# Application of my fWAR League Adjustment Method

This article is a follow-up to my previous one in which I will work through some examples. You should try to get an intuition on it. If the concept seems too complicated I have to apologize for not explaining myself well because I sincerely think this is very straightforward and no voodoo and could help improve fWAR even further… which is mindboggling if you think about it. It could improve projection systems as well as the correlation of WAR and actual wins while also handling players changing from the AL to the NL or vice versa more elegantly.

I will simply follow my steps 1-4 from my previous article to figure out the proper league adjustment and continue with some WAR calculations. I will use the 2014 season as my guinea pig.

While playing around with it I also stumbled upon a wRC+ adjustment that has to be done because of a) the independence of both leagues and b) the differing league strengths. I will tackle this issue in my next article.

All right, here are steps 1)4).

1) I need to figure out the wOBA values, R/PA, FIP, R/W, cFIP for each league individually. These can normally be found here. I will not list every single wOBA value here because that doesn’t add much to the explanation and saves me some time.

AL (2014):

wOBA: .312

R/PA: .110

FIP: 3.82

R/W: 9.25

cFIP: 3.16

NL (2014):

wOBA: .308

R/PA: .105

FIP: 3.66

R/W: 8.97

cFIP: 3.10

The exact values for all of MLB found on the Guts! page is conveniently exactly the arithmetic mean of my AL and NL values.

2) All right, we now move on to step 2 which is to figure out the interleague record. I suggested that a 3 year rolling regressed average could be a possibility with years N-1, N and N+1 as inputs. I cannot see into the future, for that reason I will simply use the 2012-2014 interleague record based on pythagenpat. This comes out to a .539 W% for the AL. Conveniently, the actual W% is exactly the same. For demonstration purposes let’s just do a farmer’s regression and call that a “true talent” .530 W%.

3) This is the seemingly tricky part but once you got your head around it is is very easy to grasp. As a reminder: the three necessary “true” replacement levels needed for all WAR calculations are .294 in general for teams – this is where the fixed 1,000 WAR each year comes from – the .380 replacement level for starting pitchers and the .470 for relievers.

Imagine an NL team that is a .500 team within the NL. This team plays a .500 AL team within the AL. That needs to be stressed. Those teams are NOT of equal strength, even if both have a .500 record. Why, you ask? Because if they were, we would not see an advantage for the AL in interleague play. We would see a balanced .500 interleague record. That is not our reality and we can confidently conclude that the NL is the weaker league as of today.

Following this line of thought, what happens if two replacement teams out of each league play each other? Well, this means a .294 NL team plays a .294 AL team. What would the outcome be? A .530 winning percentage in favor of the AL. This comes straight out of the interleague record.

How much better than a .294 W% would this NL team have to be in order to win exactly half of its games against this .294 AL team? This is where the odds ratio comes into play and it spits out a .320 winning percentage. That means if a .320 NL team faces a .294 AL team in an environment, in which the AL wins 53% of all interleague games, we would finally expect parity. A .500 interleague record. This .320 is our new “artificial” replacement level for the NL in 2014.

On the other hand we have to ask the question: How much worse than a .294 can an AL team be when facing a .294 NL team and still win half of its games? Odds ratio says a .270 AL team would still win 50% of all games against a .294 NL team in a context where the AL wins 53% of all interleague games. This .270 is our new “artificial” replacement level for the AL in 2014.

4) Remember that our “regressed” interleague record suggests the AL to be the stronger league, thus worthy of receiving more share of the WAR-pie. Now it is time to figure out how much more they deserve.

We figured out a .270 “artificial” replacement level for the AL. Therefore, we can distribute (.500-.270)*15*162 = 559 WAR towards the AL. This is split up 57/43 between position players and pitchers.

In the National League we found a .320 “artificial” replacement level. Therefore, we can distribute (.500-.320)*15*162 = 437 WAR towards the NL. Same 57/43 split.

Now 559+437 = 996, which is not equal to 1,000. This is because of the odds ratio being non-linear the closer it gets to the extremes but I might be totally mistaken here. This usually is where Tangotiger appears out of the dark and helps out with fancy math or steps in when the math gets hurt. I don’t really see it as a problem.

