Is the AL Really Superior? (Part 2)

In Part 1, I showed how players switching leagues generally performed in terms of linear weights (lwts). In this installment, I will adjust those numbers to take into account, among other things, aging and the previous baseline of offensive talent, and reveal the numbers for pitching as well.

Determining the relative quality of offensive talent in any given year

Year 	Players  Runs    Runs     Players  Runs    Runs    Which   How     Runs   
     	to AL    Before  After    to NL    Before  After   League  Many    per
     	         Switch  Switch            Switch  Switch  Gained  Runs    Game
99-00	41       -3.1    -8.3     36       -8.7    -2.2    NL      172     .066
00-01	31       -2.3    -5.0     40       -13.0   -7.5    AL      2       .001
01-02	34       -7.8    -13.0    39       -4.9    -3.6    NL      232     .090
02-03	39       -7.1    -4.9     39       -3.7    -1.4    NL      82      .032
03-04	61       -1.8    -2.6     56       -4.8    -3.2    AL      60      .026
04-05	39       -3.2    -8.5     39       -7.9    0.0     NL      199     .077
05-06	38       -12.3   -5.7     34       -15.2   -1.0    NL      198     .077

Totals   283      -5.1    -6.5     283      -7.9    -2.8    NL      821     .345

If we compare columns three and four and columns six and seven, again in the above chart, an interesting and telling pattern emerges. In 12 out of 14 (7 for the NL to AL, and 7 for the AL to NL) years, and for all 7 years on the average, players who switch from the NL to the AL, tend to “get worse” and players who switch from the AL to the NL tend to “get better.” This is exactly what we would expect if the pool of hitters in the AL were better than that in the NL. For example, an average player in the NL would, by definition, have a lwts of exactly zero per 500 PA (or per anything). If he moves to the AL and the AL hitters are better than the NL hitters, he will “become” a below-average hitter (relative to the other players in the AL), and will have a negative lwts. That is exactly what we see in the above chart. A hitter who moves from the NL to the AL gets worse (his lwts rate gets more negative) and vice versa for hitters who move from the AL to the NL.

Let’s look at the last row (totals). The average player who moves from the NL to the AL “loses” 1.4 runs per 500 plate appearances (he appears to get worse). But, as we mentioned earlier, the effects of aging should cause him to lose around 1.5 runs. So didn’t he really get just a tad better after moving to the AL (he should be -5.1 minus 1.5, or -6.6, but he is only -6.5)? Maybe the AL is not the better offensive league after all.

If we look at the average player who moved from the AL to the NL, however, we find that he gains 5.1 runs, even though we expected him to lose 1.5 runs from aging. So maybe the AL is better offensively. What is going on here?

Remember I said that the players’ pre-switch lwts do not represent their true talent levels, because they are selectively sampled as players with typically poor performances in their pre-switch years. If that is the case, then in order to “predict” their next-year’s performance, not only do we have to account for the effects of aging, we also have to regress their pre-switch performance. Since they are part-time players with only 300 some-odd PA per year, we need to regress their pre-switch performance around 50% toward the mean (which is zero by definition). You’ll have to take our word for it on the 50% regression to the mean.

So our NL to AL players, rather than “true” -5.1 players, are really “true” -2.5 players (-5.1 regressed 50% toward the mean). So we would expect them, after losing 1.5 runs from aging, to be -4.0 in post-switch performance (-2.5 minus 1.5) if both leagues had the same overall offensive talent. Instead, they are -6.5 after switching to the AL, suggesting that the average AL player over this 7-year span is 2.5 runs per 500 PA better than the average NL player. Here is the analysis in chart form:

NL to AL

Pre-switch    After regressing    Effect of aging    Total Expected    Actual Expected   Actual 
lwts          toward mean                            Lwts              Lwts                Difference 
-5.1          -2.5                -1.5               -4.0              -6.5                -2.5

AL to NL

The AL to NL players would project as -4.0 (their estimated true talent in the AL after regressing the -7.9) minus 1.5 for aging, or -5.5, in the post-switch year. Instead, they are -2.8, suggesting that the average player in the NL is 2.7 runs per 500 PA worse than the AL. Here is that in chart form:

Pre-switch    After regressing    Effect of aging    Total Expected    Actual Expected   Actual 
lwts          toward mean                            Lwts              Lwts                Difference 
-7.9          -4.0                -1.5               -5.5              -2.8                 2.7

So our former group, the NL to AL players, actually lost 2.5 runs after the switch, and our AL to NL players gained 2.7 runs. Now that is more like it! So the suggestion is that from 2000 to 2006, the AL has been, on the average, around 2.6 runs per 500 PA in offense better than the NL. That corresponds to around .19 runs per game. According to Pythagoras, that gives the AL a 51.9% advantage (offense only) if an average team from each league and from 2000 to 2006 were to face each other (assuming they were even otherwise—in pitching and defense).

