战争与格瓦特发现了更具预测性的投战

Back in May of this year, we introduced kWAR, a pitching WAR statistic which we hoped would provide a more predictive alternative to fWAR. By utilizing kwERA’s simple focus on a pitcher’s strikeout and walk rates, we hypothesized that replacing FIP with kwERA in the calculation of pitcher WAR would produce a more predictive statistic than fWAR. Since then, we have collected the data from 2009–2019 to test our hypothesis. During our review of the data, we also chose to create an additional WAR statistic. Groundball kwERA WAR (gWAR) utilizes GBkwERA, an offshoot of kwERA which includes an adjustment for groundball rates, as its central component to try to rectify kWAR’s bias against extreme groundball pitchers. This article will take you through the changes that we have made to the kWAR formula, an explanation of gWAR and our analysis as to whether kWAR and/or gWAR can serve as a more predictive metric than fWAR.

早在今年5月，我们推出了kWAR ，这是一项WAR统计数据，我们希望它可以为fWAR提供更具预测性的替代方案。 通过利用kwERA对投手的三振和走动率的简单关注，我们假设在计算投手WAR时用kwERA代替FIP将产生比fWAR更具预测性的统计数据。 从那时起，我们收集了2009-2019年的数据以检验我们的假设。 在查看数据期间，我们还选择创建其他WAR统计信息。 地面球kwERA WAR(gWAR)利用GBkwERA，它是kwERA的一个分支，其中包括对地面球速率的调整，以试图纠正kWAR对极端地面球投手的偏见。 本文将带您了解我们对kWAR公式所做的更改，对gWAR的解释以及对kWAR和/或gWAR是否可以比fWAR更具预测性的度量标准的分析。

更改kwERA和kWAR公式 (Changes to kwERA and kWAR formula)

As we previously detailed in our initial article, kWAR is calculated in the same manner as fWAR, but with a park-adjusted version of kwERA replacing FIP as the central component. As a reminder, the formula for kwERA, as conceptualized by GuyM and popularized by Tom Tango is as follows:

正如我们之前在初始文章中详细介绍的那样，kWAR的计算方法与fWAR相同，但是kwERA的公园调整版本取代了FIP作为核心组件。 提醒一下，由GuyM概念化并由Tom Tango推广的kwERA公式如下：

kwERA = 5.40 — (12*((K-BB)/TBF)))

kwERA = 5.40 —(12 *((K-BB)/ TBF)))

In our previous calculations of kWAR, we used the above kwERA formula and included a unique park factor adjustment for each pitcher. While the simplicity of a fixed constant of 5.40 makes the formula easier to remember, it suffers insofar as the league average kwERA would not be equivalent to the league average ERA. As a result, utilizing kwERA in comparison to a pitcher’s ERA in any given year would be difficult without scaling both statistics to their respective league average. Rather than utilizing a fixed constant of 5.40, we have decided to adjust the formula to include a constant that pegs the league average kwERA to the league average ERA. Now, like FIP, the formula for kwERA will include a constant that changes annually to adjust for the league run-scoring environment. As a result, the new formula for kwERA for purposes of calculating kWAR is as follows:

在之前的kWAR计算中，我们使用了上面的kwERA公式，并对每个投手进行了独特的停车系数调整。 尽管5.40的固定常数的简单性使该公式更容易记住，但是它在联赛平均kwERA不能等同于联赛平均ERA的范围内受到影响。 结果，在不将两个统计数据均缩放到各自联赛平均水平的情况下，很难在任何给定年份将kwERA与投手的ERA进行比较。 我们决定不使用5.40的固定常数，而是决定调整公式，使其包含一个将联盟平均kwERA与联盟平均ERA挂钩的常数。 现在，就像FIP一样，kwERA的公式将包括一个常数，该常数每年都会更改，以适应联盟的得分环境。 结果，用于计算kWAR的kwERA新公式如下：

kwERA = LgConstant — (12*((K-BB)/TBF)))

kwERA = LgConstant —(12 *((K-BB)/ TBF)))

where the LgConstant value varies by year to ensure that the league average kwERA is equal to the league average ERA. The formula to calculate the constant is as follows:

其中LgConstant值每年都会变化，以确保联盟平均kwERA等于联盟平均ERA。 计算常数的公式如下：

LgConstant = LgERA + (12*((LgK-LgBB)/LgTBF)))

LgConstant = LgERA +(12 *(((LgK-LgBB)/ LgTBF)))

Our 2019 kWAR leaderboard has been updated to reflect this change in the kWAR formula as well as the release of the 2019 park factors from FanGraphs.

