[情報] WAR, a case study: Fielder vs. Ryan

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The other night I tweeted that Prince Fielder's 50-homer season in 2007 --
when he hit .288/.395/.618 -- rates as the lowest wins above replacement
total among the 42 seasons a player has hit at least 50. His 3.4 WAR on
Baseball-Reference is one of just three of those 42 seasons the site
evaluates as worth fewer than 5.0 wins, Mark McGwire's 4.9 in 1997 and Sammy
Sosa's 4.5 in 1999 being the other two.

I followed up that factoid by mentioning that in 2012 Mariners shortstop
Brendan Ryan -- who hit .194 with a .277 on-base percentage and three home
runs -- was worth 3.3 WAR. How can two players of such extreme differences in
offensive production be valued so similarly? As somebody mentioned in a
follow-up tweet, it's numbers like this that make many fans skeptical of WAR
… or completely dismissive.

With that in mind, I thought it would be a good idea to do a rough example of
how WAR is calculated, using Fielder and Ryan -- and why it does work and why
it (hopefully) makes sense. (For a much more thorough description, here is
the Baseball-Reference explanation page, including the idea behind WAR and
the concept of replacement level, and here's the specific page on the steps
used for rating position players.)

As Sean Forman writes on Baseball-Reference, "The basic currency of WAR is
runs. We start with runs added or lost versus an average player and then
compare the average player to a replacement player." The formula is this:

    Players Runs over Replacement = Player_runs - ReplPlayer_runs =
(Player_runs - AvgPlayer_runs) + (AvgPlayer_runs - ReplPlayer_runs)


OK, we'll start with runs on offense.

Offense
Using the linear weights method of evaluating offense -- giving value to each
single, double, triple, home run, walk, hit by pitch, sacrifice and even
reached on error -- Fielder created 143 runs in 2007. Ryan created 35 runs,
so Fielder is off to a 108-run advantage right off the bat.

But remember that we have to factor in the context those runs were created
in. The National League in 2007 hit .266/.334/.423 (and even higher when you
filter out pitcher hitting) and the American League in 2012 hit
.255/.320/.411, which means Fielder will be compared to a better average
hitter than will Ryan. Fielder also played in Miller Park, which is rated as
a neutral park for the three-year park factors Baseball-References uses (park
factor of 100), while Ryan played in Safeco Field, an extreme pitchers' park
(park factor of 90, decreasing run scoring by 10 percent). So Ryan played in
a tougher offensive environment, which means his batting runs are accordingly
adjusted.

Also, playing time -- Fielder produced his runs in 681 plate appearances
while Ryan had 470. When each hitter is then compared to what a
league-average hitter would produce in that amount of playing time, Fielder
ends up at plus-44 runs and Ryan at minus-18, so the difference on offense is
now 62 runs.

Baserunning and runs on avoiding double plays
It should not surprise you that a guy coming in somewhere close to 300 pounds
doesn't earn extra value with his baserunning (including stolen bases and
caught stealing). Fielder is minus-3 runs on baserunning, but plus-1 on
double plays as he grounded into just nine that year. Ryan was average (zero
runs) in both areas, so picks up two more runs in value, leaving Fielder at
plus-60 runs.

Defense
This is the aspect of the game where Ryan shines. Baseball-Reference uses
defense runs saved from Baseball Info Solutions, which evaluates every batted
ball in a variety of categories, and then compares each player to the average
fielder at his position. Ryan is rated at plus-27 runs, a very high figure --
the second highest of any fielder in 2012, and the fifth highest by a
shortstop in the past decade.

Fielder, meanwhile, is rated at 15 runs worse than an average first baseman,
a very poor total.

Look, are defensive stats perfect? No. Are they pretty good these days? Yes.
Should one-year defensive stats in particular be viewed with some
reservations? Sure. Was Ryan's 2012 season a defensive fluke? I don't think
so. Defense runs saved has him at plus-25, plus-22, plus-18 and plus-27 in
his four seasons as a regular, the first two with St. Louis, so it has
consistently given high marks to his glove work.

