Neutralized and Converted Stats

First, what is not considered. There are no adjustments for:

Segregation

Changing role of bullpens

Improved travel or fitness or nutrition

Increased foreign talent

Field conditions or sizes

No consideration of changing tactics like the bunt or stolen base

or anything else not explicitly listed below.

What is adjusted?

We adjust all of a player's seasons from the park and league context of the seasons they played in into either a "neutral" setting (which is 100 park factor with 162-game season, 90% of runs earned, and 715 runs/team), or into a setting selected by the user with a particular year, league (with its runs/game and earned runs percentage) and home team (with its park factor). Originally, this was set at 750 as Bill James had done in his New Historical Baseball Abstract, but this is well over the historical average which is about 715 runs/162 games since 1900. So we've adjusted this downward to reflect this lower average run scoring. With the old number most every offensive player improved, while with the new number, half get better and half get worse. We've still provided a link to 750 if you like that better.

There is no change of role for a player, so playing time is essentially the same proportion as before, though things like At Bats go up as run scoring increases. This also means that Pedro Martinez will only make 30 starts a season even if you put him in the 1914 AL.

How are batters adjusted?

For each player/season, we have their stats (Including Runs Created--note that for neutralization the basic RC, without baserunning, GIDP, etc., is used as the player's baseline offensive level. This means that when you translate a player back into a context they actually played the RC numbers listed will be different from those listed under Special Batting for recent players.), and then the number of games their team played, their team's park factor, the league runs/game and if the DH was used that year. We handle trades in the proportional manner you would expect.

For the new setting we have the park factor, the number of games expected, and the run-scoring level. Games are adjusted proportionally and this creates a multiplier.

Runs created are adjusted using the ratio of park factors, ratio of run scoring, and a ratio determined by whether we are coming or going to a DH league.

As part of this conversion, we assume that a player will get singles, doubles, triples, home runs, walks, HBP, and SB in the same proportion to overall hits as before, so given our adjusted RC, we can then find a new level of hits for the player. (This requires using the quadratic formula, and you thought you'd never need it.)

The player's outs remain the same, so the new AB's is the new Hits plus the old outs.

We then compute new 2B, 3B, HR, BB, SB, and HBP.

We assume Runs and RBI are proportional to the change in RC, and since outs doesn't change neither will SO or SF.

And that is pretty much it for hitters.

How are pitchers adjusted?

The idea is pretty much the same except quite a bit more complicated in the details for pitchers. Here is a description by Justin Kubatko.

We start by making the assumption that a pitcher's batters facing pitcher per game are a constant, since in many settings this is determined by the pitcher's pitch count or needed rest. This is imperfect. This means that a pitcher going from a high run scoring setting to a low run scoring setting will still face the same number of batters, but a pitcher going from a 154 to a 162 game setting will face proportionally more hitters. Since batters facing pitcher data is spotty for some seasons, we estimate it using:
BFP = 3*IP + H + BB + HBP

Since total bases allowed is not available, we estimate it using:
TB = (1.252*(H - HR) + 4*HR)

Recall that Bill James's formula for basic runs created is:
RC = TB * (H + BB) / (AB + BB)

We estimate at bats against using:
AB = IPouts + H

We'll lump hit by pitches in with walks, so this makes runs created allowed equal to:
RC = TB * (H + BB + HBP) / BFP

We have to adjust the runs created allowed for league and park. First, for the park:
park = newPF / PF

Above, newPF is the park factor of the park we want to place the player in, and PF is the pitcher's park factor for that particular season. We'll assume that we're going to place him in a neutral park, so newPF is equal to 100:
park = 100 / PF

Now the league adjustment:
league = newLgR / LgR

Here, newLgR is team runs per 162 games for the league we want to place the player in, and LgR is team runs per 162 games for that particular season. We'll assume that we want to place the pitcher in an environment of 750 team runs per 162 games:
league = 750 / LgR

Now we make both adjustments to the player's runs created allowed:
newRC = RC * park * league

