After Matt Garza reportedly signed with the Brewers for $52 Million over 4 years today, the initial response was that it was a steal. Baseball writer Joe Sheehan tweeted that the signing was “Grand Theft Pitcher“. Sure, a day after the Yankees spent $175 Million on a big question mark, the price for Garza looks like a bargain. Upon closer analysis, however, the deal appears to be pretty close to what we should expect given what we know about the cost of a win, inflation, and aging curves. This can be seen by using the same model that Dave Cameron writes about so frequently.

This model assumes that in 2014, a win costs $6 million dollars, and that the cost of a win will increase by 5% each year. Steamer projects Garza for 2.8 WAR in 2014, and I subtracted 0.5 WAR each year to account for age-related decline. As with the Kershaw contract, the model pretty much nails the cost for four years of Garza. The deal appears to be slightly team-friendly, with the Brewers getting 0.13 wins of value over the course of the contract. Put in money terms, they saved about $800K for Garza’s expected production. His health concerns (he has totaled 259 innings in the past two seasons) mean extra risk for the team, making it tough for me to get really excited about the contract. According to the model, the Brewers pretty much paid market value for Matt Garza.

But despite the numbers in front of me (and you), the contract does feel like a bargain. Why is this the case? This brought me to the greater point of this article, which was to try to find out the real market value for the 2014 free agent class. To do this, I applied the same model explained above to the 14 major contracts that have been signed this offseason by MLB free agents. These contracts are all include at least 3 years and $20M guaranteed, and total nearly $1 Billion. This leaves out relievers (which never quite fit into the model), injury-prone bounce-back candidates like Josh Johnson, and of course Masahiro Tanaka (since he’s extremely difficult to project). Ten of the fourteen players are between the ages of 29 and 31. For 2014 WAR, I used an average of Steamer and ZiPS (where available), and in the few instances where there was a team option or buy-out, I included the cost of the buy-out in the final year of the contract, as players in their mid-30s are rarely worth the cost of the option year. Lastly, rather than projecting the money a player should have earned, I simply calculated the WAR that a player is being paid to be worth (Wins / Salary) and compared it to their projected WAR for the duration of the contract. Without further ado, the table:

While your first instinct may be to declare most of these contracts huge overpays, the fact of the matter is that if everything appears to be an overpay, we need to adjust our baseline. According to the model, teams have paid for 146 wins, but are only projected to get back 124. What could account for the difference between the model and reality? On one hand, we have to consider the fact that every team values a win slightly differently. The Yankees have a huge incentive to put together a competitive team or they risk alienating an impatient fanbase. A win is worth more to a team on the brink of contention than a team sitting at the bottom of its division. This could be driving much of the variation, but is impossible to fully account for.

This leaves us with four factors that could cause the discrepancy between the model and the market that we can adjust for. First is the initial evaluations of the players. For instance, Shin-Soo Choo is coming off of a 5.2 WAR season, but is projected for just 2.9 WAR by Steamer. If we pencil Choo in as a 3.5 WAR player in 2014 (Oliver has him at 5.4), then he is set to produce 14 WAR during his 7-year contract, and be worth “only” -4.55 wins relative to his contract. The second is player aging. Taking off half a win each year is a quick and relatively accurate way to calculate future WAR for players who are already around 30 years old. However, some research has suggested that elite players may peak later and/or decline slower, which could affect many of these high-priced free agents (at least for the first few years of the contract).

The third and fourth variables are the cost of a win in the present and in the future. We’re using $6 Million per win, but other research has suggested that a win may cost more like $7 Million. In addition, the model increases the cost of a win by 5% each year, and some teams might suspect that rate to be higher with all the additional money flowing into the league.

After fixing the biggest outlier of the table (by projecting Choo for 3.5 WAR in 2014), these are the adjustments that would have to be made to a single variable (with all others held constant) to give us a model that properly values this free agent class so far:

Player Evaluation: The team signing the contract expects the player to perform roughly 0.23 WAR better than the Steamer/ZiPS projects in 2014.

Player Aging: The team signing the contract expects the player to decline at roughly 0.37 WAR per season.

Present Cost of a Win: One win (+1 WAR from a player) is currently worth $6.9 Million on the open market.

Future Cost of a Win: The cost of a win is expected to increase by 11.5% each year for the life of the contracts.

