How to Account for Pitcher Batting
especially OPS+ -adjusted ERA+

22.[Wes Ferrell]
Posted by Chris Cobb   on  January 25, 2005 at 12:42 PM

I'd venture to suggest that Ferrell's real value when he was pitching, expressed as an ERA+ rate
stat, was probably 8-15 points higher than his actual ERA+. This could be estimated more
precisely with a bit of statistical analysis.

25.[Wes Ferrell]
Posted by OCF   on  January 25, 2005 at 02:30 PM 

I'd venture to suggest that Ferrell's real value when he was pitching, expressed as an ERA+ rate
stat, was probably 8-15 points higher than his actual ERA+. This could be estimated more
precisely with a bit of statistical analysis.

When I tried to account for Ferrell's offense, as I reported in the post copied by Tiboreau as
the first portion of #8, above, the effect on his equivalent W-L record was the same as raising
his effective RA+ by 10 points, from 116 to 126. The W-L record went from 167-124 to 179-113.

Any quality-of-opponent differential estimate would be on top of that. Before trying that, I'd
like to have it on a year-by-year basis for most of the important years of his career.

28.[Wes Ferrell]
Posted by jimd   on  January 25, 2005 at 07:24 PM (#1102388)

> When I tried to account for Ferrell's offense, ... the effect on his equivalent W-L record was
the same as raising his effective RA+ by 10 points, from 116 to 126.
<

I re-calculated the career ERA+ for Dean and for Ferrell as follows: Each positive BRAR (Batting
Run Above Replacement) created cancels out an Earned Run given up; Each negative BRAR (or
batting run below replacement) was equivalent to giving up an additional Earned Run.

Dean was -27 BRAR (.193 EQA, worse than a replacement hitter, somewhat below average for a
pitcher); his ERA+ moves from 130 to 125. Ferrell was 50 BRAR (.266 EQA, an above average major
league hitter); his ERA+ moves from 117 to 122.

This appears to verify the 10 point shift noted by OCF.

29.[Wes Ferrell]
Posted by OCF  on  January 25, 2005 at 08:09 PM (#1102435)

Right, jimd. Your calculation differs from mine in choice of zero point, but arrives at the same
place. I would say that pitchers are supposed to be bad hitters and left Dean's ERA+ alone (or
maybe -1), while adding +10 to Ferrell instead of +5. The overall effect is approximately the
same.

I should also do this for Red Ruffing, although we've got until 1953 before that's an
issue. (And I've got to worry about Ruffing's defensive support as well.)

30.[Wes Ferrell]
Posted by jimd  on  January 25, 2005 at 08:18 PM (#1102444)

> Your calculation differs from mine in choice of zero point

Agreed. I was doing something quick and dirty with the number available from BP and
baseball-reference.

1944 Ballot Discussion
25.
Posted by Brent   on  January 26, 2005 at 12:06 AM (#1102879)

In # 19, Ardo wrote:
> From these data, I rank the pitchers (definite HoM) Lyons-Rixey- (doubtful HoM)
Faber-Grimes-Ruffing.  
<

Don't overlook their hitting.

OPS+
Faber 10
Grimes 58
Rixey 22
Ruffing 81
Lyons 45

I figure that 7 points of OPS+ is worth roughly 1 point of ERA+. (If you think this number is
off, please let me know. I think it's close to what jimd and OCF have come up with on the
Ferrell thread.) If we take an OPS+ of 40 as our reference point for an "average" pitcher (I
admit that I don't know what the actual average for this period was), and adjust each pitcher's
ERA+ up or down based on how their OPS+ deviates from 40, this is what I get:

ERA+ adjusted for batting
Faber 115
Grimes 110
Rixey 112
Ruffing 115
Lyons 119

Other factors such as defense also affect the relative rankings as well.

51.
Posted by jimd   on  January 26, 2005 at 10:43 PM (#1104908)

> Ferrell = Wilbur Cooper.

If you insist that ERA+ is everything when measuring pitchers, then you probably will come to
that conclusion.

NRA is BP's pitching stat that includes all runs (not just earned runs) and is normalized for
league context and park. NRA+ is 4.50/NRA (analogous to ERA+). DERA adjusts NRA for defense
(DERA+ is then 4.50/DERA). BDERA+ then adjusts for hitting too (on the 7 points of OPS+ to 1
point of ERA+ discussed elsewhere).