Unfortunately (again), there is another slight problem with the above analysis. Both the pre-switch and post-switch lwts for players who transferred leagues is weighted by the number of PA either pre- or post-switch. Technically, in order to calculate the difference in offensive talent between the two leagues, for each player, we need to weight the difference between their pre- and post-switch lwts by the lesser of either their pre- or post-switch PA, and then average everything up, or out, or whatever it is. Again, if we lost you, don’t worry too much about it. Here is another chart that illustrates the average difference in offensive quality between the leagues, based on each player’s pre-and post-switch lwts, this time weighted by the appropriate number of PA.

Year 	Players  Runs    Runs     Players  Runs    Runs    Which   How     Runs   
     	to AL    Before  After    to NL    Before  After   League  Many    per
     	         Switch  Switch            Switch  Switch  Gained  Runs    Game
99-00	41       ?       -8.9     36       -5.0    -2.2    AL      4.4     .326
00-01	31       4.4     -5.4     40       -10.3   -6.8    AL      3.7     .274
01-02	34       3.7     -12.3    39       -3.8    -4.2    AL      3.4     .252
02-03	39       3.4     -6.1     39       -1.8    -2.2    AL      .8      .059
03-04	61       .8      -2.4     56       -5.4    -5.1    NL      .1      .011
04-05	39       -.1     -10.2    39       -5.1    -.4     AL      5.2     .385
05-06	38       5.2     -5.7     34       -8.8    -.8     AL      4.0     .294

Totals   283      -2.7    -6.9     283      -5.7    -3.3    NL      2.6     .193

So using the correct weighting system, it appears that the AL has been 2.6 runs better per player (per 500 PA) than the NL, the same as before, when we were using the incorrect weighting system. It also appears that the AL was the dominant offensive league from 00 to 02 and then a shift occurred such that there was approximate parity in 04 (slight advantage to the NL). Then in 05, a large shift occurred in favor of the AL, such that the AL now has around a .3 runs per game advantage in offense.

Back to the transfer of offensive talent between the two leagues

Let’s now use the numbers above (relative quality of each league in each year) to see if we can correctly estimate the shift in talent over the years based on each players’ pre-switch lwts, adjusted for the difference in talent between the leagues.

Year 	Players  Runs    Runs     Players  Runs    Runs    Which   How     Runs   
     	to AL    Before  After    to NL    Before  After   League  Many    per
     	         Switch  Switch            Switch  Switch  Gained  Runs    Game
99-00	41       -.9     -3.1     36       -3.1*   -8.7    AL      161*    .071*
00-01	31       .2      -2.3     40       -6.7    -13.0   NL      67      .030
01-02	34       -5.8    -7.8     39       -11.5   -4.9    NL      175     .068
02-03	39       -6.2    -7.1     39       -10.5   -3.7    AL      170     .065
03-04	61       -.6     -1.8     56       -2.6    -4.8    AL      111     .049
04-05	39       -3.8    -3.2     39       -3.1    -7.9    AL      120     .053
05-06	38       -2.7    -12.3    34       -17.5   -15.2   NL      24      .009

Totals   283      -2.7    -6.9     283      -7.6    -7.9    AL      2.6     .040
* Assumes offensive parity in 1999
Shift in talent versus inter-league win/loss records

Let’s take a look at the above year-by-year shifts in offensive talent next to the year-by-year inter-league win/loss records. Keep in mind that we are only dealing with offense and that obviously the win/loss records reflect the whole shebang (offense, pitching, etc.).

