Clayton Kershaw has been one of the most dominant pitchers across baseball the past few seasons, winning 3 NL Cy Young Awards and 1 NL MVP since 2011. As we will see, superior control of the strike zone is among the reasons he performs so well.

Gaining an understanding of the Basic Pitcher Statistics enables quantification of the type and amount of value a player produces for his team. Further isolating the specific value a player is responsible for and what is due to the environment and circumstances around him becomes possible with the use of advanced statistics and metrics.

This article will serve to explain some of these advanced statistics, and how they are able to better articulate a player’s value compared to the basic statistics. This article will serve as a guide into the calculation and interpretation of some of the more telling pitching statistics. This will allow understanding and participation in the sabermetric community and in particular, at SaberBallBlog.

## Fielding Independent Pitching |FIP|

Fielding Independent Pitching has its beginnings in ERA. ERA is a useful statistic in that it shows how many runs a pitched will allow on average, but it does not show how responsible he is for those runs. While the pitcher might be charged the runs, if he has a poor defense behind him the runs may not have been his “fault”. Similarly, if the pitcher has an elite defense behind him, he may have been expected to give up more runs than he actually did.

Out of this reality arose the need to create a statistic that accounted for these effects and put pitchers on a universally comparable scale. FIP is the solution to this problem, and it accomplishes this by using the statistics that a pitcher is in direct control of in addition to a normalization constant. By definition, the league average FIP is equal to the league average ERA.

The calculation for FIP is:

$\textrm{FIP} = \frac{(13 \cdot \textrm{HR}) + 3 (\textrm{BB + HBP}) - (2 \cdot \textrm{K})}{\textrm{IP}} + \textrm{C}_{\textrm{FIP}}$

Where $\textrm{C}_\textrm{FIP}$ is the constant that enables you to compare FIP on the same scale as ERA. $\textrm{C}_\textrm{FIP}$ is generally around 3.10 each season.

Breaking down the calculation of FIP, the equation uses Home Runs allowed, Walks, Hit Batsmen and Strikeouts. This makes sense, as the defense does not come into play during any of these outcomes. Additionally, pitchers can both prevent home runs, walks, and HBP, while encouraging strikeouts with good pitch locating. Pitch location is certainly something over which pitchers possess control. Holistically then, this metric succeeds in what it attempts to do: creating a statistic that compares pitchers based on the factors over which they exert control.

On the basis of analyzing pitchers’ FIP, the generally agreed upon interpretation of FIP is shown below, courtesy of FanGraphs [Note 1].

Interpretation  FIP
Excellent 2.90
Great 3.20
Above Average 3.50
Average 3.80
Below Average 4.10
Poor 4.40
Awful 4.70

Over any time period, it is possible to both compare pitchers amongst themselves (relatively) and to an absolute standard using the FIP chart above. This functions in much the same way that pitchers’ ERAs are analyzed year-to-year. It is important to note however that FIP, like ERA, is not representative of true talent over a small sample size. FIP works well as a predictive statistic, one that (over a sufficiently large sample size) indicates what to expect of the pitcher going forward rather than as an explanatory statistic of what is presently happening.

To interpret FIP relative to ERA, you can consult the chart below for a quick understanding of what may be in effect to explain the disparity.

FIP < ERA  FIP ~ ERA  FIP > ERA
Factors outside of the pitcher’s control (fielding, positioning, etc.) are causing the pitcher’s ERA appear worse than he may actually be pitching. The pitcher is pitching approximately to the talent level his ERA indicates, and he is receiving about average fielding, etc. from his team. The pitcher’s team fields and/or positions incredibly well, making his ERA appear better than he may actually be pitching.

For purposes of example, let’s look at the 2015 statistics of the man pictured at the top of the post, Clayton Kershaw of the Los Angeles Dodgers. Kershaw allowed 15 homeruns, 42 BBs, and 5 HBP, while striking out 301 batters over 232.2 innings [remember to convert to decimals!]. Plugging this into the FIP equation:

$\textrm{FIP} = \frac{(13 \cdot 15) + (3 \cdot (42 + 5)) - (2 \cdot 301)}{232.2} + 3.10 = 1.96$

Looking at the chart above, Kershaw did not just have an excellent season; he had a legendary season, coming in almost a whole run below the barometer for excellence! What is even more impressive is that is ERA for the year, 2.13, was higher than his FIP by a little over 0.1 runs. This suggests that he may have been able to produce even better numbers had factors out of his control gone his way.

A shrewd observer will notice that the FIP posted above is not equal to the FIP posted on his Fangraphs page, 1.99. This is due to the assumption that $\textrm{C}_{\textrm{FIP}}$ is 3.10 every year. Consulting the year-to-year constants shows this to be false, however. As an exercise, try to reproduce Fangraphs’ FIP for Kershaw’s 2015 season using the correct constant.