NRA+ -> DERA+ -> BDERA+
114 -> 111 -> 115 Cooper
114 -> 115 -> 125 Ferrell
141 -> 138 -> 135 Grove

As a hitter, Cooper was a bit above average (61 OPS+), but had the good fortune of playing for
some Pirate teams that featured a very good defense. The two effects largely cancel each other
out.

Ferrell played in front of below average defenses for his career, and was quite the
hitter. These are significant bonuses to his NRA+.

Grove also played in front of good defenses, and couldn't hit his way out of a pinata (OPS+ of
6). Both effects impact his gaudy pitching stats, but nowhere near enough to remove him from
pending first-ballot status.

Ferrell is about midway between the two, and given the texture of his career (8 year prime with
bad comeback attempts) should appeal to those who like a good peak/prime (long career voters may
prefer more total).

52.
Posted by Paul Wendt  on  January 26, 2005 at 10:52 PM (#1104924)

Brent #25
> I figure that 7 points of OPS+ is worth roughly 1 point of ERA+. (If you think this number is
off, please let me know. I think it's close to what jimd and OCF have come up with on the
Ferrell thread.) 
<

1:7 is too much credit for the pitcher's batting unless he works as a pinch-hitter. Indeed, 1:10
is too much if he bats ninth and doesn't pinch hit.

The OPS+ scale is comparable to ERA+. A pitcher who bats ninth, completes every game, and is
never removed for a pinch-hitter in a game-winning rally at home-- gets 10% of team plate
appearances in his games, so 1:10 is about the theoretical extreme.

If the team averages 40 plate appearances (4.44 per man; 4.00 for the ninth spot) and the
pitcher averages 3 plate appearances, then 1:13.
[That is the starting pitcher's share of run support for the whole game,
which is relevant to Chris Jaffe's RSI but not to adjustment of ERA+ -Ed.]

Koufax averaged 3 plate appearances in 1965-1966, completing 2/3 of his games in a low run
environment. It appears that Gomez averaged 3+ PA in 1936, completing 1/3 in a high run
environment.

This model presumes that OPS+ incorporates sacrifice bunting seamlessly, which it doesn't, so
the precision is an illusion even if my reasoning is correct.

53.
Posted by Paul Wendt  on  January 26, 2005 at 11:08 PM (#1104948)

Oops. Gomez averaged 2.66 PA in 1936. His career average was 3+ PA, completing 1/2 of his
games. 3.05 PA per start if 1.00 PA per relief game (3.20 per start if he never batted in 48
relief games). The Yankees averaged about 40 PA, so 1:13 is about right for Gomez.
[No, as above. -Ed.]

54.
Posted by jimd  on  January 26, 2005 at 11:09 PM (#1104953)

> The OPS+ scale is comparable to ERA+.

That's not true. A pitcher with a 120 ERA+ gives up 20% less runs than an average pitcher. A
batter with a 120 OPS+ has an OPS which is about 10% greater than an average hitter.

The OPS formula is: (BA/LgBA + SP/LgSP)*100 - 100
Somebody who is 10% better at each component would then be:
(1.10+1.10)*100 - 100 = 120.

Adding that factor of two, a 1:14 reduces to 1:7

56.
Posted by jimd  on  January 26, 2005 at 11:24 PM (#1104982)

[using 1:7]
NRA+ -> DERA+ -> BDERA+
110 -> 111 -> 110 Rixey
114 -> 111 -> 115 Cooper
113 -> 115 -> 117 Lyons
116 -> 110 -> 117 Mays
123 -> 124 -> 121 Coveleski
114 -> 115 -> 125 Ferrell
123 -> 129 -> 126 Vance
127 -> 129 -> 131 Dean
141 -> 138 -> 135 Grove

Mays' very good hitting is mostly canceled out by his fortunate fielding situation. Vance's poor hitting removes half of his large fielding adjustment. Dean and Lyons gain small positives from both adjustments.

57.  
Posted by Paul Wendt on January 27, 2005 at 02:05 AM (#1105300) 

I wrote, "The OPS+ scale is comparable to ERA+."

It's true, and it's the rationale for the definition of OPS+.

