# Inverted records

One thing I always enjoyed about reading Bill James’ books back in the day was their sense of fun. Much of what he presented had deep meaning that continues to influence research and researchers today. Some of it, though, was just plain fun.

On page 186 of The Bill James Baseball Abstract 1987, he introduced something called “Inverted Records,” which attempted to represent a hitter’s output as a pitching line. Why? Well, why not?

James conducted his exercise on the 1986 Cleveland Indians and extended it to include several other prominent players of the day. His method was simple:
For runs, use runs created
For earned runs, multiply runs by .9. {/exp:list_maker}James had a way to calculate wins and losses based on the Pythagorean theorem, but that seemed like too much effort so I didn’t bother. He also included games, complete games, and shutouts based on… something in a black box, I don’t know. I didn’t find those compelling enough to figure out either.

James didn’t explicitly state how to calculate innings, but I’m assuming it’s outs divided by three. That’s what I did, anyway.

Let’s walk through a quick example. We’ll use one of my favorite players, Adrian Gonzalez, and translate his 2009 hitting stats into a pitching line.

First we take the necessary inputs:

```Outs  RC   H  BB  SO
428 124 153 119 109```

And turn it into this:

```   IP   H   R  ER  BB  SO  ERA SO/9
142.2 153 124 112 119 109 7.07 6.88```

That’s an awful pitching line. As James notes, “Obviously, if the hitter is effective, then the pitchers facing him are not effective.” In the case of Gonzalez, it’s like every pitcher he faced had a 7.07 ERA, which sounds about right.

We’re having fun, right? But it’s impossible have too much fun, so let’s go a little further. Let’s see if we can find a pitcher that produced this actual line, or something close to it. A quick spin of Baseball-Reference’s Play Index tool spits out the following:

```Player          Year    IP   H   R  ER  BB  SO  ERA SO/9
Adrian Gonzalez 2009 142.2 153 124 112 119 109 7.07 6.88
Jason Bere      1995 137.2 151 120 110 106 110 7.19 7.19```

Kinda spooky, huh? You could, if you were so inclined, say something like, “Adrian Gonzalez hit pitchers in 2009 like they were all Jason Bere in 1995″ and be pretty well on the mark. Useful? I dunno, maybe. Fun? Most definitely.

Let’s try another. How about the highest OPS+ season of all time? Barry Bonds 2002:

```Outs  RC   H  BB SO
262 208 149 198 47```

And the translated line:

```  IP   H   R  ER  BB SO   ERA SO/9
87.1 149 208 187 198 47 19.27 4.84```

That’s ridiculous. Only one man in MLB history has reached double digits in innings pitched with an ERA over 19:

```Player      Year   IP   H   R ER  BB  SO   ERA SO/9
Barry Bonds 2002 87.1 149 208 187 198 47 19.27 4.84
June Greene 1929 13.2  33  32  30   9  4 19.76 2.63```

Obviously the sample is much smaller (because who in their right mind would keep sending a guy out to the mound that makes everyone look like the greatest hitter ever?), but you get the idea.

On the flip side, here’s our favorite outmaker, Bill Bergen (1909 version):

```Outs RC  H BB SO
314  9 48 10 ??```

We don’t have Bergen’s strikeout numbers for the season in question, but we don’t need them. That is pure domination, the likes of which hasn’t been seen in quite some time:

```Player           Year    IP  H R ER BB SO  ERA SO/9
Bill Bergen      1909 104.2 48 9  8 10 ?? 0.69   ??
Dennis Eckersley 1990  73.1 41 9  5  4 73 0.61 8.96```

How about a strikeout king? Let’s try Mark Reynolds, who broke his own single-season record in 2009:

```Outs  RC   H BB  SO
448 113 150 76 223```

That translates to this:

```   IP   H   R  ER BB  SO  ERA  SO/9
149.1 150 113 102 76 223 6.15 13.44```

Pitchers who combine the ability to surrender copious amounts of runs with the ability to put the ball past hitters are rare, but they do exist:

```Player          Year     IP  H    R ER  BB  SO  ERA  SO/9
Mark Reynolds   2009  149.1 150 113 102 76 223 6.15 13.44
Derrick Turnbow 2006   56.1  56  51  43 39  69 6.87 11.02```

To take our fun to even higher levels, let’s try a career record. In the interest of saving space, I’ll just provide the translated lines for the Hall of Fame’s newest member, Andre Dawson:

```Year      IP    H    R   ER  BB   SO  ERA SO/9
1976    23.0   20    7    6   5   13 2.35 5.09
1977   131.2  148   82   74  34   93 5.06 6.36
1978   160.2  154   80   72  30  128 4.03 7.17
1979   165.0  176   91   82  27  115 4.47 6.27
1980   142.2  178  105   95  44   69 5.99 4.35
1981    96.2  119   83   75  35   50 6.98 4.66
1982   151.0  183  106   95  34   96 5.66 5.72
1983   162.1  189  113  102  38   81 5.66 4.49
1984   141.2  132   65   59  41   80 3.75 5.08
1985   139.1  135   67   60  29   92 3.88 5.94
1986   129.0  141   75   68  37   79 4.74 5.51
1987   154.1  178  111  100  32  103 5.83 6.01
1988   145.2  179  100   90  37   73 5.56 4.51
1989   113.0  105   55   50  35   62 3.98 4.94
1990   129.0  164  101   91  42   65 6.35 4.53
1991   143.2  153   79   71  22   80 4.45 5.01
1992   137.2  150   75   68  30   70 4.45 4.58
1993   120.1  126   57   51  17   49 3.81 3.66
1994    80.0   70   30   27   9   53 3.04 5.96
1995    59.1   58   29   26   9   45 3.94 6.83
1996    14.1   16    7    6   2   13 3.77 8.16
Total 2540.1 2774 1518 1368 589 1509 4.85 5.35```