For example, here's Pedro Martinez in 2000:
BFP = 651 + 128 + 32 + 14 = 825
TB = 0.89*(1.255*(128 - 17) + 4*17 = 184.5
RC = 184.5*(128 + 32 + 14) / 825 = 38.91
park = 100 / 101 = 0.99
league = 750 / 857.9 = 0.874
newRC = 38.91*0.99*0.874 = 33.67

Now we'll express Martinez's total bases and walks in terms of the number of hits he allowed. In 2000, Martinez gave up an estimated 184.5 total bases and 128 hits, so:
TB = (184.5 / 128)*H = 1.44H

Martinez walked 32 batters and hit 14:
BB + HBP = ((32 + 14) / 128)*H = 0.36H

Now we'll plug newRC and the expressions for total bases and walks given above into the runs created formula and solve for H:
33.67 = 1.44H * (H + 0.36H) / 825

We can solve for H. Rounding off, this yields:
H = 119

The changes in his home runs, walks, and hit by pitch will be proportional to the change in his hits. For example, in 2000 Martinez allowed 17 home runs and 128 hits, so his adjusted home run total is:
HR = 17 * (119 / 128) = 16

Similarly, his adjusted walks and hit by pitch are:
BB = 32 * (119 / 128) = 30
HBP = 13 * (119 / 128) = 13

We have to modify Martinez's innings pitched to reflect the changes in his hits and walks allowed. Recall:
BFP = 3*IP + H + BB + HBP

Keeping in mind that batters facing pitcher is a constant, plug in the known values:
825 = 3*IP + 119 + 43

Solving for IP gives us:
IP = 221

In 2000, Martinez recorded 651 outs, 284 via strikeout. After adjustment, Martinez's outs recorded increases to 663, so his adjusted strikeout total is:
SO = 663 * (284 / 651) = 289

Martinez allowed 42 earned runs in 2000. After adjustment, Martinez's runs created allowed went from 38.91 to 33.67. We'll assume that the change in his earned runs will be proportional to the change in his runs created allowed:
ER = 42 * (33.67 / 38.91) = 36

From this we can easily get Martinez's ERA:
ERA = (36 / 221) * 9 = 1.47

We decided to calculate runs allowed by taking the player's adjusted earned runs and dividing by the earned run rate of the league we want to place the player in. Let's assume that we want to put him in a league with an earned run rate of 0.90. Then:
R = 36 / 0.90 = 40

And his runs allowed per 9 innings:
RA = (40 / 221) * 9 = 1.63

The final step is to get an adjusted won-lost record. we give the pitcher one decision for every nine adjusted innings pitched, so for Martinez this is:
Dec = int(221 / 9) = 24

We use his run average and the runs per game of the league/park we are placing him in to get a Pythagorean won-lost percentage. Recall that we are placing him in a neutral park in a league where the average team scores 750 runs per 612 games, or 4.63 runs per game:
Pyth = 4.63**2 / (4.63**2 + 1.63**2) = .890

Now calculate adjusted wins, losses, and won-lost percentage:
W = 24 * 0.890 = 21
L = 24 - 21 = 3
WL% = 21 / (21 + 3) = .875

Note that due to the rounding that occurs, the adjusted won-lost percentage will almost always differ from the Pythagorean won-lost percentage.

We decided that it didn't make sense to adjust things like complete games, shutouts, and saves, so we didn't include those categories. After adjustment, here is Pedro Martinez's 2000 season in a 750 run:

 Year Ag   G   W   L   WL%     IP    H    R   ER  HR   BB  SO  HBP   ERA   WHIP  ActG
+-------+----+---+---+-----+------+----+----+----+---+----+----+---+-----+------+----+
 2000 28   29  21   3  .875  221.0  119   41   37  16   30  289  13  1.51  0.674   29

What are the most extreme settings?