我们的2019 kWAR排行榜已更新，以反映kWAR公式的这一变化以及FanGraphs发布的2019停车系数。

gWAR简介 (Introducing gWAR)

Let’s start by rehashing our initial logic behind using kwERA, instead of FIP, to calculate pitching WAR. While statistics that accurately describe past events have value, being able to utilize metrics to predict future events are of utmost importance in decision making. Indeed, the goal behind ERA estimators such as FIP was to better measure how the pitcher performed and ignore other factors that affected their ERA such as defense. In doing so, FIP, as well as other ERA estimators, attempt to focus on the skill of the pitcher, as over time we would expect that the underlying skill would shine through as other external variables regress to the mean.

让我们首先使用kwERA(而不是FIP)来重新计算初始逻辑，以计算音高WAR。 尽管准确地描述过去事件的统计数据很有价值，但是在决策过程中，能够利用度量标准来预测未来事件至关重要。 确实，诸如FIP之类的ERA估算器背后的目标是更好地衡量投手的表现，并忽略其他影响其ERA的因素，例如防守。 这样做时，FIP以及其他ERA估算器都试图将重点放在投手的技能上，因为随着时间的推移，我们期望随着其他外部变量回归到均值，潜在的技能会逐渐发光。

FIP, which only considers strikeouts, walks and home runs allowed, accomplishes some of this goal. FIP has consistently proved to be more predictive of future ERA than ERA, indicating that it is more descriptive of the pitcher’s talent level than ERA. However, FIP’s inclusion of home run suppression, which has historically shown to be a statistic that varies on a year-over-year basis, reveals that some measure of batted ball luck is included in FIP. In response, kwERA chooses to completely ignore batted ball data in favor of a singular focus on strikeouts and walks, both of which are more stable from year to year on an individual pitcher basis. As a result, we would expect that kwERA would be a more predictive metric than FIP and it is!

FIP仅考虑允许三脚架，走步和本垒打，从而实现了这一目标。 事实证明，FIP比ERA更能预测未来的ERA，表明FIP比ERA更能说明投手的才华。 但是，FIP包括本垒打抑制作用，从历史上看，该统计数据逐年变化，这表明FIP包含了一些击球运气的度量。 作为响应，kwERA选择完全忽略击球数据，而将重点放在三振和走步上，这两种情况逐年逐年保持稳定。 结果，我们希望kwERA比FIP更具预测性，而且它是！

But by completely ignoring batted ball data are we throwing the baby out with the bathwater? Shouldn’t pitchers who consistently limit batted balls that are the most harmful be rewarded? As we alluded to in our initial article, both kwERA and kWAR include a bias against pitchers that induce groundballs at an above-average rate, as these pitches tend to have below-average strikeout rates. But groundballs are a positive outcome! To illustrate this point, consider the following table of statistics from 2019:

但是，通过完全忽略击球数据，我们是在把婴儿和洗澡水一起丢掉吗？ 始终限制最有害的击球的投手难道不应该得到奖励吗？ 正如我们在第一篇文章中提到的那样，kwERA和kWAR都包含对投手的偏见，这些投手会以高于平均水平的速度诱发地球，因为这些球场的三振出手率往往低于平均水平。 但是棒球是一个积极的结果！ 为了说明这一点，请考虑以下2019年的统计数据表：