As for Fielder, everyone would agree that he's not exactly Keith Hernandez at
first base. He's a big, heavy guy without much quickness who also made 14
errors that year. It's certainly plausible that he was 15 runs below an
average first baseman (his defense has rated better in recent seasons).

So Ryan has a huge 42-run advantage on defense, leaving Fielder at plus-18
runs.

There are those who will argue that the value of defense is being overrated,
that the margins between the best and worst fielders can't be that high.
Well, why not? Ryan had 601 total chances in the field in 2012 -- about a
full season's worth of plate appearances for a hitter. Sure, many of those
are routine grounders and easy pop-ups that any competent major league
shortstop can field. But a certain percentage of possible plays are not
routine, and that's where defensive value comes in to play. As for Fielder,
he made 423 outs at the plate in 2007, so he's not obtaining any value in
about two-thirds of his plate appearances, as well.

Final adjustments and wins
The final adjustment made is a positional adjustment. Obviously, it requires
more ability to play shortstop than first base, as reflected by the fact
teams will play lesser hitters there. Since Ryan was being compared only to
other good fielders at his position, and Fielder only to other first basemen,
that has to be factored in. Baseball-Reference's current values for
positional adjustment are plus-7.5 runs for shortstops (per 1,350 innings
played) and minus-10 for first basemen. This ends up giving Ryan plus-6 runs
and Fielder minus-10.

Which puts us at … Fielder at plus-2 runs.

From there, runs are converted to wins, and Fielder ends up at 3.4 wins above
replacement and Ryan at 3.3. It's important to keep in mind that WAR is an
approximation of value, not a definitive answer, but I hope this helps in
explaining why a player who hit .194 can be viewed with the same value as a
player who hit 50 home runs.

By the way, Fielder's WAR in 2012: 4.4. Even though he hit only 30 home runs.