## Expected Fielding Independent Pitching |xFIP|

As with many things in mathematics and statistics, there exists a more refined version of FIP that even further sharpens the view on a pitcher’s performance. FIP is effective in predicting a pitcher’s performance going forward based upon the pitching factors of which he is in control. Alternatively, Expected Fielding Independent Pitching (or xFIP) takes these factors and includes factors of the conditions he is playing in.

Based on research doneNote 2, over a short time most pitchers experience wide fluctuations in the number of home runs they allow per fly ball hit against them (known as HR/FB%). This ratio can vary based on the weather, stadium, competition, etc. To illustrate each of these effects, we know baseballs travel further in warm weather, causing a pitcher’s HR/FB% to inflate. In smaller stadia and/or for stadia at higher altitudes, it is easier to hit a home run, again inflating HR/FB%. Lastly, suppose a pitcher pitches several consecutive games against power-hitting teams. This is not indicative of the average roster composition across the league and so he may allow more home runs per flyball than usual. Each of these effects works in the inverse case as well, i.e. lower rates for colder, larger/lower stadia, or weaker teams.

To normalize this effect, improve FIP to assume that a league average number of home runs per fly ball are hit. Instead of using a pitcher’s home runs allowed in the equation, we use their fly balls allowed and so xFIP is calculated as below:

$\textrm{xFIP} = \frac{(13 \cdot \textrm{FB} \cdot LgAvg \frac{\textrm{HR}}{\textrm{FB}}) + 3 (\textrm{BB + HBP}) - (2 \cdot \textrm{K})}{\textrm{IP}} + \textrm{C}_{\textrm{FIP}}$

Examining, almost every element is the same as the FIP equation, only the home run term is modified. Because the goal with FIP/xFIP is to create a metric that analyzes a pitcher’s performance based upon the things he can control, this modification is justified as it removes a bias that the pitcher doesn’t control. While the difference between FIP and xFIP is much smaller than the difference between FIP and ERA, xFIP is a better indicator of what we expect a pitcher’s performance level to be. As stated, use FIP to remove variations in the performance of a pitcher’s team and use xFIP to remove variations in the performance of the pitcher himself.

Interpreting xFIP is essentially the same as interpreting FIP. The same scales are used both relatively and absolutely. However, comparing two pitchers’ xFIP is slightly different than comparing two pitchers’ FIP for one very important reason. While the average pitcher sees fluctuations in his HR/FB%, this does not mean that every pitcher does. Over extended time frames, some pitchers are able to maintain a lower-than-average HR/FB%, while others consistently have a higher-than-average HR/FB%. This is based mostly upon the type of pitches a pitcher throws.

Pitchers that throw large quantities of sinkers and/or two-seam fastballs, especially low in the strikezone, are known to have reduced HR/FB% due to the physics of the pitch. These types of pitchers are sometimes known as “groundball” pitchers, due to the higher number of groundballs hit against them.

Conversely, pitchers that throw high numbers of 4-seam fastballs or frequently pitch high in the strike zone maintain a higher HR/FB%. These pitchers are sometimes known as “flyball” pitchers. When comparing two pitchers’ xFIP, it is important to know what type of pitchers you are comparing. In other words, xFIP is best used as a relative comparison across pitchers if they are the same type of pitcher (i.e. groundball or flyball pitchers).

To interpret xFIP relative to FIP, you can consult the chart below for a quick understanding of what may be in effect to explain the disparity.

xFIP < FIP  xFIP ~ FIP  xFIP > FIP
The pitcher, either due to factors against his favor (weather, stadium, etc.) or flyball tendencies, allowed a higher-than-average number of home runs for the flyballs he allowed. If this is due to unfavorable conditions, this trend would be expected to reverse. The pitcher allowed an average number of home runs per flyball allowed. If the pitcher shows no groundball or flyball tendencies, this is the level at which the pitcher would be expected to pitch. The pitcher, either due to factors in his favor (weather, stadium, etc.) or groundball tendencies, allowed a lower-than-average number of home runs for the flyballs he allowed. If this is due to favorable conditions, this trend would be expected to reverse.

Let’s look at our friend Clayton’s 2015 statistics again to calculate xFIP. Kershaw allowed 148 FBs, 42 BBs, 5 HBPs, while accumulating 301 Ks over 232.2 innings. The league average HR/FB% was 11.4%, and the FIP constant was 3.134.