As is usually the case, the truth probably lies somewhere in between, with a little bit of each. In some cases, the driving force may be different for each team and each contract. The Mets may have signed Granderson believing that he can be worth 2.6 WAR in 2014 (as opposed to 2.2 from the projection systems), while the Mariners may have agreed with Steamer and ZiPS that Robinson Cano will be worth 5.35 WAR in 2014, but might project him for a slightly slower decline.

Just for fun, I’ll take a shot at modifying the model with a few minor adjustments so that the expected wins purchased matches the expected production. For my updated model, I’ll use the following parameters: Steamer/Zips are accurate measures of current talent, the players signed will decline 0.45 WAR per season after 2014, a win currently costs $6.4 Million, and the cost of a win will rise by 6% in the foreseeable future. Here’s the adjusted table:

Reducing the rate of decline and increasing the cost of a win helps out the longer contracts quite a bit, so Robinson Cano’s contract starts to look a lot better. However, the net benefit is largely offset by committing such a massive amount of money to a single player who could get seriously injured or decline sooner than expected. With the new model, the Garza deal looks more like a bargain (although I would still hardly call it a steal), and a few contracts that looked like a market value or a slight overpay appear to be more team-friendly than initially anticipated (McCann, Peralta, Infante, Feldman, and Saltalamacchia). Carlos Ruiz looks like a downright steal. Keep in mind that even just netting half a win translates into an extra $3 Million of value, so we’re talking about a pretty significant savings here.

In closing, Cameron’s quick-and-dirty model works quite well, but given the contracts signed so far this season, appears to require some minor adjustment. It’s impossible to know which of the factors require adjusting and how they vary from one team to another, which is what makes projecting these contracts and determining whether a contract is a bargain or an overpay so difficult. As is always the case, only time will tell, and as more free agents sign we’ll be able to see if the new model checks out and make necessary adjustments.

All projections are from Steamer and ZiPS. Contract information is from Fangraphs and Baseball-Reference.

Last week I wrote an article on a little bit of research I had done regarding the contributions of domestic vs. international players in 2013, among players who had accumulated at least 300 plate appearances. See the link below in case you are interested to see the first piece:

http://www.fangraphs.com/community/do-international-players-contribute-more-than-domestic-players/

I got several great comments and ideas, which was the idea, so thank you for that, and I moved ahead to further the research with an extra question that was raised in a few of the comments. I investigated whether most of the international players are All-Star caliber. Obviously, “All-Star caliber” is a very vague description, but the idea is essentially to see if front offices aim to sign international players that they believe will contribute a significant amount at the Major League level, rather than just acting as an organizational filler.

In my experience in international baseball, players are not brought States-side from the Dominican academies because the front office believes the player will be a great organizational piece, so let’s bring him over and groom him to be a coach or scout some day when his playing days are over. That’s not the thought process. Those types of players are likely never going to make it off the island as a player.

So the first thing I did was to take all the position players from the 2013 All-Star team and average all of their WAR values. That value comes out to 4.7 (WAR values taken from Baseball-Reference.com). I then sorted through each team to find how many players, domestic and international, had at least 4.7 WAR for the 2013 season. As I started to do this, however, I realized quickly that this 4.7 value might not be such a great marker. The All-Star roster is not the best way to find the best players in the game. Instead, I decided to make several markers and find the percentages of players that reached each of those marks. The average (4.7), median (4.4), and first (3.1) and third quartiles (6.1) were used to find percentages over a spectrum.

The results are summarized in the Table 1 below:

The data shows that there was a slightly higher percentage of international players that contributed at least 4.7 and 6.1 WAR when compared to domestic players in 2013 – 1.20% and 1.36%, respectively. This is an insignificant increase to make any great conclusions, especially given the small sample size of looking only at the 2013 season.

At the lower levels of the spectrum, there is a much more sizable difference in the proportion of players that have contributed certain levels of WAR – at least 3.1 and at least 4.4 WAR. 3.1 WAR is not elite, but it still represents a significant role in a team’s lineup. The most interesting piece of information I gathered from the results came from looking at the percentage of players that contributed less than 3.1 WAR in 2013. The percentage is significantly higher (41.12%) for domestic players than international (26.39%). This indicates that the hypothesis was correct in saying that roster filler spots are more likely to be composed of domestic players. Almost 75% of all international players contributed at least 3.1 WAR, whereas only 58.88% of domestic players contributed at least 3.1 WAR. Keep in mind this sample only takes into account players that accumulated at least 300 plate appearances.

