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# Player-Seasonal Notation:  Part One

by Steve Treder
September 20, 2005

This is a simple little thing I’ve played around with ever since I was a kid. It’s easy and it’s fun, and it might also be of some use at making complicated things clearer.

It goes like this: every team always has nine batters in its lineup, right? So if you want to know exactly what the average batter’s stat line looked like for any team in any year, all you do is divide the team batting line by nine. That’s it.

We did a little bit of this in an article several months ago, on the 1957 Kansas City Athletics. We took the 1957 A’s team stat line:
```  AB    R     H   2B  3B   HR  RBI   BB   SO  SB  CS   BA  OBP  SLG  OPS
5170  563  1262  195  40  166  536  364  760  35  27 .244 .294 .394 .688```
And then we divided it by nine, to illustrate just exactly what a team batting line such as that meant, in terms of what kind of a threat the typical 1957 A’s batter represented:
``` AB   R    H  2B  3B  HR  RBI  BB  SO  SB  CS   BA  OBP  SLG  OPS
574  63  140  22   4  18   60  40  84   4   3 .244 .294 .394 .688```
We contrasted this with the very different sort of line that had been put up by the same franchise just eight years earlier, the 1949 Philadelphia A’s:
```  AB    R     H   2B  3B  HR  RBI   BB   SO  SB  CS   BA  OBP  SLG  OPS
5123  726  1331  214  49  82  680  783  493  36  25 .260 .358 .369 .727```
And what a dramatic contrast that presented in terms of the average batter they sent up to the plate:
``` AB   R    H  2B  3B  HR  RBI  BB  SO  SB  CS   BA  OBP  SLG  OPS
569  81  148  24   5   9   76  87  55   4   3 .260 .358 .369 .727```
As I say, I’ve been doing this for a gazillion years. Mostly it’s just kind of a silly little timewaster, the baseball stat geek’s version of doodling. But I do think there can be some real value to it.

How it Helps

Obviously, dividing any row of numbers by a constant doesn’t change the relationship between any of the values; in a sense they’re just the same line of figures, just expressed differently.

But that different mode of expression can be useful. Bill James used to do a similar thing with players’ career stats by dividing them by a constant to convert them into a per-162-games rate, calling it “Seasonal Notation.” Baseball Reference performs that calculation today. Doing so doesn’t change the relationship between any of the values in the player’s career stat line, but it expresses them in a form more familiar to us, one which allows us to more easily assimilate and assess. We’re all used to seeing stat lines of players compiled in single seasons, so presenting a player’s career stats in that format puts them in easily digestible and comparable context.

Dividing a team’s batting stats by nine performs a similar service. It allows us to more easily comprehend just how good or bad a team’s batting performance was and understand more readily what style of offense they presented. It helps to make the large figures in a team stat line more sensible, more resonant. I suggest that this form of team stat presentation, following James's lead, can reasonably be called "Player-Seasonal Notation."

What it Shows

Let me throw a couple more examples of Player-Seasonal Notation at you. These are the team stat lines produced by the offenses that scored the most and the fewest runs in the majors in 2004, the Boston Red Sox and the Arizona Diamondbacks:
```  AB    R     H   2B  3B   HR  RBI   BB    SO  SB  CS   BA  OBP  SLG  OPS
5720  949  1613  373  25  222  912  659  1189  68  30 .282 .360 .472 .832
5544  615  1401  295  38  135  582  441  1022  53  32 .253 .310 .393 .703```
Now here are those stat lines divided by nine:
``` AB    R    H  2B  3B  HR  RBI  BB   SO  SB  CS   BA  OBP  SLG  OPS
636  105  179  41   3  25  101  73  132   8   3 .282 .360 .472 .832
616   68  156  33   4  15   65  49  114   6   4 .253 .310 .393 .703```
Player-Seasonal Notation demonstrates that it was as if the Red Sox, all year long, in every inning of every game, in every at-bat, sent someone roughly equivalent to Scott Rolen or Hank Blalock to the plate. Meanwhile the Snakes, also in their every plate appearance all season, were putting somebody more like Alex Gonzalez or Alex Gonzalez (either one, take your pick) up there.

Could the contrast be any more vivid?

