71 ERA in those 650 innings. And 3.71 free-agent starters are about as common as reasonably priced ballpark nachos.

And at 20 weeks, he needs 300 innings at a 2.46 pace. Clearly his paths are greatly restricted—so restricted, it seems, as to be impossible. Even if he does manage to drop a 4.50 stiff for a 3.50 ace, his overall ERA drop from 4.20 to only 4.16.


These calculations rely on a few assumptions that are not going to be true in all, even most, instances. One such assumption is that the team needs to move by a full 25 points, from 4.20 to 3.95. But lots of leagues have ERA points available for smaller gains.

To test the numbers in a real-world case, I projected a current 15-team mixed experts league and then picked a team at random from that league. The team’s pERA was 4.205 (not far from the earlier example), worth seven points in the category.

But instead of setting a pERA target of 3.95, which would have jumped this team to 14 points, I just tested what would happen if this owner had swapped out his worst starter (Zach Davies) for Mychal Givens of BAL, a top-quality reliever from the league’s free-agent pool.

At the time, Davies’ projection was for 41 remaining innings at a 4.17 ERA pace. Givens projected 17 innings at a 3.17 pace. The team pERA fell to 3.985, a nice 4-point gain in the category. Even more impressive, the team pWHIP fell from 1.301 to 1.178, gaining the team a terrific 8 points there.

To be sure, the ratio gains were offset by losses in the counting stats—two points in wins and one in strikeouts—but the net was still +9 points, good for a jump of five spots in the overall.

It works!


A lot of this excellent outcome again depended on some factors that are not universally applicable:

  • The standings gaps were favorable in ERA and, especially, in WHIP
  • A net +9 will not always move a team five spots in the overall (in my league, +9 would barely jump me two spots) and
  • Givens’ Ks in his limited innings were not far short of Davies’ Ks in his, and the category gaps were again favorable.

Another hugely important factor here was that the example was a 15-mixed league, because such a league has an enormous free-agent pool, especially for LIMA-style relievers.

Sure enough, in an single-league format, it didn’t work as well.

I used my own team in Tout-AL, where I project to a 4.377 ERA, worth four points, and a 1.326 WHIP, worth five. I wondered what might happen if I dropped my worst pERA/pWHIP starter (Marco Estrada, 4.600/1.378) and acquired the best available free-agent reliever (Danny Barnes, 3.214/1.000).

The result was: Not much happened, and certainly I saw no progress in the standings.

My final decimals dropped to 4.355/1.321, improvements of 0.022/.005 in WHIP—not even close to moving me in those categories. I might have fared even worse, but I stayed put in wins, as the BHQ projection machine seems to be taking into account that every time Estrada starts, the Blue Jays’ offense takes the night off and the bullpen mistakes the occasion for batting practice. But I did lose a couple of spots in the Ks category.

Just to see, I also checked what would happen if I dropped all my starters and replaced them with lower-ERA/WHIP LIMA guys. I still didn’t move in the decimals and lost even more ground in Ks and wins.

(In my case, I could get eight points with eight net wins. And I see more chance of catching a hot streak in wins, which are way more luck-based, than in skillier categories like ERA and WHIP. And yes, I know “skillier” isn’t a word. But “truthiness” wasn’t a word, either, and Stephen Colbert turned it into $15-million a year!)

One last issue: with six weeks left in the season, any projection is prone to huge variability, and relief pitchers maybe the most variable of all because of their limited innings.

When I did the research for this report, teams had about 40 games left in the season. Based on 2016-17, in 40 Orioles games, Mychal Givens appears about 18 times. So I checked Givens’ ERA and WHIP for all the 18-appearance spans this season, to find now much variation there among the spans. It turns out acquiring Givens for 18 appearances could get an owner a 0.479 ERA and 0.532 WHIP, Givens' cumulative line from June 17 to Aug. 2. On the other hand, you might get the 4.932/1.644 bomb he dropped from April 26-June 6. Or something in between. 


The first lesson in all of this is that time is of the essence. In talking with Todd about this, I made the point about the large denominators, but I didn’t even think to mention the reinforcing effect of having so little time left to move the ratio. Unfortunately, it’s harder earlier in the season to know where you and the league stand in the categories.

Also, league format matters. Mixed leagues have deeper free-agent pools, especially the LIMA-type non-closing relievers who can help a team in the decimals. But in single-league formats, the best LIMA guys, the ones who have those gaudy 2.05/0.90 lines, are long-gone by this point—drafted, reserved or long since picked up to replace injured pitchers. The best available are the Danny Barnes types, 3.10/1.20 guys who can't move the needle. (Insert your own BALCO joke here.)

But the main lesson is that anyone looking for a category bump in the decimals needs to start by projecting the league and seeing how big the potential gains are and how wide the category gaps are. Like the man said, you gotta do the math.

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  For more information about the terms used in this article, see our Glossary Primer.