This might be due to the fact that there are so many more players that come through each organization’s system from the Rule 4 draft compared to from international talent. It’s easier to find, easier to scout, and overall a cheaper process to go through. As mentioned earlier, teams are probably looking to promote international prospects from their academies that will be more than organizational fillers in the minor leagues.

Thanks so much for reading and, as always, I’d love to hear thoughts, criticism, and possible future directions to continue!

Ah, the quality start. It’s one of several stats (along with Bill James’ Game Score and even the venerable, much-maligned pitcher win) designed to answer an age-old question: How well did the starting pitcher do his job? Most would agree that a pitcher’s job is to keep his team in the game and give his offense a good chance to win, and most would agree that even the bare-minimum quality start (6 IP, 3 ER) is at least an acceptable performance.

That said, the criteria for a quality start are pretty arbitrary, and they’ve invited a bit of criticism. Why is a six-inning, three-run performance a QS, but an eight-inning, four-run outing is not? Why do we say a pitcher had a “quality” performance if he pitched to the tune of a 4.50 ERA? What if a pitcher has a quality start through six, then blows it in the seventh inning or later?

The usual response to those criticisms is that, hey, they tend to get worked out in the aggregate. Overall, pitchers actually do post very good numbers in their quality starts. The 4.50 ERA “quality” pitcher is a myth.

Then again, if we want something that works out in the aggregate, why bother with QS? Most of the issues with plain old pitcher wins get worked out over time, too. Aren’t they a good enough proxy for quality performances?

Of course not. The idea behind quality starts is a good one. All we need is a clearer look at the question the stat is designed to answer, and we’ll have a better definition for the stat itself.

The question: “How many times did the pitcher give his team a good chance to win?”

The definition: A pitcher is awarded an Adjusted Quality Start (AQS) if he:

1. Starts the game.
2. Pitches at least six innings.
3. Posts a run average (RA9) no worse than the league average.

#1 is, well, a requirement for something with the word “start” in its name. Moving on.

#2 is admittedly still arbitrary, but it’s a pretty good criterion, I think. A six-inning performance leaves only three innings to the bullpen, which isn’t all that much strain for most teams.

#3 is the change that gets to the heart of the issue. If the starter gives his team a decent number of at least league-average innings, then his teammates (assuming an average offense and average bullpen) should have at least a 50/50 shot at winning.

I use RA9 rather than ERA partly because of the well-documented issues with the definition of “earned” runs and partly because, as far as winning is concerned, it doesn’t especially matter whether a run is “earned” or not. A team that loses 4-3 because of four unearned runs still loses.

So, let’s put this metric to the test. In the American League in 2013, the league-average RA9 was 4.29, yielding three ways to post an AQS.

1) Pitch at least 6 innings, give up 2 or fewer runs.

This is by far the most common AQS because it includes all the zero-, one- and two-run starts. The top 10 in this sort of AQS were:

James Shields 20
Max Scherzer 20
Hisashi Iwakuma 19
Felix Hernandez 19
Bartolo Colon 19
Derek Holland 17
Ervin Santana 16
Anibal Sanchex 16
Justin Masterson 16
5 tied with 15

2) Pitch at least 6.1 innings, give up 3 runs.

Chris Sale was the master of the exactly-three-run AQS, as he did it 8 times in 2013. The top 10:

Chris Sale 8
Justin Verlander 7
James Shields 7
CC Sabathia 6
Jarrod Parker 6
Doug Fister 6
Yu Darvish 6
C.J. Wilson 5
7 tied with 4

3) Pitch at least 8.1 innings, give up 4 runs.

Unsurprisingly, this was by far the least common sort of AQS. It’s not often that a starter who gives up that many runs is allowed to pitch into the ninth. In fact, it only happened twice in the AL last year: CC Sabathia’s four-run, complete-game victory on June 5, and Corey Kluber’s 8.2-inning, four-run win on July 31.

Overall, your 2013 AL leaders in AQS:

James Shields 27
Max Scherzer 23
Hisashi Iwakuma 22
Chris Sale 22
Bartolo Colon 21
Doug Fister 21
Jarrod Parker 21
Justin Verlander 21
Yu Darvish 20
Felix Hernandez 20

Over in the National League, the average RA9 was a tick lower at 4.04. That’s not going to affect the two-and-fewer starts, but it’ll set the bar for the three- and four-run AQS a little higher.

