Robert **Dvorchak** wrote about the
**sharp rise in teenage Tommy John type ligament surgeries** for the March 6, 2005
*Pittsburgh Post-Gazette*. He describes a scene at the office of **Dr. James Andrews** of Birmingham, Alabama - the famous practitioner
of this procedure.

When the parents of a young pitcher with a damaged arm visit his clinic,
Andrews has them write on a chalkboard when the child started pitching, how many teams he's played for, what baseball camps
he attended, how much extra throwing he does in the back yard and other items pertinent to his pitching background. In extreme
cases, he found that youngsters are taking off only two weeks a year -- Thanksgiving and Christmas – while concentrating
exclusively on baseball.

"I point to that blackboard and tell them why their child is seeing me
for surgery. That's when the light goes on for them," Andrews said. "No 13-year-old should have that kind of wear and tear
on his arm."

Among his laundry list of recommendations to young pitchers are don't
throw a breaking pitch until you shave and don't try to push the speed readings on the radar gun. "I think the radar gun ought
to be eliminated in high school," Andrews said.

**Can we know what is a safe annual workload
for a pitcher?** There is still no definitive
answer. Experts in baseball statistics continue to come up with what they believe are useable rules of thumb and we think
we are on to something. However, exceptions are common. Some of the conclusions just don’t make complete sense. Other
baseball statisticians point to the flaws in the studies. Can we even agree that there is such a thing as a too heavy workload
for some pitchers? – or that younger pitchers are more vulnerable to overuse than those in their prime baseball years?

The work of Baseball Prospectus writers Jany **Jazayerli** and Keith **Woolner**
on **Pitcher Abuse Points **(PAP – the wear and tear caused by high pitch counts)
cannot be dismissed just because in 2004’s *The
Neyer/James Guide to Pitchers* the godfather of baseball stats **Bill James**
conducted 8 studies which blasted away at their theory. James used 7 different control groups. Each control group was strongly
outperformed by the pitchers identified as most abused! However, James used an old version of PAP that Jazayerli and Woolner
admitted was wrong. They feel they have made much better tests on their newest PAP formula. They claim and I see their points
that there were fallacies in James’ control groups despite his many attempts to perfect them. They make the point, which
I had forgotten, but was going to make here anyway: based on the way pitchers are used nowadays, the MLB community appears
to have heeded their warning. However, high pitch count abuse was dropping steadily before Jazayerli reported his study in
BP around 1999. Baseball Prospectus has PAP data going back to 1988. Twenty years ago, there were 60 pitchers with over 100,000 Pitcher Abuse Points for the season. In 2007,
that number dwindled down to two. The seasons with the steepest drops in PAP measured abuse among the 30 most abused pitchers
in Major League baseball were 1990 and 2001, although the last three years have had about as large a three year decline in
such abuse as any measured. Have pitching injuries been reduced over that time? If not, there could be other explanations
than PAP doesn’t matter.

Incidentally, those two pitchers with over 100K PAP in 2007 were Daisuke Matsuzaka and Carlos Zambrano.
This season it was just Tim Lincecum and C.C. Sabathia. Number three wasn’t even close. Roy Halladay had only 78,018
PAP.

Tom **Verducci** of *Sports
Illustrated* came up with the **Year-After Effect** which stated that any pitcher
25 years old or younger who exceeds any of his previous years’ workloads by more than 40 innings can be expected to
be headed for a downturn in his career. His March 04, 2003 article for SI.com stated:

The Year-After Effect is based
on a rule of thumb, not exact science. Body type, pitch counts, physical maturity, run support and other elements are important
components of the growth and evaluation of young pitchers. But as a rule of thumb, the Year-After Effect should grab the attention
of Kansas City and all organizations. Why? Over the previous
three years I identified 16 pitchers as high risks. Of those 16 pitchers:

15 wound up with worse ERAs

13 won fewer games

12 threw fewer innings

seven were put on the disabled list

their major league win total dropped
an average of 30 percent

Verducci doesn’t mention any control group in the study. Why wouldn’t a group of pitchers
who suddenly improved enough to increase their workload so heavily be expected to regress the following year? Regressing this
overwhelmingly does seem more than what you would expect.

