# SIERA: Evaluating One of Pitching's Most Advanced Statistics

If you’re familiar whatsoever with this publication or sabermetric thinking in general, you would know that only considering a pitcher’s ERA comes nowhere close to telling the whole story. There are so many aspects that pitchers cannot control about Earned Run Average, making the consideration of newer, advanced metrics necessary to evaluate talent effectively. Since the pioneering of DIPS (defensive-independent pitching statistics) by Voros McCracken, there are lots of new analytical numbers regarding pitching evaluation that more accurately adjust for all the aspects a pitcher can control. This piece will specifically focus on what is one of the most accurate predictive metrics of them all: Skill-Interactive Earned Run Average.

**Background**

To understand SIERA, there needs to be a little background on FIP (Fielder Independent Pitching) and xFIP (Expected Fielder Independent Pitching). After all, both were the main predecessors to this new calculation. Knowing that pitchers can’t control a lot of the field, Tom Tango invented FIP to isolate factors that he knew they can control - HRs, uBBs, HBPs, and Ks. Any balls in play within the park are completely excluded from this number, as the statistic argues that pitchers cannot control their balls in play (which is contested in future statistics). Like any expected statistic, xFIP is just a regressed version of FIP. Arguing that pitchers cannot control how many home runs they give up on fly balls, xFIP regresses a pitcher’s HR/FB rate to the league average rate of the given season. This is considered to be more predictive of future production, as above or below-average rates when compared to league averages are considered unsustainable in the long term.

In making SIERA, these primary concepts were utilized in setting up the formula. However, some major differences completely differentiate this measure from FIP and xFIP. The first, and arguably most important, is the consideration of balls in play. Disagreeing with the claim that pitchers can’t control the level of contact or success on balls in play, SIERA adjusts to include this as a factor. As fly balls generally lead to more runs than ground balls, a pitcher that gives up more ground balls than fly balls will be rewarded. This especially comes into play with runners on base, with different batted ball types being exponentially more valuable to one side or another (a factor that FIP considers). A player can afford to allow more contact if he is generally allowing fewer baserunners, as that contact is ever less likely to lead to a run. But if the player is known to generally let people on before he gets out of an inning, that contact could prove to be detrimental, making a strikeout much more important. This is all taken into account with SIERA, which adjusts for the average situation of a given pitcher and rewards him appropriately for what is likely to lead to the least amount of runs scored.

Another interesting implementation was the impact of high strikeout pitchers inducing weak contact. As a strong correlation between strikeout rates and overall BABIP rates seemed evident, it concluded that pitchers that are able to induce lots of strikeouts also further benefit from weak contact. When hitters have shown an inability to hit a ball whatsoever, the contact they occasionally make is not desirable. Strong strikeout pitchers often allow lower BABIPs on average compared to their low-strikeout counterparts. This yields the need to consider the secondary effect of high strikeouts. SIERA identifies the effect of the runs prevented from the weak contact due to the great strikeout rate and includes it in the overall run calculation, thus rewarding the run prevention aspect of high strikeout rates.

In trying to ultimately knock its predecessor out of the water, SIERA is park- and run-environment-adjusted. In other words, it considers both the number of runs being scored in a given season and the number of runs in a given park when evaluating a player's performance. As FIP and xFIP do not adjust for this, the numbers can often look askew. A pitcher at Coors Field in 2019 (high run park factor and extremely high run environment year) and a pitcher at Busch Stadium in 2021 (low run park factor and moderately low run environment year) could have the same FIP, yet the former pitcher would obviously be more impressive. At Coors Field in 2019, the pitcher had to go through conditions that were playing against him and still generated decent results. The man on the mound in St. Louis in 2021 was given every advantage possible over his Denver counterpart and still produced an identical FIP. SIERA adjusts for this.

With all this in mind, this is the current SIERA formula (via MLB.com):

**SIERA = 6.145 - 16.986( K / PA ) + 11.434( BB / PA ) - 1.858(( GB - FB - PU )/ PA ) + 7.653(( SO / PA )^2) +/- 6.664((( GB - FB - PU )/ PA )^2) + 10.130( SO / PA ) * (( GB - FB - PU )/ PA ) - 5.195( BB / PA ) * (( GB - FB - PU )/ PA )**

The nominal numbers being shown are coefficients, which are the estimated values for each aspect. Some of these numbers are subject to change based on the year and the organization producing the calculation, but this shows an outline of what goes into the ultimate number of SIERA.