Pete Palmer chose Adjusted Production [once PRO/A, now OPS+] the sum of relative OnBase and relative Slugging rather than relative (OnBase + Slug) in order to track scoring routhly.

As ERA+ tracks scoring.

So that a team with ERA+ 105 and OPS+ 95, or vice versa, scores about as many runs as it allows.

--
jimd #54
> That's not true. A pitcher with a 120 ERA+ gives up 20% less runs than an average pitcher.
[16.7Actually, 100/120 ==> .833 ==> 16.7% less]
A batter with a 120 OPS+ has an OPS which is about 10% greater than an average hitter.
<

Yes, which produces about 20% more runs.

> The OPS formula is: (BA/LgBA + SP/LgSP)*100 - 100
> Somebody who is 10% better at each component would then be:
> (1.10+1.10)*100 - 100 = 120.

Yes, and would add about 20% more runs to his team offense.

67.
Posted by jimd   on  January 27, 2005 at 02:43 PM (#1106208)

> Pete Palmer chose Adjusted Production [once PRO/A, now OPS+] the sum of relative OnBase and
relative Slugging rather than relative (OnBase + Slug) in order to track scoring routhly.  
<

Having never done any studies of this, I have to concede that this is most likely true. Playing
around with the OPS+ formula, I see that it linearly tracks the following:

(OBP * LgSLG) + (SLG * LgOBP)  [as corrected by David Foss]

This certainly looks like a compromise formula between vanilla OPS and James' Runs Created.

I stand corrected, and will reexamine the batting portion of the BDERA+ calculation.

68.
Posted by DavidFoss   on  January 27, 2005 at 03:04 PM (#1106242)

You're right in that its like RC in that its OBP times SLG. But also note that its fortuitously
"lineup-adjusted"... it eliminates some of the batting-yourself-in that can happen with RC with
great players.

91.
Posted by Paul Wendt   on  January 28, 2005 at 02:45 PM (#1108688)

I wrote and jimd replied, in part:
> > Pete Palmer chose Adjusted Production [once PRO/A, now OPS+] the sum of relative OnBase and
relative Slugging rather than relative (OnBase + Slug) in order to track scoring routhly.

> Having never done any studies of this, I have to concede that this is most likely true.
<

I'm not sure it was based on any empirical study of OPS+, only on the empirical result that
OnBase*Slug tracks runs better than OnBase+Slug. Hence OPS+ is defined to increase by 10% when
OnBase increases by 10% or Slug increases by 10%.

104.
Posted by jimd   on  January 28, 2005 at 10:28 PM (#1109840)

Using Paul Wendt's suggested ratio of 1:13, here is an update for BDERA+, with a few more
pitchers added. The calculations are still crude (I'd really prefer having pitching BRAAP which
I could add to PRAA), though I don't think a more precise calculation will change things by more
than a point either way (two points tops).

[using 1:13]
NRA+ -> DERA+ -> BDERA+
102 -> 105 -> 107 Grimes
111 -> 107 -> 107 Welch
110 -> 111 -> 110 Rixey
113 -> 113 -> 111 Faber
114 -> 111 -> 113 Cooper
116 -> 110 -> 113 Mays
123 -> 114 -> 114 Keefe
103 -> 110 -> 114 Whitney
113 -> 115 -> 115 Lyons
119 -> 116 -> 115 McGinnity
120 -> 114 -> 115 Radbourn
125 -> 117 -> 117 Clarkson
116 -> 118 -> 119 Griffith
128 -> 119 -> 119 Brown
135 -> 121 -> 121 Nichols
129 -> 123 -> 121 Joss
114 -> 115 -> 121 Ferrell
123 -> 124 -> 122 Coveleski
118 -> 122 -> 122 Rusie
123 -> 124 -> 123 Waddell
126 -> 124 -> 126 Mathewson
123 -> 129 -> 127 Vance
132 -> 129 -> 128 Young
127 -> 129 -> 130 Dean
132 -> 132 -> 132 Alexander
141 -> 138 -> 136 Grove
136 -> 138 -> 141 Johnson

Also, the early 1880's guys are at a disadvantage in any ERA+ based calculation, due to the
shallow pool in which they competed. There were no 4th/5th starters, just 1st and 2nd starters,
so there was less room for variation in the stat (assuming that the NL took the best pitchers
available).