Year	AL Wins 	NL Wins	Shift in Offense	Offense Per Game
2000	136	115	161 runs to AL*	.07 to AL *
2001	132	120	67 runs to AL	.03 to AL 
2002	123	129	175 runs to NL	.07 to NL
2003	115	137	170 runs to NL	.07 to NL
2004	126	125	111 runs to AL	.05 to AL
2005	136	116	120 runs to AL	.05 to AL
2006	128	75	24 runs to NL	.01 to NL
Totals	896	817	90 runs to the AL	.04 to AL
* Assumes offensive parity in 1999

We may have gotten lucky, since we haven’t even addressed pitching yet, but the year-by-year shift in offensive talent appears to be reflected in the year-by-year inter-league win/loss records. In 2000 and then again in 2001, there was a large shift in offensive talent from the NL to the AL. The AL has the win/loss advantage in both of those years. In 2002 and again in 2003, there was a large shift back to the NL. In both of those years, the NL has the win/loss advantage. We then see over 230 runs shifted to the AL in 04-05. In those two years, the AL has the win/loss advantage. We even see a small win/loss advantage for the AL in all seven years combined, which corresponds with the total shift in offensive talent of 90 runs (at least they are on the same side of the ledger).

As to why there is a large upswing in the AL win/loss advantage in 06 (as compared to 05), even though we have seen an apparent small shift in offensive talent to the NL this year remains to be seen (or not). Perhaps there has been a large shift in pitching talent to the AL in 06. Jim Baker of Baseball Prospectus, in a February 17, 2006 article, suggests that there has, at least with respect to starting pitchers. Let’s see if he is right.

Since we already explained the methodology and broke down all the numbers with respect to offense, we’ll cut right to the chase with pitching.

Year 	Players  NERC*   NERC     Players  NERC    NERC    Which   Runs   
     	to AL    Before  After    to NL    Before  After   League  per
     	         Switch  Switch            Switch  Switch  Gained  Game
99-00	24       4.29    4.35     26       4.74    4.40    AL      .10 
00-01	33       4.60    4.73     34       4.07    3.75    AL      .39 
01-02	40       3.86    4,41     41       4.37    3.78    AL      .46
02-03	30       3.81    4.10     29       4.50    4.05    AL      .15
03-04	58       3.74    4.12     55       4.26    3.88    AL      .22
04-05	49       4.01    4.29     59       4.06    4.11    AL      .08
05-06	35       4.14    4.51     39       4.41   4.03     AL      .28

Totals   269      4.02    4.34     283      -7.6    3.98    AL      .22
* NERC = “Normalized component ERA.”  4.00 is defined as league average.  
An NERC of 4.00 is just like an offensive lwts of zero.  A pitcher with an 
NERC above 4.00 is a below-average pitcher.  As with offensive lwts, a 
pitcher’s NERC is relative to his league only.

In order to compute the last column, we regressed the pre-switch NERC’s two-thirds toward the mean (because they are pitchers and because they had fewer batters faced than the batters had PA), and added a .10 decline due to aging.

Expected win/loss records versus actual win/loss records

Let’s combine the pitching advantage per year above with the hitting advantage per year and try and reconcile the totals with the year-by-year interleague win/loss records.

Year    AL          AL          AL          AL Wins    NL Wins    AL Win %   Expected
        Offensive   Pitching    Advantage                                    Win %
        Advantage   Advantage   (Total)
2000    .33         .10         .43         136        115        .542       .545
2001    .27         .39         .66         132        120        .524       .571
2002    .25         .46         .71         123        129        .488       .577
2003    .06         .15         .21         115        137        .456       .523
2004    -.01        .22         .21         126        125        .502       .523
2005    .38         .08         .46         136        116        .540       .547
2006    .29         .28         .57         128        75         .630       .560

Totals  .19         .22         .41         896        817	  .523       .544

The numbers computed so far seem to overstate the AL advantage in every year but 2006, and in the seven years combined. We do seem to be in the general ballpark, however. Perhaps there is something going on which is not evident using the methodologies described thus far.

Or perhaps these methodologies are just too blunt or coarse an instrument to finely measure what we are trying to measure. Or maybe there is too much random fluctuation in the year-by-year and seven-year interleague win/loss records. After all, the AL win/loss advantage of 52.3% over the 7-year span is really 52.3% plus or minus 2.4%, at two standard deviations above and below the mean.

Tomorrow, we will come up with another, more direct and accurate, method for identifying and quantifying any differences in talent between the two leagues.

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