Given that we know groundballs are generally a good result for a pitcher and that groundball rates, unlike home run rates, are stable on a year over year basis, shouldn’t pitchers who induce groundballs at an above-average rate be rewarded? Enter groundball kwERA (GBkwERA). Other than being a mouthful, GBkwERA is an ERA estimator developed by Jeff Zimmerman which incorporates a groundball rate adjustment to the kwERA formula. While the logic behind GBkwERA may be simple, the formula is a bit more complicated:

考虑到我们知道投球一般对投手来说是一个很好的结果，而且与本垒打率不同，投球率每年都稳定，难道不应该奖励以高于平均水平投球的投手吗？ 输入陆球kwERA(GBkwERA)。 GBkwERA除了让您大吃一惊外，还是由Jeff Zimmerman开发的ERA估算器，它在kwERA公式中加入了地面球费率调整功能。 尽管GBkwERA背后的逻辑可能很简单，但公式却有些复杂：

GBkwERA = kwERA*(-3.518 * GB²+2.344*GB+.629)

GBkwERA = kwERA *(-3.518 *GB²+ 2.344 * GB + .629)

Zimmerman’s analysis revealed that GBkwERA was one of the most successful ERA estimators in predicting future ERA, having a stronger correlation than both kwERA and FIP, the central components for kWAR and fWAR, respectively. As we were already collecting the data for kWAR in prior years, we chose to also develop gWAR to test whether replacing FIP with GBkwERA would create a better pitching statistic.

Zimmerman的分析显示，GBkwERA是预测未来ERA的最成功的ERA估算器之一，其相关性比kwERA和FIP(分别为kWAR和fWAR的核心组件)更强。 由于我们已经收集了前几年的kWAR数据，因此我们选择开发gWAR，以测试用GBkwERA代替FIP是否会产生更好的俯仰统计数据。

So how exactly do we calculate gWAR? As you might have expected, it is calculated similarly to kWAR (which as you may recall, is calculated similarly to fWAR). As a reminder, kWAR is calculated by calculating fWAR with a park-adjusted version of kwERA replacing FIP as the central component. As with kWAR, gWAR is calculated using a park-adjusted version of GBkwERA replacing FIP, with the park factors being unique to each pitcher based on the parks that they actually pitch in to ensure that pitchers who pitch more often in ballparks with extreme park factors for strikeouts, walks or groundballs don’t skew results. Note that the formula for kwERA used to calculate GBkwERA and gWAR use a slightly different league constant than the formula of kwERA used in kWAR. This is done to ensure that the league average GBkwERA is equal to the league average ERA. For a more in-depth discussion of how gWAR is calculated, please refer to our previous article introducing kWAR and FanGraphs’s description of how to calculate fWAR.

那么我们如何精确计算gWAR？ 如您所料，它的计算方式与kWAR类似(您可能还记得，其计算方式与fWAR类似)。 提醒一下，通过将fwAR替换为FIP作为主要组成部分，用停泊调整后的kwERA版本计算fWAR来计算kWAR。 与kWAR一样，gWAR是使用GBkwERA的公园调整版本代替FIP来计算的，公园系数是每个投手基于他们实际投球的公园而独特的，以确保在具有极端公园因素的球场中投球的频率更高对于三脚架，步行或垒球不会歪曲结果。 请注意，用于计算GBkwERA和gWAR的kwERA公式使用的联盟常数与kWAR中使用的kwERA公式略有不同。 这样做是为了确保联赛平均GBkwERA等于联赛平均ERA。 有关如何计算gWAR的更深入讨论，请参阅我们之前介绍kWAR的文章，以及FanGraphs对如何计算fWAR 的描述。

Now that we have gone through the nuts and bolts of gWAR, let’s take a look at some of the pitchers where gWAR and kWAR disagree the most:

现在，我们已经遍历了gWAR的基本知识，让我们看一下gWAR和kWAR最不一致的一些投手：

As would be expected, the pitchers whose gWAR most exceeded their kWAR were pitchers with extreme groundball tendencies and otherwise average to below-average strikeout rates. On the other side, the pitchers whose kWAR most exceeded their gWAR tended to be pitchers whose combination of high strikeout rates resulted in a kWAR that exceeded their fWAR, but whose groundball rates were below the league average. Zack Britton’s extreme variance between his fWAR, kWAR and gWAR help portray an important note for the use of WAR statistics. As with kWAR (and fWAR), gWAR should be used as a guidepost for measuring players and not as an absolute measurement as to how many wins they provided relative to a replacement player. kWAR and gWAR should be used in conjunction with other statistics.