We could either distribute the remaining 4 WAR 50/50 between both leagues or adjust the replacement levels slightly to arrive at exactly 1,000 WAR. Both would change individual WAR figures only on an atomic level.

I want to point out that this kind of inconsistency is very common in the implementations of WAR. rWAR and fWAR both have some adjustment runs to match inconsistencies like that. This doesn’t even make a difference on a player level. It would not even change a team’s WAR figure by 1/10 I guess.

WAR calculations

After you have come this far you are probably interested in how much certain player’s WAR figure might change. Again, I won’t list every step necessary but only the actual results. If you ask yourself how I have done it, you should take a look here, here and here. If that doesn’t help out, just comment with your question and I will walk you through.

My example will be Mike Trout. I will show the differences of some of the more important and interesting stats as (OLD/NEW). Forgive me for not being a formatting wizard.

NOTE: For sake of better comparison I will present the “new” run values with an exchange rate of 9.117 R/W (currently used). Otherwise 1 run wouldn’t have the same meaning since in my WAR calculations 1 win equals 9.25 runs.( See step 1  ) This makes this an apples to apples comparison.

Trout:

wOBA: (.403 /.402)

wRC+* : (167 / 170)

WAR**: (7.8 / 8.0)

batting: (52.1 / 54.0)

UBR: (3.0 / 3.0) unchanged

wSB: (1.8 / 1.7)

Fld: (-9.8 / -9.8) unchanged

Pos: (1.4 / 1.4) unchanged

Lg: (2.9 / 2.9)

Rep***: (19.9 / 19.9 )

*  I use a slightly different wRC+ calculation here. My league adjustment method would also improve the accuracy of wRC+ as a comparison tool between the two leagues. I will write another article dealing with the modified wRC+ calculation, as well as the wRAA and replacement runs modifications to improve the accuracy of fWAR.

** Fielding runs, UBR and positional adjustment were not changed. These three will never change, the league adjustment however will undoubtedly change, as well as wSB, although the changes would be tiny. It involves complete league stats, i.e. every single player’s stats.

*** The value of replacement runs will never be affected in my league adjustments even though I use different replacement levels for my calculations. Replacement runs will always be based on the .294 baseline. I hope this makes sense to you. If not I point out to the upcoming article of mine.

Outlook

In my next article I will lay out the modifications that have to be applied to wRAA, wRC+, batting runs and the replacement runs. I will show why my modifications make wRC+ more accurate in comparing both leagues and explain why this new league adjustment influences position player WAR more than pitcher WAR. Because right now, the fWAR-process for pitchers leans heavily, not entirely though, towards the independency treatment of both leagues – a cornerstone of my league adjustments.

Also look forward to a table of the players with the biggest and the smallest increase in WAR and the corresponding losses. In both the AL and NL there are players who gain or lose more than others. This has to do with the different run environments is my best educated guess so far. In the NL – the lower scoring league – extra-base hits become slightly more valuable. So does base-stealing. Opposite for the AL. So look forward to my next piece, fellows!

Guest
Noah Baron

A few thoughts: 1. Is it really necessary to use three years of data when calculating interleague play? Does the AL-NL interleague record in 2012 really have anything to do with the qualities of each league in 2014 and beyond? I think I would want to use the least amount of data possible where you still have a significant sample size – season N-1 and Season N. 2. I think your WAR calculations for each league are incorrect. While I’m somewhat unfamiliar with the particulars of your calculation, if you prorate to 1000 WAR you have the AL at 561… Read more »

Guest
Rahi

Just a quick question. In step two, you find that the American League has a .539 winning percentage against the National League and then regress that to .530. If you keep using this value of .530 in your calculations, doesn’t that imply that in inter-league games, its just one random AL team against another random NL team. IRL though, its not random scheduling of inter-league play. The league chooses teams that may have had a rivalry in the past or are within close proximity to each other in terms of geography. The last point may mean something if you look… Read more »