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WAR is wins above replacement. Replacement is defined very specifically for my purposes: it’s the talent level for which you would pay the minimum salary on the open market, or for which you can obtain at minimal cost in a trade.

For nonpitchers, that level is set at -2.25 wins per 162 games, below the average for that league. Since the same stats of an average AL player is better than the same stats of an average NL player (i.e., the AL is the better league), we have different replacement levels. Those levels are -2.5 wins per 162 games in the AL, and -2.0 wins in the NL.

The positional adjustments are:

+1.0 wins C

+0.5 SS/CF

+0.0 2B/3B

-0.5 LF/RF/PH

-1.0 1B

-1.5 DH

These are needed so that an average fielding 1B is not valued the same as an average fielding SS. The DH and PH should be at -2.0 wins (that is, a poor fielding 1B and a DH have the same fielding+positional value). However, as per The Book, it’s harder to DH, so we give them a 0.5 win boost. The PH gets an extra 1 win boost over the DH, because PHing is much harder.

For pitchers, that level is set at .380 win% for starters and .470 for relievers. The exact same pitcher will perform much better in a relief role than in a starter role. So, you need different baselines. You can read the relevant chapter in The Book for that. As with nonpitchers, you need different baselines in each league: .370, .460 in the AL, and .390, .480 in the NL.

For closers, there is a closer replacement level of .570 win%. Any wins above this level gets multiplied by his Leverage Index (LI). That is, while he is not responsible for the LI he finds himself in, he is responsible for his talent that allows him to take advantage of the extra leverage (sort of like Ozzie Smith gets to play SS and reaps the benefit of all the extra opps). We are only giving credit to the closer for the leverage above the .570 win% level. Credit GuyM for this insight.

This section below is not required to understand the above. It is presented here for the hardcore among you.

To convert wOBA for a hitter into wins: (wOBA - .338) / 1.15 * 700 / 10.5 will give you wins above average. (The .338 is whatever the league average wOBA is, which is EXACTLY equal to whatever the league average OBP is; 1.15 is the relationship between wOBA and runs; 700 is the number of PA per 162 games; 10.5 is the relationship between runs and wins.) Adding in the wins above average at the position plus the positional adjustment gives you wins above average per 162 games. Add in the replacement level, and that gives you WAR per 162 games. Simply multiply that number by the percentage playing time you expect (no more than 90%, typically at 85% for regulars), and you have your WAR.

For starters, you multiply the wins above replacement by the number of full games (expected innings divided by 9). Use 20-24 for your full-time starters. Use 7-9 full games for your relievers.

Ok, so how many wins above replacement are there in AL and NL?

For nonpitchers in AL:

2.5 * 8 * 14

+ 1.0 * 1 * 14

+ 2.0 * 0.1 * 14

= 297 wins.

That’s 2.5 wins for every average AL nonpitcher at the 8 fielding positions, times 8 AL nonpitchers times 14 teams. The second line is the average hitter as a DH. The third line is the average hitter as a PH.

For starters in AL:

(.490-.370) * .66 * 162 * 14 = 180 wins

That’s a .490 win% for the average starter, times 66% of the innings per game, times 162 games times 14 teams.

For relievers in AL:

(.520-.460) * .34 * 162 * 14 = 46 wins

For closers bonus in AL:

(.610-.570) * 1.8 * 8 * 14 = 8 wins

The 8 is the number of full games (72 innings) we give a closer. The 1.8 is his LI.

Adding it up, and we get 531 replacement wins in the AL. Nonpitchers get 56% of that and pitchers get 44%. Of pitchers, starters get 77% and relievers 23%.

Repeating for the NL.

For nonpitchers in NL:

2.0 * 8 * 16

+ 0.5 * 0.05 * 16 (DH)

+ 1.5 * 0.40 * 16 (PH)

= 266 wins.

For starters in NL:

(.490-.390) * .64 * 162 * 16 = 166 wins

For relievers in NL:

(.520-.480) * .36 * 162 * 16 = 37 wins

For closers bonus in NL:

(.610-.570) * 1.8 * 8 * 16 = 9 wins

Adding it up, and we get 478 replacement wins in the NL. Nonpitchers get 56% of that and pitchers get 44%. Of pitchers, starters get 78% and relievers 22%.

As you can see, despite having 2 more teams, there is more talent in the AL, on the order of +53 wins. This was of course manipulated by me with the replacement levels. This would imply about $120MM more payroll (above the minimum) in the AL than the NL. And that’s close to reality.

The total number of replacement wins is 531 in the AL and 478 in the NL for 1009 wins (average of +33.6 wins above replacement; since the average team wins 81, that sets the replacement team at 47.4 wins, or 0.292 win%).

The average AL team is 531/14= +38 wins above replacement (or +.234 wins above replacement per game), while the average NL team is 478/16= +30 wins (or +.184 wins above replacement). Since the replacement level is .292, that gives us the following as the average win levels in each league:

AL: .292 + .234 = .526

NL: .292 + .184 = .476

A head-to-head of a .526 team facing a .476 team would result in a win% of .550 for AL. That’s also the reality of the situation, and the replacement levels for the two leagues was set with this in mind.

The totals by position:

563 wins nonpitchers

346 wins starters

100 wins relievers

1009 wins total

This implies that 56% of your payroll (above the $400K minimum per player) should go to nonpitchers, 34% to starters, and 10% to relievers. For reasons of risk, you might give a bit less to your pitchers.