可以预见，gWAR最大超过其kWAR的投手是具有极强的垒球倾向的投手，否则其平均出球率会低于平均水平。 另一方面，其kWAR最大超过其gWAR的投手趋向于其高三振出击率相结合导致kWAR超过其fWAR，但其垒球率低于联盟平均水平的投手。 Zack Britton在fWAR，kWAR和gWAR之间的极端差异有助于描绘有关使用WAR统计信息的重要说明。 与kWAR(和fWAR)一样，gWAR应该用作衡量玩家的指导，而不是绝对地衡量他们相对于替代玩家提供的胜利数。 kWAR和gWAR应该与其他统计信息结合使用。

预测未来表现 (Predicting Future Performance)

The goal of both kWAR and gWAR is to create a statistic that better predicts future pitcher performance. To test our theory, we collected pitcher data from 2009–2019, calculated the kWAR and gWAR for each pitcher and analyzed the effect of fWAR, kWAR and gWAR on the pitcher’s fWAR and RA9 in the following season.

kWAR和gWAR的目标都是创建一个能够更好地预测未来投手性能的统计数据。 为了验证我们的理论，我们收集了2009-2019年的投手数据，计算了每个投手的kWAR和gWAR，并分析了下个赛季fWAR，kWAR和gWAR对投手的fWAR和RA9的影响。

For each of these models, we needed to convert our WAR statistics into a rate-based statistic. At their cores, each of fWAR, kWAR, gWAR is the equivalent to a performance rate, less a baseline multiplied by playing time. Comparing raw WAR statistics from year to year would be skewed by variabilities in playing time. To solve this issue, we computed each of these WAR statistics on a per 100 total batters faced basis (i.e. WAR/TBF *100). As a point of reference, 100 TBF is ~25 IP. When referring to each of these WAR statistics in the sections detailing our analysis, we will be referring to the rate-based version of the statistic.

对于每个模型，我们需要将WAR统计信息转换为基于费率的统计信息。 从本质上讲，fWAR，kWAR，gWAR相当于性能速率，减去基准乘以播放时间。 逐年比较原始WAR统计信息会受到播放时间变化的影响。 为了解决这个问题，我们以面对面的每100个击球手(即WAR / TBF * 100)为基础来计算每个WAR统计信息。 作为参考，100 TBF为〜25 IP。 在详细说明我们的分析的各个部分中引用这些WAR统计信息时，我们将引用基于比率的统计信息。

未来战争 (Future fWAR)

In our analysis, we looked at each pitcher from 2009–2019 who (i) pitched in consecutive seasons and (ii) had at least 170 TBF (~35–40 IP) in each of those seasons. While our inclusion of the pitching brilliance of someone like Mike Ford or Adam Dunn (of the Cy Dunn Award) surely brings Maxwell Greenfield and I much joy, the small sample size noise dragged down the effectiveness of the models when they were included. The sample size of pitchers who met this threshold from 2009–2019 varied from 362 to 403. Fortunately, this equates to around 12–13 pitchers per team, the equivalent of a full pitching staff.

在我们的分析中，我们研究了2009-2019年的每个投手(i)连续几个赛季投球，并且(ii)每个赛季中每个赛季至少有170个TBF(〜35-40 IP)。 虽然我们加入了像迈克·福特(Mike Ford)或Cy Dunn Award奖的亚当·邓恩(Adam Dunn)这样的人，一定会给麦克斯韦·格林菲尔德 ( Maxwell Greenfield)和我带来很多快乐，但当样本加入时，小样本噪声却降低了模型的有效性。 2009-2019年达到此阈值的投手的样本数量从362到403不等。幸运的是，这相当于每个团队约12-13个投手，相当于一支完整的投手队伍。

Using a simple linear regression (for those familiar with R, we used the lm function), we created linear models showing the relationship between each of fWAR, kWAR, and gWAR in the first year (referred to in the plots below as Year X) and fWAR in the following year (referred to in the plots below as Year X+1). The plots below show each of the data points across our sample and the linear model that the regression function produced.