1) Pitch at least 6 innings, give up 2 or fewer runs.

I doubt anyone will be surprised by the name at the top of the list.

Clayton Kershaw 22
Cole Hamels 20
Patrick Corbin 20
Jordan Zimmermann 19
Travis Wood 19
Madison Bumgarner 19
Zack Greinke 18
Gio Gonzalez 18
6 tied with 17

2) Pitch at least 7 innings, give up 3 earned runs.

Adam Wainwright 6
Cliff Lee 6
Mike Minor 4
Kris Medlen 4
Clayton Kershaw 4
Kyle Lohse 3
Cole Hamels 3
Andrew Cashner 3
Bronson Arroyo 3
13 tied with 2

(As an aside, the 6.2-inning, 3-run start just missed the cut-off in the NL, as that would be a 4.05 RA9 against a league average of 4.04. There were 22 starts that met those criteria in the NL last year, and I debated including them, but it would only make minor changes to the leaderboard. Mat Latos takes home the Just Missed Award with three such starts.)

3) Pitch at least 9 innings, give up 4 earned runs.

Only one NL pitcher pulled this one off in 2013. That was Brandon McCarthy, who gave up four in a complete-game loss on September 2.

Finally, your 2013 NL leaders in AQS:

Clayton Kershaw 26
Cole Hamels 23
Adam Wainwright 23
Cliff Lee 22
Madison Bumgarner 21
Patrick Corbin 21
Travis Wood 21
Jordan Zimmermann 21
Matt Cain 18
Zack Greinke 18
Gio Gonzalez 18
Lance Lynn 18

(If we include the 6.2-inning, 3-run starts, Gonzalez and Lynn take sole possession of ninth and tenth place with 20 and 19 AQS, respectively.)

There’s more that could be done with Adjusted Quality Starts – park factors, for instance – but that’s probably too much work for a stat that’s supposed to answer a pretty narrow question. If you want to know how often a starter kept his team in the game, this is a good, er, start.

I have always wondered what the contribution of international players, players signed as amateur free agents, was compared to that of domestic players, players who went through the Rule 4 Draft process. So much money is spent annually on academies in the Dominican Republic and, to a lesser extent, in Venezuela. Of course, each team has a different budget for these international operations. The Yankees’ complex in the Dominican Republic is much more extravagant than the Marlins’, for example. Regardless, a question I have always asked is what the return on investment (ROI) is for these teams, seeing as greater than 90% of the players that come through these academies don’t ever reach the big leagues or develop into true prospects.

A little background on why I am so interested in this topic: I spent a year in the Dominican Republic, initially volunteering at a successful amateur agency in San Pedro de Macoris (an hour east of Santo Domingo), then helping out with the Dominican Prospect League’s showcases and tournaments, eventually landing with the Yankees as a Player Development/Video Operations intern.

Without access to financial statements, it is nearly impossible to determine a ROI for each team. Instead, I decided to do something much more simple. I looked at the WAR contributions for each team from international players and from domestic players.

I used Baseball-reference.com for all my information, sorting position players by plate appearances and used an arbitrary minimum of 400PA in order to include players that had enough opportunity to contribute in 2013, either positively or negatively.

On the extremes, in 2013 the Cardinals, Orioles, Nationals, and Phillies all had zero international players with at least 400PA, whereas the Diamondbacks, Rangers, Tigers, and Brewers each had four international players with the minimum plate appearances. Overall, 48 international players with at least 400PA combined for 141.6 WAR in 2013. On the other side, 151 domestic players combined for 396.5 WAR. Translated into WAR per player, international players contributed a rate of 3.0WAR/player and domestic players at a rate of 2.6WAR/player.

While going through the players of each team, I realized that I am leaving out players who contributed a significant WAR even though they did not accumulate 400PA, so I decided to lower the minimum to 300PA and change the rate statistic to WAR per 600PA, instead of per player. Players such as Hanley Ramirez were previously left out due to injury. Also, players who were traded midseason and did not have sufficient playing time to post 400PA with one team were previously excluded, such as Alfonso Soriano, are now included with the lowered minimum. Here is what the new results show:

Table 1: WAR per 600PA for international and domestic players during 2013 season. Minimum 300PA. WAR values taken from Baseball-reference.com.