Yin and Yang

All right, let’s have some fun with this. Let’s compare the approaches of the 1960s Detroit Tigers with those of the 1980s St. Louis Cardinals. Here they are in high performance mode:
```Team             AB   R    H  2B  3B  HR  RBI  BB  SO  SB  CS   BA  OBP  SLG  OPS
1962 Tigers     606  84  150  21   4  23   80  72  99   8   2 .248 .328 .411 .739
1985 Cardinals  607  83  161  27   7  10   76  65  95  35  11 .264 .336 .379 .715```
And here’s when they were operating a bit less efficiently:
```Team             AB   R    H  2B  3B  HR  RBI  BB   SO  SB  CS   BA  OBP  SLG  OPS
1968 Tigers     610  75  144  21   4  21   71  58  107   3   4 .235 .302 .385 .687
1984 Cardinals  604  72  152  25   5   8   68  57  103  24   8 .252 .317 .351 .668```
And here are a couple of contemporaries who were trying to do similar things, but with less success:
```Team            AB   R    H  2B  3B  HR  RBI  BB   SO  SB  CS   BA  OBP  SLG  OPS
1965 Senators  597  66  136  20   4  15   63  63  125   3   2 .228 .302 .350 .652
1980 Padres    616  66  157  22   5   7   61  63   88  27   8 .255 .323 .342 .665```
Okay, how about two teams that played in the Polo Grounds in New York 33 years apart, but could scarcely have achieved more starkly different results:
```Team          AB    R    H  2B  3B  HR  RBI  BB   SO  SB  CS   BA  OBP  SLG  OPS
1930 Giants  617  107  197  29   9  16   98  47   42   7   ? .319 .367 .473 .840
1963 Mets    593   56  130  17   4  11   51  51  120   5   6 .219 .281 .315 .596```
And file this one under "Evidence That There Is More Than One Way To Skin A Cat:"
```Team           AB   R    H  2B  3B  HR  RBI  BB   SO  SB  CS   BA  OBP  SLG  OPS
1922 Robins   601  83  174  26   8   6   75  38   35   9   7 .290 .332 .392 .724
2001 Brewers  610  82  153  30   3  23   79  54  155   7   4 .251 .319 .426 .745```
On the Mound

Player-Seasonal Notation can also be applied to team pitching stats. But with pitchers, we don’t have the obvious factor of nine to use as our constant: teams aren’t required to constantly rotate nine pitchers through each ball game (though it may appear that way sometimes). We could just divide team pitching lines by nine, but with pitchers there’s no compelling reason to use that figure the way there is with batters, and moreover, the result of dividing by nine—a pitching line of somewhere around 160 innings pitched—doesn’t resonate the same way that a batting line of about 600 at-bats does.

Therefore, with pitching lines, I prefer to use a constant of 6.5 as the divisor, for no reason other than the fact that it yields a line of around 210 to 220 innings—a proportion that mimics a full-season starting pitcher.

So here’s the Player-Seasonal Notation we get when we apply the divisor of 6.5 to the pitching staff that allowed the fewest runs in the majors in 2004 and the one that surrendered the most:
```Team             IP    H  HR   BB   SO   W   L   ERA
2004 Cardinals  224  212  26   68  160  16   9  3.75
2004 Rockies    221  251  30  107  146  10  14  5.54```
How about a nice contrast-and-compare between the staffs of a 116-game winner and a 119-game loser:
```Team            IP    H  HR  BB   SO   W   L   ERA
2001 Mariners  225  199  25  72  162  18   7  3.54
2003 Tigers    221  249  30  86  118   7  18  5.30```
This one’s always fun, as an illustration of mastery and mockery of the strike zone, by the same franchise 18 years apart:
```Team            IP    H  HR   BB   SO   W   L   ERA
1967 Twins     225  206  18   61  168  14  11  3.14
1949 Senators  207  221  12  120   69   8  16  5.10```
In terms of ERA, the absolute all-time best and worst occurred just 23 years apart, in the same league:
```Team            IP    H  HR  BB  SO   W   L   ERA
1907 Cubs      211  162   2  62  90  16   7  1.73
1930 Phillies  211  307  22  84  59   8  16  6.71```
...and Just Different

Speaking of Cubs' staffs, here are a couple of versions, 80 years apart, that used greatly differing methods to achieve just about exactly the same result:
```Team        IP    H  HR  BB   SO   W   L   ERA
1923 Cubs  210  218  13  67   63  13  11  3.82
2003 Cubs  224  201  22  95  216  14  11  3.83```
The Flow...

Okay, for now we've just been having fun. But now let's look at how Player-Seasonal Notation can illustrate the trends of team development and decline.

