A KBO WAR

As I (and the world as a whole thanks to Ryu Hyun-Jin) have been gaining more interest in the Korean Baseball Organization, I have looked at different trades, signings, and potential Korean prospects mainly through a scouting perspective. While advanced stats and scouting reports are pretty easy to find and use, I decided that I wanted to see if I could design a WAR to compare the players in the league. Google basically laughed at me when I tried searching to see if anyone had done anything like this for the KBO. I have always tried to do different stuff on this blog to make it unique, and I think this will qualify.
Just out of ease, I decided not to do positional adjustments or use park factors. You can find the KBO park factors here. As you can see, the differences between parks aren't big, not nearly as much as you would see in the minors or majors. My guess is that this is because South Korea doesn't have the differences in climate that the United States (the country is smaller, and it seems like when one game is rained out, many times the others are rained out as well) has, so the difference would just be how the parks are designed. If anyone wants to do the work to add positional adjustments or park factors, go ahead (and I will retweet it or link to it or whatever).

For offensive numbers, we will use the most basic runs created formula, which is OBP * TB (total bases, not tubercle bacillus). For baserunning, we will use just the first formula (the stolen base percentage) for speed score, which looks like this:

 ((SB+3)/(SB+CS+7)-0.4)*20

Traditionally, speed score has anywhere from 5 to 7 different components, but it is difficult to calculate and I am really just looking for a launching point here (feel free to compute the whole speed score formula, including the one in the link above, if you want).

Instead of converting to runs literally (which would most likely be more difficult), I will use percentages. I usually consider baserunning as equally important to what one does with the bat (it is, after all, one of the 3 facets of the game), even though WAR calculus usually doesn't. Here, I think the range that we found in FanGraphs' baserunning metric in 2012 may be helpful. The best in baseball was 12 runs above average, while the worst was 6.7 runs below average. We will just assume that Mike Trout is somewhat otherworldly, as no one else was worth more than 8.3 runs of baserunning value and set the max at 10 runs. So a speed score of 10= 10 runs above average (and zero is 10 runs below average, a .5 speed score 9 runs below average etc.). This isn't perfect or anything, but I don't know how else to do it really (unless you use some kind of run based baserunning metric). When using examples of a few players below, I will show both the WARs and WAA (Wins Above Average, something I have grown to like more and more as I like the baseline better than a "replacement player") of players with and without the baserunning for transparency (in case someone wants to tweak it or just hates the way I am measuring baserunning). I am also going to assume a few things when it comes to baserunning that may or may not be wise, but will help me since we aren't using a run based metric. Because we are just using percentages and speed score is a rate stat and not a counting stat (HRs are counting stats, batting average and OBP are rate stats for example. WAR is somewhat of a mixture of both, as it can go down, but it generally trends up as the seasons and sample sizes get larger), I am assuming that speed and baserunning is a skill that would translate (as long as the sample size is decent, I will avoid small sample size guys) regardless of plate appearances. Since I won't be dividing by plate appearances like I am doing with batting, this stat will be more predictive than descriptive. It won't measure up to actual wins exactly (or at least as close as batting), but it should be predictive, which is more important anyway. We will set replacement level speed score at 3.5 speed score (since replacement level is usually set at .320 winning percentage, 3.5 just makes it easier here), or -2.5 runs below average, while average is 5.0. So a 4.5 speed score is -1 run to the WAA but + 2 runs better than replacement and so on. Just using our heavily simplified speed score, Billy Hamilton would have a 8.2 speed score in A + this year where he stole 104 bases (penalized somewhat by his 21 caught stealings), worth about 5 and a half runs better than average and nearly 10 runs above replacement while a fictional player whole stole 9 bases in 10 attempts would have a 6.1 Speed Score, worth just over 2 runs above average and 5 runs above replacement. Something I have never liked about WAR is that defense and baserunning is weighed versus average while hitting is weighted versus "replacement". This is why I am doing both, including looking at replacement baserunning.

When looking at general batting, we will use 64% of average runs created as replacement level (.32 * 2, if 1 is average, .64 is replacement). Of course, we will have to convert total runs created to runs created per plate appearance. I think OBP * TB /PA should work. For instance, KIA's Ahn Chi-hong had a 64.195 RC in 2012 or .11504 RC per PA. With league average OBP being about .334 and 12814 total bases accumulated (by my count) in about 38,897 plate appearances, there were 4279.876 runs "created" or .11003 runs created per plate appearance. Since Ahn had 558 PAs in 2012, he was worth just short of 3 runs more than an average hitter. Using this same formula, replacement level is .07042 runs created per plate appearance.