109.
Posted by Paul Wendt   on  January 29, 2005 at 03:05 PM (#1111299)

jimd #[10]4
> Using Paul Wendt's suggested ratio of 1:13, here is an update for BDERA+, with a few more
pitchers added. 
<

complete game rate approaches 100%. Radbourn's batting was more important that 1:13, even if he
never pinch hit or batted eighth.

I used Lefty Gomez because Lou Gehrig's record shows ~how many times the Yankees batted around
the 4th spot in the order, minus 5/9 per game is a good estimate for the 9th spot. My estimates
use a uniform rate of team outs by plate appearance, so that each batting position makes the
final out in 1/9 of team games. That is easy to improve with a spreadsheet simulation but not
easy to improve in a closed form, I think.

Given team-season plate appearances PAt, my estimate for the jth spot in the batting order is

PAj/G ~= PAt/G/9 + (5-j)/9

PAj ~= PAt/9 + G(5-j)/9

111.
Posted by Brent   on  January 29, 2005 at 09:49 PM (#1111893)

Paul Wendt # 52:
> 1:7 is too much credit for the pitcher's batting unless he works as a pinch-hitter. Indeed,
1:10 is too much if he bats ninth and doesn't pinch hit.

> The OPS+ scale is comparable to ERA+. A pitcher who bats ninth, completes every game, and is
never removed for a pinch-hitter in a game-winning rally at home-- gets 10% of team plate
appearances in his games, so 1:10 is about the theoretical extreme.

> If the team averages 40 plate appearances (4.44 per man; 4.00 for the ninth spot) and the
pitcher averages 3 plate appearances, then 1:13.
<

My reasoning for 1:7 was something like this. I looked at the ratio of BFP to PA for several
pitchers. For example, Grimes had 17959 BFP, 1685 PA, 1:10.7; Rixey had 18754 BFP, 1667 PA,
1:11.3. So if we were looking just at these two pitchers, we'd guess that 11 points of OPS+ is
equal to 1 point of ERA+.

However, the denominator of OPS is PA, while the denominator of ERA is outs (actually 27*outs),
so I figured we also need to take account of the fact that a pitcher who makes fewer outs per PA
is providing his teammates with more opportunities to bat and score. So I added the extra outs
avoided times the league runs per out. For example, Rixey made 1322 outs, whereas Grimes made
only 1236, a difference of 84 outs, even though Grimes had 18 more PAs. (Note that this factor
is really should depend just on the OBP, rather than on OPS - a pitcher with a low OBP and high
SLG wouldn't be saving outs.) Figuring that during their careers each out was worth about
.17-.18 runs , I solve for the ratio that would count the total runs (directly and indirectly
through avoiding outs) and it comes to about 1:8. Is the effect of avoiding outs already
included in the OPS factor? I don't think so, but some of you may know more than I do.

So that gets us to 1:8, but why did I propose 1:7 in my earlier post? In retrospect, I think it
was a mistake, but in my earlier calculation I included several better hitting pitchers. The
better hitting pitchers tended to get more PA per BFP. We've already seen that with Rixey (22
OPS+; 1 PA: 11.3 BFP) and Grimes (58 OPS+; 1 PA: 10.7 BFP). It's even more pronounced with the
really good hitters. For Ruffing (81 OPS+) the ratio is 1 PA: 8.9 BFP, and for Ferrell (100
OPS+) it is 1 PA: 8.6 BFP. I had taken an average over a group containing both good and bad
hitters, giving me a ratio of 1:10 (rather than the 1:11 I mentioned above, based on Rixey and
Grimes). Now I think the ratio should vary to reflect the fact that the really good hitters get
more PAs. Of course, that complication makes it harder to use a ratio as a simple
back-of-the-envelope calculation.

So, if OPS+ already takes account of the effects of outs, than I'd think a ratio of about 1:11
would be appropriate for "ordinary" hitting pitchers, and maybe 1:9 for those really good
hitters with OPS+ greater than 75. But if OPS+ doesn't take account of the effects of outs, then
ratios of 1:8 and 1:6 may be more appropriate.

116.
Posted by Joe Dimino   on  January 30, 2005 at 12:30 AM (#1112302)

"The better hitting pitchers tended to get more PA per BFP."