使用简单的线性回归(对于熟悉R的人，我们使用lm函数)，我们创建了线性模型，显示了第一年fWAR，kWAR和gWAR之间的关系(在下图中称为X年)和第二年的fWAR(在以下图表中称为X + 1年)。 下图显示了样本中的每个数据点以及回归函数生成的线性模型。

The results of our regressions suggest that both kWAR and gWAR are stronger predictors of the following season’s fWAR than fWAR itself. While the F-Test for each of the three models indicates that fWAR, kWAR and gWAR are statistically significant in explaining the variation in Year X+1 fWAR, the R^2 values for the kWAR and gWAR regression models indicate that these metrics explain 3–4% more of the change in fWAR than fWAR. We should note, however, that none of these models are particularly strong, as even the linear regression model which explains the highest amount of the change in Year X+1 fWAR, kWAR, leaves ~79% of the variation in the Year X+1 fWAR unexplained.

我们的回归结果表明，与fWAR本身相比，kWAR和gWAR都是下个季节fWAR的更强预测指标。 虽然这三个模型中的每个模型的F检验都表明fWAR，kWAR和gWAR在解释X + 1年fWAR的变化方面具有统计学意义，但kWAR和gWAR回归模型的R ^ 2值表明这些指标可以解释3 fWAR的变化比fWAR多–4％。 但是，我们应该注意的是，这些模型都不是特别强大，因为即使线性回归模型也能解释X + 1年的最大变化量fWAR，kWAR，却留下了X +年79％的变化量。 1 fWAR无法解释。

There are further reasons to suggest that both kWAR and gWAR are more predictive than fWAR. The table below shows the R^2 values for models in which each of fWAR, kWAR and gWAR from Year X are used to predict the same metric in the following season:

还有其他原因表明kWAR和gWAR比fWAR更具预测性。 下表显示了模型的R ^ 2值，其中使用X年的fWAR，kWAR和gWAR分别预测下一个季节的同一指标：

fWAR is the least predictive of itself amongst each of these WAR statistics, indicating that more of the variation in fWAR is due to external variables. While the R^2 values are not particularly strong, kWAR and gWAR are more heavily correlated with themselves on a year over year basis, which hopefully indicates that more of what they are capturing is the underlying skill of the pitcher, rather than random variability.

在所有这些WAR统计数据中，fWAR对其自身的预测性最低，这表明fWAR的更多变化是由外部变量引起的。 尽管R ^ 2值不是特别强，但kWAR和gWAR的年比值与它们之间的相关性更高，这有望表明它们所捕获的更多内容是投手的基本技能，而不是随机可变性。

未来RA9 (Future RA9)

We also wanted to test each of the WAR statistics in predicting future results. For our dependent variable, we used Year X+1 Runs allowed per 9 IP (RA9). By choosing RA9 as our dependent variable, we will limit the sample to pitchers with at least 170 TBF in each of consecutive seasons during our time period in which they played for different teams

我们还想测试每个WAR统计信息，以预测未来的结果。 对于我们的因变量，我们使用了每9个IP(RA9)允许的X + 1年运行。 通过选择RA9作为我们的因变量，我们会将样本限制在我们为不同球队效力的每个连续赛季中，每个赛季至少有170 TBF的投手

Why is it necessary for us to exclude players who pitched for the same team in consecutive seasons? Unlike each of our WAR statistics, which are derived using park-adjusted fielding independent metrics, RA9’s simple formula of runs allowed and innings pitched includes some measurement of the pitcher’s park and the defense behind him. As a result, the inclusion of players who played for the same team in consecutive seasons would skew the results since RA9 in year X would likely be correlated with RA9 in year X+1.