So here are a few KBO hitters' WARs and WAAs from the 2012 season:

Park Yong-taek (LG): 2.038 Batting WAA, 4.23 Batting WAR, 6.666 Speed Score, 2.3712 Offensive WAA, 4.8532 Offensive WAR

Lee Seung-yeop (Samsung): 3.291 Batting WAA, 5.493 Batting WAR, 5.85 Speed Score, 3.461 Offensive WAA, 5.963 Offensive WAR.

Park Suk-Min (Samsung): 4.005 Batting WAA, 6.1796 Batting WAR, .33 Speed Score, 3.061 Offensive WAA, 5.5356 WAR (the differences between Lee and Park make it important that you factor in baserunning. He is the better hitter, but his complete lack of baserunning skills makes him less valuable).

Choi Hee-Seop (KIA): .478097 Batting WAA, 1.670358 Batting WAR, 3.7648 Speed Score, .22513 Offensive WAA, 1.78331 Offensive WAR

Kim Hyun-Soo (Doosan): .576127 Batting WAA, 2.520978 Batting WAR, 3.25 Speed Score, .226127 Offensive WAA, 2.53097 Offensive WAR

Choi Jung (SK): 3.732841 Batting WAA, 5.923274 Batting WAR, 5.1428 Speed Score, 3.7614 Offensive WAA, 6.25183 Offensive WAR

Lee Ho-Jun (SK): 2.920088 Batting WAA, 4.916432 Batting WAR, 1.2308 Speed Score, 2.17392 Offensive WAA, 4.51182 Offensive WAR

Park Jae-Hong (Free Agent, formerly of SK): .25284 Batting WAA, .72816 Batting WAR, 0 (technically negative) Speed Score, -.74716 Offensive WAA, .02816 Offensive WAR

Kang Jung-Ho (Nexen): 4.366643 Batting WAA, 6.42202 Batting WAR, 6.5454 Speed Score, 4.67755 Offensive WAA, 7.03293 Offensive WAR

Park Byung-ho (Nexen): 4.17422 Batting WAA, 6.39238 Batting WAR, 4.7778 Speed Score, 4.12978 Offensive WAA, 6.63678 Offensive WAR

Lee Jong-wook (Doosan): -4.32519 Batting WAA, -2.356574 Batting WAR, 5.3334 Speed Score, -4.25851 Offensive WAA, -1.92323 Offensive WAR

Lee Yong-kyu (KIA): -.23664 Batting WAA, 2.06074 Batting WAR, 6.9206 Speed Score, .14748 Offensive WAA, 2.74486 Offensive WAR
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Park Yong-Taek (LG): 2.027332 Batting WAA, 4.229648 Batting WAR, 6.6666 Speed Score, 2.356063 Offensive WAA, 4.86297 Offensive WAR

Kim Joo-Chan (Lotte): .720164 Batting WAA, 2.653104 Batting WAR, 5.46154 Speed Score, .812 Offensive WAA, 3.0454 Offensive WAR

Jang Sung-ho (Hanwha): .6027 Batting WAA, 2.58716 Batting WAR, .33 Speed Score, -.33063 Offensive WAA, 1.95386 Offensive WAR

For pitchers, we will create two different WARs and WAAs, one using ERA and one using FIP (much like the difference between FanGraphs' and Baseball Reference's pitching WARs). Using ERA is very simple, as you simply determine how many earned runs a pitcher allowed more/less than average/replacement. League average ERA in the KBO was about 3.82125, which I believe would set replacement level ERA at 5.0443. For ease, we would round to two decimal places, to make average 3.82 and replacement 5.04. This would mean a replacement pitcher would give up .56 runs per inning and an average pitcher would give up .42 runs per inning. Of course, ERA is not always a very helpful way to evaluate pitchers as there are many variables (official scoring, defense, luck or randomness) that go into how many runs a pitcher allows (ones that, most importantly, they do not control). So this is why we will also use FIP, or Fielding Independent Pitching, which is relatively easy to calculate (this link is helpful). League average FIP in the KBO in 2012 was about 3.80506. This is close enough to league average ERA that we will just use the league average and replacement ERA when calculating the FIP part of the WAR and WAA. When calculating FIP WAR and WAA, one must find the FIP, then divide it by 9, then multiply it by the innings pitch to find "FIP runs" (I left the raw FIP runs totals just because). Then, we subtract the average and replacement runs like above with the ERA WAR. I did not adjust for reliever or starter runs, so this setup may overrate relievers. Some notables:

Ryu Hyun-Jin: 2.2692 ERA WAA, 4.8256 ERA WAR, 50.93 FIP runs, 2.5762 FIP WAA, 5.1326 FIP WAR

Dave Bush: -.58414 eWAA, .55448 eWAR, 40.79146 FIP runs, -.663286 FIP WAA, .475334 FIP WAR