Don't forget Brent that many of those extra PA are as PH or in some cases (especially pre-1893)
as a position player. So the replacement level for those extra PA is higher than it typically is
for a pitcher.

I've accounted for this in the replacement level I use in Pennants Added, pitchers that played
in the field or were used as PH have those PA estimated and factored in as being at position
player replacement level. Normal pitcher PA have a replacement level of 0 WS. Note this isn't
'0', it's roughly .200. Pitchers below the 'marginal offense' level are docked in their pitching
WS (Bill James' decision, not mine). So I treat all offensive WS for pitchers as being above
replacement level.

118.
Posted by Joe Dimino  on  January 30, 2005 at 07:19 AM (#1112952)

"So I treat all offensive WS for pitchers as being above replacement level."

Just to clarify, all offensive WS for pitchers that didn't play the field or pinch-hit is what I
meant.

122.
Posted by Paul Wendt   on  January 30, 2005 at 10:45 AM (#1112997)

Brent's approach isn't quite right, but I see that mine isn't quite right, either.
[Brent's ratio, PA:BFP, is the way to go for a quick estimate. -Ed.] 

I stand by 1:10 as the practical maximum share of Team PA while he has pitching responsibility,
for a pitcher who bats ninth --since 1/10 is the approximate share of PA for the ninth spot. But
the practical minimum for a good pitcher is not much less, probably more than 1/12 for a full
season. Sure, 1/18 for a pitcher who is always removed for a pinch-hitter on the second PA for
the ninth spot; 1/13 for a pitcher who is always removed on the third PA. But that is
impractical.

The relative impact of pitcher batting on run scoring is less than the pitcher share of Team PA,
because the pitcher bats when less is at stake: first, because the 8th batter is relatively
weak; second, because pinch-hitter is more likely when more is at stake.

125.
Posted by Paul Wendt   on  January 30, 2005 at 11:34 AM (#1113027)

That is, a weak-hitting pitcher does not diminish Team run scoring as much as he diminishes Team
OPS+. The pitcher's sacrifice bunts probably amplify the difference between impacts; further
diminish the impact of weak pitcher batting on run scoring.

--
Lefty Gomez, OPS+ = -7
pitched in 100% of his mlb games. He sacrified in 68 of 1024 plate appearances, almost 7%.

Ted Lyons, OPS+ = 45
pitched in 85% of his mlb games, fielded another position in 1 game, and evidently served as
pinch-hitter or runner in 15% of his games (110g). He sacrified in 83 of 1726 PA or 5%.

Red Ruffing, OPS+ = 81
pitch 71%, field 3 games, ph/pr 29% (255g).
SH/PA = 43/2083 = 2%

Wes Ferrell, OPS+ = 100
pitch 68%, field 2%, ph/pr 29% (161g).
SH/PA = 40/1345 = 3%

129.
Posted by Paul Wendt   on  January 30, 2005 at 02:05 PM

1.
Per jonesy, the sacrifice bunt stats in #125 may be corrupted by on and off distinction between
bunts and flies in the historical record.

2.
>>
jimd #54
A batter with a 120 OPS+ has an OPS which is about 10% greater than an average hitter.

Paul Wendt #57
Yes, which produces about 20% more runs.

David Foss #68

[OPS+] is like RC in that its OBP times SLG. But also note that its fortuitously
"lineup-adjusted" ... it eliminates some of the batting-yourself-in that can happen with RC with
great players.

Paul Wendt #125
That is, a weak-hitting pitcher does not diminish Team run scoring as much as he diminishes
Team OPS+. The pitcher's sacrifice bunts probably amplify the difference between impacts;
further diminish the impact of weak pitcher batting on run scoring.
<<

My observation and David's are two may be two sides of the same coin.  

Anyway, a 20% difference in player OPS+ such as {120 100} in #54-57 produces about 20%
difference in runs at the margin (for small differences) and within a uniform lineup.

-- 3. --
In Wes Ferrell #22-30, OCF and jimd discussed accounting for a pitcher's batting by
adjusting his pitching record. That was continued by Brent, me, and others in 1944 Ballot
Discussion, focusing on the adjustment of ERA+ for the pitcher's OPS+. I have extracted 
that "thread" from these boards and posted it on the web, for HOM reference only.

How to Account for Pitcher Batting, espy OPS+ -adjusted ERA+ (this page)