为什么我们必须排除连续几个赛季为同一支球队投球的球员？ 与我们的每个WAR统计信息(均使用公园调整后的野外独立指标得出)不同，RA9允许的奔跑和局限的简单公式包括对投手公园及其后防的一些测量。 结果，连续几个赛季为同一支球队效力的球员的加入会导致结果产生偏差，因为X年的RA9可能与X + 1年的RA9相关。

The below plots show RA9 in year X+1 plotted against fWAR, kWAR and gWAR in year X as well as the linear model produced by our regression.

下图显示了X + 1年的RA9与X年的fWAR，kWAR和gWAR的关系，以及我们回归分析得出的线性模型。

While the plots generally show the negative relationship we would expect (i.e. that pitchers with higher WAR in year X will have lower RA9 in year X+1), we can see from the R^2 values that the models do not explain the vast majority of the change in RA9. Even the statistic with the best R^2, gWAR, only explains ~3.5% of the change in RA9. Additionally, while each of the metrics is statistically significant in explaining some portion of the change in RA9, when the models are combined, gWAR is the only independent variable that is statistically significant in explaining RA9. While it is encouraging that gWAR and kWAR outperformed fWAR in predicting RA9, the overall fit of the models underscores the notion that WAR statistics are not particularly predictive of future RA9.

虽然这些图通常显示出我们期望的负相关关系(即，在X年中WAR较高的投手在X + 1年中的RA9较低)，但我们可以从R ^ 2值中看出，这些模型无法解释绝大多数RA9的变化。 即使具有最佳R ^ 2的统计数据gWAR也只能解释RA9变化的〜3.5％。 此外，尽管每个指标在解释RA9中的某些变化方面在统计上都是有意义的，但是当组合模型时，gWAR是唯一在解释RA9上在统计学上有意义的自变量。 尽管在预测RA9方面gWAR和kWAR优于fWAR令人鼓舞，但模型的整体拟合度突显了以下观点：WAR统计数据不能特别预测未来的RA9。

结论思想和笔记 (Concluding Thoughts and Notes)

We have found some encouraging results in our analysis of kWAR and gWAR. While both have shown to be better than fWAR at predicting both future fWAR and future RA9, neither by itself comes close to explaining even half of the future variation in fWAR. If it were so easy, there would not be a need for complex projection systems such as ZiPS, PECOTA or Steamer to project future performance. However, given our results, we think that kWAR and gWAR can be added as another tool in the analytical toolbox

我们在分析kWAR和gWAR时发现了一些令人鼓舞的结果。 尽管两者在预测未来fWAR和未来RA9方面都比fWAR更好，但两者都无法单独解释fWAR未来变化的一半。 如果如此简单，则无需使用复杂的投影系统(例如ZiPS，PECOTA或Steamer)来投影未来的性能。 但是，根据我们的结果，我们认为kWAR和gWAR可以作为分析工具箱中的另一个工具添加

We would like to thank the following individuals who helped us collect the data for certain: Jamar Bostic, Jeremy Siegal and Matt Fronduto. Their help was invaluable in collecting the data and as a result, our analysis. As was the case with our previous article, all data, including the component park factors used to calculate kWAR and gWAR, were pulled from FanGraphs.

我们要感谢以下帮助我们确定收集数据的个人：Jamar Bostic，Jeremy Siegal和Matt Fronduto。 他们的帮助对于收集数据和我们的分析非常宝贵。 与我们上一篇文章一样，所有数据，包括用于计算kWAR和gWAR的组件停车系数，均从FanGraphs中提取。

While our analysis was limited to the data from 2009–2019, we collected going back to 2002. The full leaderboards for kWAR and gWAR for 2002–2019 can be found here: https://bit.ly/2SZbN41

尽管我们的分析仅限于2009-2019年的数据，但我们收集的数据可以追溯到2002年。有关2002-2019年kWAR和gWAR的完整排行榜，请访问： https ：//bit.ly/2SZbN41