--
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◆ From: 140.112.25.133
推 jet113102:別小看Fielder的速度好嗎? 好歹人家也有跑過場內全壘打
推 catsondbs:Brendan Ryan也有出頭天 XD
推 jojo2147:其實看完還是不大理解QQ
→ jojo2147:多打的分數跟多守下的分數同價值!?
→ jojo2147:runs不也跟打線位置後面的人有關係嗎? 雖然前提是自己要
→ jojo2147:先上壘
推 gn02530640:好文，我試著翻翻看好了@@
推 nickyang:計算WAR的runs不是真正創造的runs(沒人可以計算這個)
→ nickyang:是根據wOBA算出來的理論值
→ nickyang:所以跟前後打者無關
推 Guillen:推這篇，淺顯易懂！
推 nickyang:然後根據畢氏定理，多打的分數跟多守的分數長期而言等價
推 catsondbs:看Fangrahs的WAR兩人差遠了
推 catsondbs:這篇文另一方面完全是指出了WAR的不足
→ shancko:因為Fangraphs的WAR是用UZR 而不是Defensive runs saved
推 nickyang:用的方法不一樣算出來不一樣的結果怎麼會是問題-_-
→ nickyang:如果當初一家叫WAR一家叫XWB就問題了吧
→ nickyang:沒問題
推 bztfir:畢氏定理? 不是算三角形斜邊長的那個吧@@
推 maxspeed150:棒球的畢氏定理: 勝率~(得分)^2/(得分^2+失分^2)
→ maxspeed150:反正只要知道一點: BR和FG都"想要"做同樣的量化工作
→ maxspeed150:只是用的評鑑標準不一樣所以當然就會得到不同結果
→ maxspeed150:如果喜歡BR的模型 就以BR的當參考
→ maxspeed150:如果喜歡FG的模型 就以FG當參考
推 julians:我很好奇的是說，如果是這樣的話，那我們擺九個Ryan跟擺
→ julians:九個Fielder最後得到的勝場會不會差不多呢?
推 Guillen:不會，因為Ryan移去一壘的話WAR會大降，可能會變成負的。
推 julians:那如果是九個光靠守備就可以拿到近似或相等WAR的選手呢?
推 nickyang:不太可能，有些位置你守得再好也產出不了這麼多分
→ nickyang:即使是理論上，極端值應該都會有偏差
→ uranusjr:一壘手什麼都不做就 -10, 要在跑壘和守備 +40 實在太難
推 Guillen:在火力需求較高的位置，你守備再好也要打出一定水準才能產
→ Guillen:出相近的WAR，例如Kotchman在11'的WAR也是3.4，他的打擊三
→ Guillen:圍是.306/.378/.422。
推 julians:然後，如果Fielder移到游擊去WAR不也會因此大降呢?
→ pujos:胖王子去守游擊WAR可能會升.而且機率不是一般的大*-*
推 Guillen:這也不一定，要看他守備多掉的分數能不能跟打擊增加的分數
→ Guillen:抵銷，雖然有守位調整的優勢，但是他守備可能不是普通悽慘
推 gn02530640:胖王子照公式算移到游擊先加17.5好了，但守備也會扣吧
→ pujos:守備要扣到比在1b慘有可能嗎xdd
→ pujos:只要不是連一壘都傳不了.範圍小就小了
推 hunterqiji:任憑WAR再怎麼合理﹐真正付錢的老板和GM還是不認的
→ hunterqiji:一個簡單的問題﹐Ryan能簽到20M/y的合約嗎?
→ uranusjr:@pujos  游擊的守備機會比一壘手多很多; 即使守備一樣慘,
推 julians:這樣的話，那我把Fielder擺在游擊，這個Fielder跟Ryan
→ uranusjr:Fielder 站游擊會因為守備機會增加而被狂扣
推 Guillen:討論Fielder守SS的WAR意義不大，不會有人會讓他站的 XDDD
→ julians:因為WAR差不多，而貢獻獲價值近似的命題不會因此無效嗎?
推 NickWeglarz:理論上Fielder守一壘1年比平均一壘手多掉5分的話
→ NickWeglarz:那他守游擊一年應該比平均游擊手多掉25分
推 s9527206:@hunterqiji:這不就是之前討論過的命題嗎?因為現在的FA
→ s9527206:市場機制的效率並不高阿
推 pujos:胖王子去守ss假設只比ss平均多掉25分那早該去了xdd
→ pujos:加上Rpos比他在1B還賺阿.而且賺不少
推 NickWeglarz:理論上，是說如果他會守游擊的話
→ pujos:然後一B還可以換一個守備更差的大砲
→ NickWeglarz:理論上多掉25分就是守位校正啊，怎麼可能比1B還賺？
→ NickWeglarz:最差的游擊手1年也才多掉15分
→ pujos:所以說單以位子論.WAR對守備光譜越靠左的越不利
→ pujos:最差的游擊手=>DJ兄一年掉過27分的勒-.-
→ pujos:生涯平均18個賽季掉12.8分
→ pujos:超過15分的賽季8個.然後A-Rod守3B
推 NickWeglarz:守備數據本來就沒有在看一年的
→ pujos:對了他掉27分那一年.靠吃Rpos該年度WAR還比胖王子07年多0.3
推 NickWeglarz:我說的是說2012年最差的
→ NickWeglarz:Derek Jeter一年的UZR最差是-17.9
→ NickWeglarz:BIS的DSR有一些非常誇張的數據，我是沒研究過為什麼
→ NickWeglarz:會那樣
推 pujos:2012最差的是誰我不知道.不過Derek Jeter:-18
→ NickWeglarz:*DRS
→ pujos:不過BR用的是TZ.而不是UZR
→ NickWeglarz:Fielder的DRS平均每1200局是-9
→ NickWeglarz:守位校正理論上如果他能守游擊會是-29
→ NickWeglarz:Jeter的DRS平均每1200局是-9
→ NickWeglarz:打錯，-13
推 NickWeglarz:BR2003年後用的是DRS
→ sneak: 不會，因為Ryan移去 https://noxiv.com
→ sneak: 會那樣 http://yofuk.com