The results show that international players contributed a slightly higher rate of WAR per 600PA in 2013. The 0.2 greater WAR/600PA is not significant enough to conclude that international players contribute more talent per PA than did domestic players.

The next question I had was to determine what percentage of players who had 300PA were international and what percentage of WAR they contributed out of the total players with 300PA. What I found was that 24% of players with at least 300PA were international and they contributed 26% of WAR out of a total of 586.9 WAR. The percentage of players that are international seem to have contributed a similar percentage of overall WAR in 2013.

One small issue I came across was that there were a handful of players that went through the draft even though they are international players. A few examples are Jose Bautista (Dominican), Edwin Encarnacion (Dominican), Yan Gomes (Brazilian), Pedro Alvarez (Dominican), and Yonder Alonso (Cuban). I decided to switch this group of players from domestic to international. Table 2 shows WAR per 600PA, while changing this group of players from domestic to international.

Table 2: WAR per 600PA for international and domestic players during 2013 season, taking into account international players who were part of Rule 4 Draft. Minimum 300PA. WAR values taken from Baseball-reference.com.

The data from Table 2 shows that the gap between international and domestic players of WAR/600PA increased to 0.3, but this gap is still not significant. The question about percentage of WAR contributed changes slightly, but also not significantly. International players contribute 29% of total WAR while international players only make up 27% of total players who had at least 300PA in 2013.

In conclusion, from this short study, I cannot say that international players contributed significantly more WAR than do domestic players in 2013, but there was a difference of 0.3 WAR/600PA in favor of international players. Furthermore, 27% of players with at least 300PA were international and they contributed 29% of the total WAR in 2013 of all players with at least 300PA.

I did not look at pitchers yet, but am open to hear thoughts, criticism, and possible future directions to continue this brief study!

One of the best features of the wins above replacement (WAR) statistic is that it allows us to compare the greatest single-season performances across different eras in baseball history.  Anyone who has browsed the FanGraphs Leaders page should know that Babe Ruth had the top-five WAR seasons in history, all in the 1920s.  In terms of offensive runs added (batting and base running), Ruth’s 1921 season ranks as the best ever, followed by Barry Bonds’ 73 home run “asterisk” season of 2001.  But what about fantasy baseball?  Were these also the greatest (read most valuable) rotisserie seasons ever recorded?  That’s the question I set out to answer.

Using a slightly modified version of Zach Sander’s fantasy value above replacement (FVAR) system for valuing fantasy players, I estimated the auction value for every hitting season from 1920-2013.  First, I determined every player’s position eligibility based on some simple assumptions (meant to reflect Yahoo’s approach) whereby a player is eligible for a position if they meet any of the following criteria:

• Played at least 20 games at the position in the previous season.
• Started at least 5 games at the position during the current season.
• Played at least 10 games at the position in the current season.

With that established, I proceeded to calculate the z-scores, FVAR and  auction values (FVAR$) for roto leagues.  Based on a 5×5 12-team mixed league with $260 budget per team (and quite a few other assumptions) here are the ten most valuable fantasy seasons for hitters since 1920 (5×5, 12-team mixed):

At this point you’re probably asking: “What, A-Rod?!?!”  I know, as a Red Sox fan and sentient being I was not happy to see A-Rod at the top of the heap.  As much as you may like or dislike A-Rod in real life, if you drafted him first overall in your 2007 fantasy league you were not disappointed with his across-the-board production.  But, you might also be asking, as I did, how was A-Rod’s 2007 season worth $5 more than Babe Ruth’s 1921 season?   Ruth’s hitting and base running in 1921 added 119 runs compared to 75 runs added for A-Rod in 2007, so what gives?  As best I can tell, here are some reasons why A-Rod-2007 had a higher FVAR$ than Ruth-1921:

• Ruth’s replacement in 1921, Ralph Miller, was much worse than A-Rod’s replacement in 2007, Melky Cabrera.
• As a result Ruth-1921 had a much higher FVARz score than A-Rod-2007, but the average above-replacement player in 1921 also had a higher FVARz than the average above-replacement player in 2007.
• As shown in Zach Sanders’ third post on FVAR, the auction values are a function of FVARz divided by the average FVARz for above-replacement players.  Hence, Ruth’s FVARz was divided by a larger number to calculate FVAR$.