**Bill James** gives us a clue of how much all pitchers normally declined over the course of their career in
that *Neyer/James Guide to Pitchers *article that tested Jazayerli & Woolner’s
PAP system. In terms of Win Shares, he found these average declines in pitchers of four different Win Share levels at four
different ages:

**Age 24 Age 27 Age 30 Age 33**

20 Win Shares 11% 41%
43% 14%

16 Win Shares 35% 40%
24% 23%

12 Win Shares 23% 22%
5% 32%

8 Win Shares
6% 18%
24% 30%

**Verducci** has since reduced red flag threshold to 30 innings. Is that a meaningful number? Phil **Birnbaum** in Sabermetric Research asks “…if
the starter set a new high, he's probably pitching well, which means he's giving up fewer hits, which means that he's not
throwing as many more pitches as the 30 inning figure would suggest.”

Without saying so explicitly that I could find, Verducci seems to have moved away from comparing
the new output with the previous pro high towards just the previous season.

Will **Carroll** of Baseball Prospectus has refined Verducci’s
rule of thumb even further (and renamed it “**the Verducci Rule**”). One
of the refinements he makes is taking the minor league innings out of the equation. In a guest column of the LoHud Yankees Blog by Peter Abraham in January of 2008, Carroll proposes an explanation, but practically admits it might be hogwash.

Why are minor league innings any different than major league innings? There
are only theories, but the best and most testable center around a selection bias. A pitcher good enough to go over 100 innings
in the major leagues is almost by definition a quality pitcher. We know that major league hitters are harder to get out than
minor league hitters, not to mention the stress of pitching in front of big crowds. The type of pitcher that can get over
100 innings in the majors is likely to be coasting through the minors on less than his best effort. He’s seldom taxed.
He’s seldom forced to bear down or throw long innings. Granted, we don’t know this is the reason why and mathematically
and physiologically, it shouldn’t be the case, but until someone can develop a working model for translation, we have
to simply ignore those minor league innings.

If you ignore Minor League Innings, how does any pitcher work his way up to 200 innings without
passing the Verducci threshold? That would take seven years. He would be a free agent before he ever gave his drafting team
a 200 inning season. There must a qualification to Carroll’s method that I am not aware of. Nor do I know the route
Carroll took to arrive at the conclusion that we are better off ignoring those Minor League innings. I’m sure it was
logical and methodical. Yet, it is so counter-intuitive, it needs to be confirmed by an independent study.

** **

Another controversial aspect of the Verducci Rule is the **age
at which a pitcher suddenly becomes less vulnerable** to a large increase in workload. Is it 25 as originally proposed by
Verducci or is it 23? This Baseball Prospectus study by Nate Silver and Will Carroll shows that pitchers suddenly become far less prone to injury at 23 years old.

** **

**What we really want to know is the optimal way of building
a productive starting pitcher. **The best way to solve
these mysteries would be to find similar pitchers who were handled differently and seeing which paths had more success. Unfortunately,
**identifying such a controlled grouping of pitchers is probably impossible**. No
two pitchers are alike and there are significant details about each pitcher that I have little or no idea about – such
as the smoothness and efficiency of their delivery, the amount of pitching they did before they went professional, how they
exercised, and what they ate and drank. Those things likely matter more than whether they increased their Major League pitching
load by 35 innings instead of 25 innings one year. Just the fact that two nearly identical pitchers were pushed at different
paces could indicate that one was deemed better suited to handle the extra workload due to some of these circumstances unknowable
to us.

Undaunted, I set out to see what I could see equipped with an Excel spreadsheet and Windows Explorer
tabs on Baseball Reference, Baseball Cube, FanGraphs, and a Body Mass Index Calculator from the National Heart Lung and Blood Institute. At my side was the *Neyer/James Guide
to Pitchers* and a library of *STATS Notebook*s and Sickels’ *Baseball Prospect Books *just to check each pitcher’s favourite weapons. Although, Will Carroll himself kindly
advised me to narrow my search, there were many burning inter-related issues to explore. I could not resist approaching them
together.