As it happens, there is a pitcher whose career qualititative numbers match up nicely with Dawson’s translated line:

```Player           IP    H    R   ER  BB   SO  ERA SO/9
Andre Dawson 2,540.1 2774 1518 1368 589 1509 4.85 5.35
Mark Redman  1,238.2 1364  712  668 407  747 4.85 5.43```

Dawson’s career lasted twice as long as Redman’s, for the obvious reason that pitchers who make everyone look like a Hall of Famer tend not to stick around forever. It might be fun (although now this is teetering on the precipice of actual work, so I leave it to someone else) to conduct this exercise on other Hall of Famers.

What the heck, let’s do one. Here’s Ted Williams:

```Year      IP    H    R   ER   BB   SO  ERA SO/9
1939   131.1  185  149  134  107  64  9.18 4.39
1940   128.2  193  145  131  96   54  9.16 3.78
1941    95.0  185  183  165  147  27 15.63 2.56
1942   116.2  186  168  151  145  51 11.65 3.93
1946   116.2  176  170  153  156  44 11.80 3.39
1947   119.2  181  166  149  162  47 11.21 3.53
1948   110.1  188  156  140  126  41 11.42 3.34
1949   131.2  194  180  162  162  48 11.07 3.28
1950    80.0  106   98   88   82  21  9.90 2.36
1951   124.1  169  137  123  144  45  8.90 3.26
1952     2.0    4    5    5    2   2 22.50 9.00
1953    18.2   37   41   37   19  10 17.84 4.82
1954    88.2  133  126  113  136  32 11.47 3.25
1955    72.2  114  118  106   91  24 13.13 2.97
1956    91.2  138  121  109  102  39 10.70 3.83
1957    90.1  163  167  150  119  43 14.94 4.28
1958    99.2  135  112  101   98  49  9.12 4.42
1959    71.2   69   45   41   52  27  5.15 3.39
1960    74.0   98   95   86   75  41 10.46 4.99
Total 1,763.2 2654 2382 2144 2021 709 10.94 3.62```

This is pointless, but the man we want is Stu Flythe, who pitched for the Philadelphia A’s in 1936 and then disappeared:

```Player           IP    H    R   ER   BB  SO   ERA SO/9
Ted Williams 1763.2 2654 2382 2144 2021 709 10.94 3.62
Stu Flythe     39.1   49   63   57   61  14 13.04 3.20```

Flythe was a bit “strike-zone challenged”; in addition to the walks, he uncorked 16 wild pitches. I also like the fact that Williams at his absolute worst (1959) “only” turned pitchers into Bere (or Shawn Boskie, or Esteban Yan… whatever floats your boat).

An active player? OK, how about Albert Pujols:

```Year      IP    H    R   ER  BB  SO   ERA SO/9
2001   142.2  194  141  127  69  93  8.01 5.87
2002   144.1  185  126  113  72  69  7.05 4.30
2003   132.2  212  176  158  79  65 10.72 4.41
2004   143.2  196  157  141  84  52  8.83 3.26
2005   140.0  195  156  140  97  65  9.00 4.18
2006   127.2  177  151  136  92  50  9.59 3.52
2007   140.1  185  132  119  99  58  7.63 3.72
2008   121.1  187  160  144 104  54 10.68 4.01
2009   139.0  186  165  149 115  64  9.65 4.14
Total 1,231.2 1717 1364 1227 811 570  8.97 4.17```

Again, pitchers who put up those kinds of numbers don’t last long. Here’s how Pujols compares to the one that actually managed to work 100 innings:

```Player            IP    H    R   ER  BB  SO  ERA SO/9
Albert Pujols 1,231.2 1717 1364 1227 811 570 8.97 4.17
Andy Larkin    105.2  139  112  104  75  69 8.86 5.88```

I don’t really remember Larkin either. Apparently he wasn’t good at pitching.

So, does any of this have practical applications? I doubt it, although you never know. Nobody ever thought Cheez Whiz would be anything other than disgusting, and now… well, maybe that’s not a great example.

Go. Play. Have fun.

References & Resources
The Bill James Baseball Abstract 1987, Baseball-Reference, the friendly voices in my head that make me think about these things.

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1. Charles Gates said...

Perhaps as a proof of concept, but were you able find a matching batter/pitcher combo with enough actual AB’s to compare what they did against each other?

2. Tom M. Tango said...

Good stuff.  One suggestion, and it helps with Mark Reynolds: why not show the HR for all the pitching lines?

3. Josh Fisher said...

Geoff—

Some of the coolest stuff I’ve seen lately. Nice work.

Josh

4. Lew said...

That was very cool. thanks. However the extremes are intuitively obvious. What I would love to see is how “average” pitchers and batters match up; ie what pitcher’s line looks the most like Bobby Richardson, or what batter hit like, I dunno, Bob Ojeda, pitched? As you said, too much work fopr the likes of me, but I would love to see it.

5. Geoff Young said...

@Charles: I didn’t even think of that. Interesting idea…

@Tom: I’d originally included HRs, but for reasons that now escape me, I removed them. I also think BB/9 would be nice as a parallel to K/9.

@Lew: I was thinking along those lines and then got so caught up in the “joy of discovery” that I never followed through. Still, I like the idea. Perhaps more research is in order…

Thanks again.

6. Larry Smith Jr. said...

You’ve inspired something fun for me to do when I’m off work next week.  As a Tiger fan, I’m now compelled to see exactly what pitcher each member of the ‘10 team hit like in ‘09.  Thanks alot for this!

7. Oskar said...

Yes, that was fun.  Thanks, Geoff.