Scott Proctor: 1.22386 eWAA, 1.99848 eWAR, 16.3301 FIP runs, .60685 FIP WAA, 1.35347 FIP WAR

Mitch Talbot: -.29014 eWAA, 1.64648 eWAR, 63.62903 FIP runs, -.553043 FIP WAA, 1.383577 FIP WAR

Yoon Suk-Min: 1.126 eWAA, 3.268 eWAR, 47.95632 FIP runs, 1.630368 FIP WAA, 3.772368 FIP WAR

Dustin Nippert: 1.248 eWAA, 3.964 eWAR, 85.3115 FIP runs, -3.8315 FIP WAA, 2.33285 FIP WAR

Henry Sosa: .38786 eWAA, 2.45048 eWAR, 55.26643 FIP runs, .659957 FIP WAA, 2.723837 FIP WAR 

Ryan Sadowski: -.9 eWAA, 1.2 eWAR, 59.889 FIP runs, .3111 FIP WAA, 2.4111 FIP WAR

Bong Jung-Keun: 1.096 eWAA, 1.628 eWAR, 10.28888 FIP runs, .567112 FIP WAA, 1.099112 FIP WAR

Shane Youman: 2.44572 eWAA, 4.96096 eWAR, 59.21234 FIP runs, 1.624486 FIP WAA, 4.139726 FIP WAR

Seo Jae-Woong: 2.12 eWAA, 4.36 eWAR, 62.55522 FIP runs, .464478 FIP WAA, 2.704478 FIP WAR 

  Denny Bautista: .212 eWAA, 1.416 eWAR, 33.57784 FIP runs, .254216 FIP WAA, 1.458216 FIP WAR

Mario Santiago: .40386 eWAA, 1.73848 eWAR, 44.66235 FIP runs, -.463635 FIP WAA, .870565 FIP WAR

Radhames Liz: .15586 eWAA, 2.27448 eWAR, 53.13953 FIP runs, 1.041907 FIP WAA, 3.160527 FIP WAR

The Korea Herald gives us the best context when it comes to salary:

"total of 425 South Korean players, excluding rookies and foreign players, will receive 94.4 million won ($84,108) on average for the 2012 season"

While KBOData has both the official salary and signing bonus for each foreign player, this is usually not considered reliable, as it is widely believed that these players receive money off the record to avoid salary cap issues. Because of that, while we will look at many foreign players, we won't put too much weight in their listed salaries.

Since there were 8 teams in the KBO in 2012 (the Dinos joining in 2013), this means that each team is paying about 53 players (even though there are 43 players on most active rosters. This number must include minor league and inactive players). This means that the average payroll in the KBO is about 4.458 million dollars. If .320 is considered "replacement level", then a team just looking to make the playoffs would need approximately 22.44 wins over replacement (the worst playoff team won 65 games in a 133 game season in 2012). This means that (without free agent contracts considered) a team looking to make the playoffs with an average payroll can spend 198,660 per "win". This number seems weird because they are so many players. You aren't trying to fill out an 25 or even 40 man roster, you are paying 53 players, so you are only expecting .4234 wins per player.

Of course, as someone mentioned to me, KBO free agency (and player moves in general) is not a "free market". Inefficiencies are basically built in. Of course, the MLB is the same way, and perhaps in many ways, worse (players are subject to the draft and can only negotiate with the team they were drafted by, receive very little money money outside of the signing bonus with no opportunity to willingly leave until after 6 years, and if they do make it to the Majors, they are subject to 6 more years of "team control). This is why an average player can be worth ~10 million in the MLB, while mean salary is around 3.1 million dollars. The best way to really measure the salary per WAR is for someone to gather up all the free agent signing sin the KBO few years or so.

Again, this isn't a projection to be used to project how certain KBO players would perform in the Majors, the NPB, or even the minors. This is just to put the statistics in a better context and give us an idea of how the market there is working and allows us to evaluate KBO signings more clearly (hopefully).

On a side note, 9 of the pitchers listed about pitched in the Majors (and Mario Santiago pitched in the Minors). In the KBO, according to the FIP WAA (just in 2012 of course, they ranked like this):
1. Youman
2. Liz
3. Sosa
4. Proctor
5.Bautista
6.Sadowski
7. Talbot
8. Bush
9. Nippert

Here are there rankings according to career Baseball WAA in the Majors:
Sadowski: 0.0
Youman: -.3
Sosa: -.8
Nippert: -1.9
Proctor: -2.3
Talbot: -2.8
Bautista: -3.0
Liz: -3.0
Bush: -5.3
Obviously there are some major sample size issues, but there seems to be a little bit of "correlation" (using that term very loosely), but not much.
If anyone finds any mistakes/obvious flaws or has an idea of how to improve this, let me know. I am open to suggestions.