One contribution I set out to provide is an** improvement
in the data set selection**. Most studies start out with the pitchers who appeared on a most abused list. Others studied
pitchers selected from many decades ago when pitchers were used differently and our training knowledge was more primitive.
Another BP study began with active pitchers listed in a 1997 almanac who had accumulated 175 innings by the age of 22. That is mixing in almost
all the pitchers who started their major league careers at a young age in the mid 90s with only the most successful pitchers
who started their careers in earlier times. Furthermore, 175 innings by 22 would rule out the university guys and the late
bloomers. We want to know if we can identify any pitcher who has been overworked. I looked at all the pitchers who pitched
their first 162 inning season in any year from 1990-2005. 162 innings was chosen because I wanted to include all the pitchers
who were given a real shot at making it as a starter. 162 innings happens to be the ERA qualifying amount since expansion
began (except for strike years). I started in 1990, because too much about pitching has changed since the 80s. I ended in
2005, because we need some year-after results to measure.

Among other things, I looked at** three different
ways of measuring a pitcher’s largest jumps in innings pitched** and the gain or decline in usage after those jumps.
The first way is using the original Verducci method of comparing total innings from both Minor & Major Leagues and comparing
them to any previous season. Secondly, I looked at the more refined Carroll method of only comparing Major League innings.
Thirdly, I made my own rough rule of combining MLB and Minor League innings, but only counting largest jumps at predominantly
the Major League level. I further refined the Carroll’s and my methods by comparing one year’s inning total to
the previous year’s innings total if that was the pitcher’s previous high of the last three years. If it wasn’t,
I use the average of that previous year’s innings total with the higher innings total of the previous two seasons. You
may feel that is unfair to take this liberty with Carroll’s method, but a) I don’t know the precise details of
his method and b) I can’t imagine how it could be a significantly objectionable adjustment.

Note that I am comparing the same set of pitchers – not just the pitchers who had a particular
level of abuse by one measuring method or the other. Hence, neither method is getting more talented or more durable pitchers
than the other. Obviously, though, where the results differ will be with pitchers at different stages of their careers.

So far, I have only scrounged up the time to gather data for qualifying pitchers
whose last names begin with “A”, “B”, or “C”. **What
can these 53 pitchers tell us so far?** By just entering in the numbers by hand, I noticed that the Carter method of measuring
jumps in usage correlated to a precipitous decline in subsequent usage much stronger than the Carroll method. Verducci’s
original Year-After method falls somewhere in-between. Summarizing the data for these pitchers bears this out.

**
162+ IP in any season ‘90-‘05 **

**Abuse Avg. Avg. Yr. +1 Yr. +2**

**
****Measuring Age. Max Ing. Inning
Inning**

**Method MaxAb Increase
Increase Increase**

Carter (ignore max >3 yrs. old; MLB
level) |
25.6 |
51 |
-42.4 |
-66.7 |

Carroll ( “
“ “ “
& MLB innings only) |
24.5 |
123 |
-12.7 |
-30.0 |

Verducci (compared to prev. career max) |
22.8 |
51 |
-33.4 |
-20.3 |

I made all sorts of conjecture from this data. I refined the comparisons separating
the more highly prized pitchers from the fellows who were happy to crack a rotation (based on draft round, *Baseball America* Top 100 ranking and K:BB – HR9 in their first 162 inning season). I separated the pitchers
into age groups. I separated them into degrees of abuse. However, all the comparisons involving these three variations of
the Verducci Rule have an **underlying fault**. The data selected has a natural bias
against the Verducci method and in favour of the Carter method. That is because, the selection of pitchers for this study
is based on having a 162 innings season in the Majors and the Carter requires a predominantly Major League season, while the
Carroll method requires Major League innings.

As you can see from the Average Age of Max abuse, the Carter method generally comes
a year after they pitch enough in the Majors to be tallied for the Carroll method. That is mostly because starters are frequently
first called up at some point in the middle of a season – if not broken in as relievers. They may pitch somewhere between
80 and 150 MLB innings that first season. They might even pitch 60, go back to the minors and before returning to pitch 110
in the majors the following year, then 160+ in year three. In any case, after doing all the studies, thinking about them,
and writing about them, I realized the reason the Yr. +1 Inning Increase with the Carroll method is low is because it will
so frequently be followed by that 162 inning season that qualified them for this study.