**Evaluation**

*Premise*

Before looking at the actual calculation, it is worth starting with the premise - FIP and xFIP needed to be improved upon. The idea that a pitcher cannot control the level of contact allowed is somewhat outlandish, as pitch placement, pitch shape, and other factors can contribute to how a ball is hit. Besides, if it has already been established that a pitcher can somewhat control hitting or missing bats, how could they not somewhat control where the ball lands on the bat? The actual swing by the batter is difficult to significantly manipulate, but the given flight path of the ball could warrant contact to be made in non-ideal spots on the bat head. And as xFIP is just further readjusting FIP, it wrongly assumes the same preconceived notion about pitchers not controlling balls in play. If anything, it makes it worse.

In the xFIP calculation, Home Run over Fly Ball rate is regressed to reflect the Major League average, making a further assumption that pitchers cannot control how far their fly balls go. This further assumption is deeply misguided, as it is known that given pitchers can generally control how hard their balls are hit on average. If Pitcher A has an average exit velocity on fly balls of 86 mph and Pitcher B has an average exit velocity on fly balls of 91 mph, which one has the higher HR/FB rate? The majority of the time, Pitcher B will allow more home runs on fly balls. This is obviously a one-dimensional approach to estimating a pitcher’s future home-run/fly-ball rate, but all else being equal, it is the correct assumption. Pitchers can control the types of balls they allow and the distance of said balls, making considering contact crucial in evaluating pitching. SIERA correctly weighs these factors. It provides a much-needed advancement to outdated FIP-related statistics.

On top of that, environmental adjustments, from park factors to run environments, obviously add to the legitimacy of the statistic. No sabermetric can be completely accurate without these measures, as so many things change as time goes on. To treat such shifting factors equally throughout time is to be completely unfair.

*The Formula*

The numbers above can be considered to be quite complicated, so this evaluation will be an attempt to break them down. It’s worth pointing out that some factors are considered and later squared in the same formula. That may seem curious, but there is generally a light of genius in this consideration. By squaring for the strikeouts later, it factors in the aspect that not all strikeouts are created equal in leading to value. A given strikeout for a player who is likely to have few people on base is worth less than a strikeout for the player who generally allows more contact and therefore more people on base. As you have more of something, it is generally worth less to you - preventing runs in baseball is no different. The same concept applies to net ground balls (ground balls minus fly balls and pop-ups), which is also squared later in the formula. A given ground ball is likely to be worth less to a player who gives up lots of ground balls, as he will probably let fewer people reach base. These squares reward optimal rates of ground balls and strikeouts, which is exactly what should be done in trying to produce the most value.

Within the calculation, both strikeouts and walks are multiplied by net ground balls (separately). The walks are subtracted from the strikeout calculation. This is the implementation of the theory discussed earlier, which suggests that strikeouts and walks both carry positive or negative value outside of their given effects; they arguably impact contact. I’ll admit that I am somewhat weary of this idea. The correlation between the two is there, and I am sure that strikeout and walk rates do contribute to how players put the bat on the ball. But, correlation does not directly lead to causation. The two factors may be correlated, but the actual impact that a given strikeout rate or walk rate has on a given ground ball rate is unknown. Regressions could be conducted on the factors, but even those come with a decent level of uncertainty. Factoring actual Statcast data into what pitchers tend to elicit weaker contact seems to be on more solid footing than making the leap from strikeouts and walks. It appears safer (and possibly more accurate) to just include the direct impacts, not the possible runoff effects in general.

**Conclusion**

** **With SIERA, baseball has immediately improved upon its prior metrics. It is a clear upgrade when evaluating talent in comparison to the age-old ERA, and the flaws of FIP and xFIP made an improvement necessary. SIERA accounts for and considers the types of balls in play while ultimately adjusting for the optimal rates at which runs are saved. It may make some bolder assumptions regarding the runoff value of certain aspects, but overall, I deem it one of the best-articulated pitching statistics available to the public. And along with its known predictive value, SIERA can prove to be a great guide for evaluating pitchers when compared to most of the alternatives.

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