Does this make sense?  Yes actually, I think it does.  What it means is that in 2007 A-Rod and Melky Cabrera together were worth more than Babe Ruth and Ralph Miller together in 1921.  In a fantasy auction in 1921 it would have been unwise to spend too many fake dollars on the best players like Ruth and Hornsby (or drink in public because of that Prohibition thing) because you would have been stuck with the bottom players, like Ralph Miller, who were really, really bad (there were only 16 teams back then and no DH).

For fun, below is a dream fantasy lineup with the best hitters since 1920 at each position (5×5, 12-team mixed).  Enjoy.

I’m hoping to write more posts like this using historical FVAR, especially if readers/commenters think it worthwhile.

Twitter: @FVARBaseball

Website: fvarbaseball.wordpress.com

Pitching statistics are mostly based on rates. Sure, we have innings pitched, and if you want to annoy me, you can talk about wins and losses, and of course there are the “three true outcomes” of strikeouts, walks, and home runs, plus WAR. But nobody ever looks at how many runs a pitcher was above or below average. Runs allowed isn’t all that common of a statistic; you’re more likely to see ERA or RA9. Even strikeouts and walks are often expressed as a percentage of all plate appearances, or as an amount per nine innings. The defense-independent ERA estimators like FIP and its spinoffs are rates, just like ERA. Where batters have regressed plus-minus or counting stats like wRAA and wRC, pitchers have nothing.

However, there has got to be some value in counting stats for pitchers. If we want to know how many more or fewer runs a team would allow by putting in an average pitcher instead of any given pitcher, that statistic would be able to tell us. So I’m going to present here three basic different numbers, one based off of FIP, one based off of straight runs allowed, and the third based off of linear weights. Each will be in two forms – raw runs allowed and runs allowed above or below average. I’ll call them FIP-Runs and FIP-Runs Above Average (FIPRAA), wRC-Runs and wRC-Runs Above Average (wRCRAA), and, obviously Runs and Runs Above Average (RAA). Kind of long, yeah, but I didn’t want to call the FIP one FRAA because that already exists.

All data was obtained from FanGraphs except for the singles, doubles, triples, home runs, walks, and HBP against used to calculate wRC; FanGraphs does not have some of those so I used Baseball-Reference.

FIP-Runs

This should be pretty simple. Take a pitcher’s FIP. FIP is scaled like ERA, but we want to scale it to RA9 because we want to scale it to all the runs a pitcher allows, not just the earned runs. To do this, multiply it by a constant that changes yearly – for 2013, it was 1.08. This is the league RA9 divided by the league ERA.

Take that figure, multiply it by the number of innings they pitched, and divide by nine to get the number of runs that FIP says a pitcher should have allowed. That’s their FIP-Runs. Great. But now how do we get that to express how many runs above average they were worth?

Well, we already have FIP-, which tells us how much better a pitcher’s FIP was than league average – and it’s already park- and league-adjusted, to boot. So what I did was subtract each pitcher’s FIP- from 200 to get the inverse of their FIP- (so if a pitcher had a 90 FIP-, the inverse would be 110) and multiplied that by their FIP-Runs. That gave me the number of runs (adjusted to the park and league) that an average pitcher would give up in the same number of innings. Just subtract the pitcher’s FIP-Runs, and you have your FIPRAA. And while I was at it, I did the same thing for xFIP. You can find the numbers at the end of the article. But first, the next part:

Runs

I didn’t have to calculate these like I did with FIP-Runs because the numbers are already there – it’s just the total number of runs a pitcher allowed. I did, however, have to calculate RAA, for which I used the same method as I did with FIP-Runs: find the RA9- (this was not park- or league-adjusted because I calculated it myself), take the inverse, multiply it by the runs, and subtract the runs from that. Piece of cake. Now for the last, and hardest, part of this:

wRC-Runs

These were tricky. I had to calculate each pitcher’s wRC against by first finding their wOBA against with the raw number of singles, doubles, triples, etc. they gave up and converting that into wRC. (I’ve actually already put this in a community post in a different form). But from there, I could follow the same instructions as before: use the wRC against as runs allowed, find the wRC/9- (if you didn’t read the article I linked to earlier, wRC/9 is just wRC against scaled like RA/9), and from those two find the wRCRAA (quite a mouthful, I know).

So, without further ado, here are the numbers (sorted by FIPRAA):