The Verducci method is frequently a minor league season. Hence, that first 162 IP
season is often even further into the future. Hence, it is the one method where the decline in second year is less pronounced.
**Let’s call their first 162 IP season** **Y1**.
In fact, only one of the 53 pitchers had a maximum increase after his Y1. Bronson Arroyo’s logged an up-till-then career
high 179 IP in his Y1 – his first full season in the majors. The next year he jumped to 205 innings then almost 241
innings in Y1 + 2. Previous to Y1, Arroyo’s highest inning total in the Majors was 88, so Y1 is his max increase by
Carroll’s method of ignoring minor league innings. His usage greatly increased the two seasons which followed. However,
his max increase when you include minor league innings was two years later. That season was followed by a decrease in usage
(and performance) to 211 and 200 innings. Of course, a sample of one does not make a study.

By eliminating pitchers who had their largest Carroll jump before their Y1, we can,
at least, compare the Carroll and Carter methods. There were nine pitchers who had their largest Carroll jump on or after
their Y1 and on a different year than as measured using the Carter method. All nine did worse the year after their Carter
measured jump than after the Carroll measured jump. Eight of the nine did even worse relative to Carroll’s method two
years later. Combining those nine with all the others who had their max jumps after Y1 we get:

** pitchers w/ max jump > Y1**

**
****Abuse Avg. Avg. Yr. +1 Yr. +2**

**Measuring Age. Max Ing. Inning
Inning**

**Method MaxAb Increase
Increase Increase**

Carter (ignore max >3 yrs. old; MLB
level) |
25.4 |
50 |
-37.8 |
-64.7 |

Carroll ( “
“ “ “
& MLB innings only) |
24.5 |
132 |
-20.0 |
-38.7 |

At first glance these numbers are roughly in line with the normal James’ Win
Share decline chart I showed earlier. This puts the entire year-after effect into question.

**Age 24 Age 27 Age 30 Age 33**

20 Win Shares 11% 41%
43% 14%

16 Win Shares 35% 40%
24% 23%

12 Win Shares 23% 22%
5% 32%

8 Win Shares
6% 18%
24% 30%

The average number of innings pitched in Y1 of my test group is 194. Typically, a
194 inning pitcher will rack up about 9 or 10 Win Shares. However, many of those 194 innings includes minor league innings.
It is much more reasonable to estimate that these pitchers averaged about 8 Win Shares in their year of greatest abuse. Interpolating
James’ chart at the ages of their highest abuse according to our methods (24-26) we should expect about 6-14% decline
amongst such a group of pitchers. Converting my data to align with this chart, the Carter method of measuring abuse showed
a 19½% decrease in these pitchers during the first year after their max abuse, then a 33% decrease in the 2^{nd} year
after. The Carroll method showed just what you would expect from any 8 Win Share pitcher the year after his age 24 or 25 season
(not just abused ones) – a 10% decline, then a 20% decline in the second year. There you have my evidence that **minor league innings do matter in measuring abuse by yearly IP increases.**

**What about the age nexus?** Carroll and Verducci only look at younger pitchers, while I don’t look
at any cut-off age. Most of the maximum seasonal inning increases in this study occurred when the pitcher was 23 years or
older. As mentioned before, Silver & Carroll suggest that a pitcher’s injury nexus occurs before the age of 23.
Tom Verducci only red flags pitchers 25 and under. If I use the well researched 22 and under cut off, my list, so far, would
include only four pitchers (Rick Ankiel, Kevin Appier, Steve Avery and Mark Buehrle) who had career high jumps by all three
measures before the age of 23. Extending the cut-off age to 23 allows us to add 7 more arms – hopefully enough to give
the data some significance: Wilson Alvarez, Andy Benes, Jeremy Bonderman, Bartolo Colon, Steve Cooke, and Nate Cornejo.

**
**** 13 youngest pitchers
in study**

**Abuse Avg. Avg. Yr. +1 Yr. +2**

**Measuring Age. Max Ing. Inning
Inning**

**Method MaxAb Increase
Increase Increase**

Carter (ignore max >3 yrs. old; MLB
level) |
22.4 |
48 |
-32.5 |
-65.0 |

Carroll ( “
“ “ “
& MLB innings only) |
22.0 |
142 |
-23.0 |
-44.0 |

As we expected, the **year-after effects are stronger across
the board**. However, the increases in decline are so** **miniscule that I am **not convinced it is significant** – certainly not with these few pitchers. Rationalizing
this result, injuries and decline from abuse are likely off-set by the increases in productivity that healthy pitchers this
age normally have. Perhaps, younger pitchers recover from their injuries more strongly as well.