Best for pitchers

| year | lg | Team                | lgRPG | BPF  | adjRPG |
+------+----+---------------------+-------+------+--------+
| 1907 | NL | Brooklyn Superbas   | 3.399 |   92 |   3.13 |
| 1908 | NL | St. Louis Cardinals | 3.327 |   95 |   3.16 |
| 1968 | NL | Los Angeles Dodgers | 3.430 |   92 |   3.16 |
| 1908 | AL | Washington Senators | 3.444 |   92 |   3.17 |
| 1908 | NL | Brooklyn Superbas   | 3.327 |   96 |   3.19 |
| 1909 | AL | St. Louis Browns    | 3.439 |   93 |   3.20 |
| 1908 | NL | Cincinnati Reds     | 3.327 |   97 |   3.23 |
| 1968 | AL | Oakland Athletics   | 3.406 |   95 |   3.24 |
| 1908 | NL | Boston Doves        | 3.327 |   98 |   3.26 |
| 1972 | AL | California Angels   | 3.467 |   94 |   3.26 |
| 1909 | AL | Washington Senators | 3.439 |   95 |   3.27 |
| 1968 | AL | California Angels   | 3.406 |   96 |   3.27 |
| 1906 | NL | Brooklyn Superbas   | 3.567 |   92 |   3.28 |
| 1916 | NL | New York Giants     | 3.449 |   95 |   3.28 |
| 1972 | AL | Oakland Athletics   | 3.467 |   95 |   3.29 |
| 1909 | AL | Chicago White Sox   | 3.439 |   96 |   3.30 |
| 1968 | AL | Washington Senators | 3.406 |   97 |   3.30 |
| 1968 | AL | New York Yankees    | 3.406 |   97 |   3.30 |
| 1907 | NL | St. Louis Cardinals | 3.399 |   97 |   3.30 |
| 1917 | NL | Boston Braves       | 3.526 |   94 |   3.31 |

Best for Hitters

| year | lg | Team                  | lgRPG | BPF  | adjRPG |
+------+----+-----------------------+-------+------+--------+
| 2000 | NL | Colorado Rockies      | 5.004 |  131 |   6.56 |
| 1999 | NL | Colorado Rockies      | 5.004 |  129 |   6.46 |
| 1930 | NL | Philadelphia Phillies | 5.684 |  107 |   6.08 |
| 1996 | NL | Colorado Rockies      | 4.684 |  129 |   6.04 |
| 1936 | AL | Boston Red Sox        | 5.671 |  106 |   6.01 |
| 1995 | NL | Colorado Rockies      | 4.632 |  128 |   5.93 |
| 1936 | AL | Chicago White Sox     | 5.671 |  104 |   5.90 |
| 1930 | NL | St. Louis Cardinals   | 5.684 |  103 |   5.85 |
| 1936 | AL | St. Louis Browns      | 5.671 |  103 |   5.84 |
| 1930 | NL | Chicago Cubs          | 5.684 |  101 |   5.74 |
| 1929 | NL | Philadelphia Phillies | 5.364 |  107 |   5.74 |
| 2001 | NL | Colorado Rockies      | 4.701 |  122 |   5.74 |
| 1936 | AL | Cleveland Indians     | 5.671 |  101 |   5.73 |
| 2000 | AL | Minnesota Twins       | 5.296 |  108 |   5.72 |
| 1996 | AL | Toronto Blue Jays     | 5.387 |  106 |   5.71 |
| 1938 | AL | Detroit Tigers        | 5.368 |  106 |   5.69 |
| 1930 | NL | Pittsburgh Pirates    | 5.684 |  100 |   5.68 |
| 1936 | AL | Detroit Tigers        | 5.671 |  100 |   5.67 |
| 1996 | AL | Milwaukee Brewers     | 5.387 |  105 |   5.66 |
| 1997 | NL | Colorado Rockies      | 4.603 |  123 |   5.66 |

Aaron with the 2000 Rockies has 1030 career home runs, and with the 1968 Dodgers has 653 home runs.

Cobb has a .436 career average playing for the Rockies.

Pedro with the 1968 Dodgers has a career ERA of 1.75 and with the 2000 Rockies a career ERA of 3.98.

Credits

Much of the reasoning in these conversions comes from Bill James's New Historical Baseball Abstract, p. 740-743.

Justin Kubatko of Basketball-Reference.com designed the pitching methodology and did almost all of the programming.