Here are the batters of the Boys of Summer Dodgers, in their final dozen years in Brooklyn:
```Team           AB    R    H  2B  3B  HR  RBI  BB  SO  SB  CS   BA  OBP  SLG  OPS
1946 Dodgers  587   78  153  26   7   6   71  77  64  11   ? .260 .346 .361 .707
1947 Dodgers  583   86  159  27   6   9   80  81  62  10   ? .272 .361 .384 .745
1948 Dodgers  592   83  155  28   6  10   75  67  76  13   ? .261 .336 .381 .717
1949 Dodgers  600   98  164  26   5  17   91  71  63  13   ? .274 .350 .419 .769
1950 Dodgers  596   94  162  27   5  22   86  67  70   9   ? .272 .346 .444 .790
1951 Dodgers  610   95  168  28   4  20   88  67  72  10   8 .275 .347 .434 .781
1952 Dodgers  585   86  153  22   4  17   81  74  78  10   5 .262 .345 .399 .744
1953 Dodgers  597  106  170  30   7  23   99  73  76  10   5 .285 .362 .474 .836
1954 Dodgers  583   86  158  27   6  21   82  70  69   5   4 .270 .349 .444 .793
1955 Dodgers  577   95  156  26   5  22   89  75  80   9   6 .271 .355 .448 .803
1956 Dodgers  566   80  146  24   4  20   76  72  82   7   4 .258 .342 .419 .761
1957 Dodgers  582   77  147  21   4  16   72  61  94   7   4 .253 .324 .387 .711```
That could very plausibly be an individual player who develops power into his peak and then loses speed and enters his decline phase.

...and The Ebb

Even more dramatically, check out the systematic, stage-by-stage unraveling of the 1960s New York Yankees' offense:
```Team           AB   R    H  2B  3B  HR  RBI  BB   SO  SB  CS    BA  OBP  SLG  OPS
1960 Yankees  588  83  153  24   4  21   78  60   91   4   3  .260 .328 .426 .754
1961 Yankees  618  92  162  22   4  27   87  60   87   3   2  .263 .328 .442 .770
1962 Yankees  627  91  168  27   3  22   88  65   94   5   3  .267 .336 .426 .762
1963 Yankees  612  79  154  22   4  21   74  48   90   5   3  .252 .307 .403 .710
1964 Yankees  634  81  160  23   4  18   76  58  108   6   2  .253 .315 .387 .702
1965 Yankees  608  68  143  22   3  17   64  54  106   4   2  .235 .298 .364 .662
1966 Yankees  592  68  139  20   4  18   63  54   91   5   3  .235 .299 .374 .673
1967 Yankees  605  58  136  18   2  11   53  59  116   7   4  .225 .294 .317 .611
1968 Yankees  590  60  126  17   4  12   56  63  106  10   6  .214 .290 .318 .608```
What's eerie is how closely the team decline was paralleled by that of Tom Tresh.

The Success Cycle

The Detroit Tigers of 1978-1989 (the Trammell-Whitaker-Gibson era, for the most part) demonstrated a distinct beginning-middle-end pattern:
```Team          AB    R    H  2B  3B  HR  RBI  BB   SO  SB  CS   BA  OBP  SLG   OPS
1978 Tigers  622   79  169  24   4  14   74  63   77  10   4 .271 .338 .392  .730
1979 Tigers  597   86  161  25   4  18   81  64   90  20  10 .269 .340 .415  .755
1980 Tigers  628   92  171  26   6  16   85  72   94   8   8 .273 .348 .409  .757
1981 Tigers  400   47  102  16   3   7   45  45   56   7   4 .256 .331 .368  .699
1982 Tigers  621   81  165  26   4  20   76  52   90  10   7 .266 .323 .418  .741
1983 Tigers  621   88  170  31   6  17   83  56   92  10   6 .274 .334 .427  .761
1984 Tigers  627   92  170  28   5  21   88  67  105  12   8 .271 .341 .432  .773
1985 Tigers  619   81  157  28   5  22   78  58  103   8   5 .253 .318 .424  .742
1986 Tigers  612   89  161  26   3  22   83  68   98  15   6 .263 .336 .424  .760
1987 Tigers  628  100  171  30   4  25   93  73  101  12   6 .272 .347 .451  .798
1988 Tigers  604   78  151  24   3  16   72  65   93  10   5 .250 .323 .378  .701
1989 Tigers  604   69  146  22   3  13   63  65  100  11   6 .242 .316 .351  .667```
The strike-shortened 1981 season looks just like an injury-hampered year, doesn't it?

Coming Together...

Remember those Dodgers from earlier? Here we pick up their pitchers, after they moved across the continent, and the developing Koufax-centered staff mastered its control. (They also derived great benefit out of the move from the Coliseum to Chavez Ravine in 1962 and the enlargement of the strike zone in 1963):
```Team           IP    H  HR  BB   SO   W   L   ERA
1958 Dodgers  210  215  27  93  132  11  13  4.47
1959 Dodgers  217  203  24  94  166  14  10  3.79
1960 Dodgers  215  187  24  87  173  13  11  3.40
1961 Dodgers  212  207  26  84  170  14  10  4.04
1962 Dodgers  229  213  18  90  170  16  10  3.62
1963 Dodgers  226  204  17  62  168  15  10  2.85
1964 Dodgers  228  198  14  70  163  12  13  2.95
1965 Dodgers  227  188  20  65  166  15  10  2.81
1966 Dodgers  224  198  13  55  167  15  10  2.62```
...and Falling Apart

And on the other side of the coin, as far as relentless descents from heaven to hell go, it's hard to top the 1931-1936 Philadelphia Athletics:
```Team       IP    H  HR   BB  SO   W   L   ERA
1931 A's  210  206  11   70  88  16   7  3.47
1932 A's  213  227  17   79  92  14   9  4.45
1933 A's  207  234  12   99  65  12  11  4.81
1934 A's  206  220  13  107  74  10  13  5.01
1935 A's  204  229  11  108  72   9  14  5.12
1936 A's  208  253  20  107  62   8  15  6.08```
All right, enough of this. Next time we'll apply this fun little tool in a more rigorous manner and see what insights it may help us derive into the ever-changing nature of run production and prevention.

Steve Treder can often be found spending way too much time talking baseball at Baseball Primer. He welcomes your questions and comments via e-mail.