What if we go back to the larger test group; then narrow the list down to **pitchers who have not had a large jump in innings?** None of the pitchers in the “young group” were
spared a jump of less than 40 innings at some point in their career – and that’s not even considering Carroll’s
MLB IP only method. In Verducci/Carter jumps, Appier (40/37) and Bonderman (32/45) were the young pitchers closest to having
no large jumps. Verducci and Carroll both raise the red flag at jumps of 30 or more innings. The pitchers in the original
larger group who never experienced a Verducci/Carter jump of more than 30 innings are:

Rene Arocha – converted to relief

Joe Blanton – held to a max increase of 29 innings as both a
23 year old to no ill effect and as a 26 year old after which he pitched 15 fewer innings. That was this past season where
he struggled mid season with Oakland, but revived himself in Philadelphia pitching effectively all the way through the World Series.

Ricky Bones – appears to have had a relatively healthy career.
Except for one lucky season, which actually included a decrease in innings from his previously established level, he just
wasn’t a very good pitcher.

That’s it! Depending on how far off my estimates are of various pitchers’ amateur workloads,
these three might also qualify:

Rick Ankiel – after 7 Midwest League starts was promoted to
the high A Carolina League for 21 more starts logging 161 innings as a tender young 18 year old super prospect. Sure, he is
Floridian and may well have pitched more than the estimated 125 innings in a previous year, but 18 is young to push a pitcher,
isn’t it? You know his story, in the Majors by the end of the following season, 175 innings of 3.50 ERA in his first
full season, then three appearances in the play-offs on top of that. Voila: severe arm troubles, Tommy John surgery, etc.,
and eventually a new life as a starting MLB outfielder!

Jason Bere was a year and three months older than Ankiel when he pitched
his first year in pro ball – which consisted of a similar 27 starts and 163 innings. He attended a Community College
after high school in his native state of Massachusetts.
He may not have been established himself at the 125 inning level as teenager. Early in Bere’s third pro season he established
himself as a fine starter and continued that success into his first full MLB season. After that, he struggled to stay in the
majors for the rest of his career.

Rheal Cormier pitched 170 innings his first professional season. Considering
Cormier is from New Brunswick (eastern Canada)
and came south to pitch for Community College of Rhode Island, 125 innings could be a very generous estimate of his previous annual workload.
Otherwise, it is worth noting that Cormier’s highest jump in innings came at age 29 – a mere 30 innings. He missed
almost all of the next season, but the left-hander came back as a reliever and lasted in the Majors until he was 40.

**
max increase < 30 IP**

**Abuse Avg. Avg. Yr. +1 Yr. +2**

**Measuring Age. Max Ing. Inning
Inning**

**Method MaxAb Increase
Increase Increase**

Carter (ignore max >3 yrs. old; MLB
level) |
24.2 |
25 |
-55.8 |
-58.4 |

** **

There was no point in including my interpretation of Carroll’s method in this box of the
least abused pitchers. The young pitcher with the smallest max jump in Major League innings only was Brian Bohanon with a
jump of 49 innings.

I’m not sure what to make of this particular test. Unexpectedly, the year-after effect increased
in the first year. **Let’s chalk this up to a small sample size.** Rheal Cormier
missed almost the entire season after his maximum jump. If you have any other suggestions besides “keep trying with
more data”, please let me know.

**Conclusion: **My tests here indicate Minor League IP do indeed count when assessing a pitcher’s likely
decline in innings over the following two seasons based on a large increase in innings. Before I continue with the numerous
tests regarding optimal starting pitcher usage, I would like to settle this point. Hence, I will pause in my study here until
I hear from Will Carroll, Nate Silver, or anyone in the Sabermetric community who reads this.

In the meantime, I found no strong indication of a magical 30+ inning jump or age 23 threshold,
but more pitchers need to be studied. A younger pitcher’s greater fragility may be off-set by his greater natural progress
and/or his greater ability to recover from injury.

This entire theory of identifying likely abused pitchers by a large jump in innings may be exaggerated.
It may have been a considerable phenomena in the past, but the in the pitchers I have looked at so far since 1990, it is not
shouting. Perhaps, most Major League teams these days are already leery of overworking their pitchers in all manners. They
do not let it happen to pitchers they feel cannot handle the additional workload.