$\textrm{xFIP} = \frac{(13 \cdot 148 \cdot 0.114) + (3 \cdot (42 + 5)) - (2 \cdot 301)}{232.2} + 3.134 = 2.10$

Kershaw’s xFIP remains very impressive, still coming in under 0.8 runs of what we would consider “excellent”. Notice however, that his xFIP is larger than his FIP (but lower than his ERA). This means that Kershaw benefitted slightly from weather, his stadium, or some other environmental factor. On the whole though, because both his FIP and xFIP are lower than his ERA, the factors outside of his control made Kershaw’s basic statistics appear ever so slightly worse than he actually performed.

One final note, the answer for xFIP above varies slightly from the Fangraphs result of 2.09. This is likely due to a rounding error, as the calculation above only uses 3 digits for the constant, whereas Fangraphs’ goes out a few more. This is fairly inconsequential, and is likely to happen when quoting statistics from outside sources.

## Batting Average on Balls in Play Against |BABIP|

FIP demonstrates that it is possible for a pitcher to look better or worse depending on how the defense behind him plays. Another way to express this sentiment is through the batting average on balls in play against the pitcher, or BABIP.

BABIP works in much the same way that batting average does, except it only takes into account balls that are put into play. This statistic works as the converse to FIP; where FIP only accounts for plays in which the pitcher is in control, BABIP accounts for plays in which the defense is in control. Thus, BABIP removes home runs and strikeouts. The equation for BABIP against then is:

$\textrm{BABIP} = \frac{\textrm{H} - \textrm{HR}}{\textrm{AB} - \textrm{HR} - \textrm{K} + \textrm{SF}}$

Notice that it is necessary to add sacrifice flies into the denominator as they are not counted in at-bats but the defense does play a role!

The league average BABIP over any period of time is generally around .300Note 3. This means that approximately 30% of balls hit into the field of play fall in for a hit. Most pitchers (except those of exceptional talent) are generally unable to control their BABIP. It also takes up to 2,000 balls in play (~400 – 500 innings) for a pitcher’s BABIP to normalize with a sufficiently large sample size. These two factors in tandem allow for identification of pitchers who are benefitting from good/bad luck (in small sample sizes) or good/bad defense (in very large sample sizes).

In a small sample size, a BABIP notably above or below .300 indicates that there is probably some amount of “luck” involved with the number. As more balls are put into play against him, the number will likely regress back to approximately .300. A pitcher with a BABIP notably above or below .300, especially one who has remained with the same team and teammates over a long period, can likely have his variance explained due to the skill and/or positioning of the defense behind him (or lack thereof).

It is worth noting that flyball pitchers will frequently have a lower BABIP, as less pop flies will fall in for hits than groundballs and line drives. This however will be reflected in their xFIP, as they will also allow more home runs (which are not factored into BABIP).

Referencing Kershaw’s 2015 numbers again, we will examine his BABIP. Clayton allowed 163 hits, 15 of which were HRs, and no sacrifice flies. Additionally, he had 301 Ks in 843 ABs against (determine this by subtracting BBs and HBPs from “TBF” or Total Batters Faced).

$\textrm{BABIP} = \frac{(163-15)}{843 - 15 - 301 + 0} = .281$

This value falls below the average of .300, but as mentioned it is hard to derive value from this because it does not look at a big enough timeframe. Looking at Kershaw’s Fangraphs page, notice that his BABIP has routinely been below .300 over the past 7 seasons. This is certainly a large enough timeframe, and suggests that he is indeed one of the truly elite pitchers that is able to exert some control over the opponent’s ability to get a hit.

## Earned Run Average Minus |ERA-|

ERA-, like other statistics that use the “+/-” indicator, is a way of putting ERA on a comparative scale. For this metric 100 is the average over a time period, and each integer above/below 100 represents a percentage point above/below average. For example, a pitcher with an ERA- of 85 has an ERA that is 15% lower than average. It is important to note that since a lower ERA is better, this ERA- would indicate that the actual ERA is 15% lower than average (but the pitcher is performing 15% better than average).

ERA- normalizes all pitcher ERA using the home “park factor” for the pitcher, and his respective league’s average ERA. The park factor is a number, with 100 as average, that indicates how many runs his home stadium allows relative to the league average. A park factor of 90 indicates that the pitcher’s home stadium allows 10% less runs than the league average, and a park factor of 105 indicates 5% more runs. This serves to demonstrate that a pitcher with an ERA better than average in a high run environment (park factor > 100) should receive even more credit for his performance. The calculation of ERA- is as follows:

$\textrm{ERA-} = \frac{\textrm{ERA} + (\textrm{ERA} - \textrm{ERA} \cdot \frac{\textrm{PF}}{100} ) }{\textrm{ERA}_\textrm{AL or NL}} \cdot 100$

As you can see, the only factors that play into ERA- are the pitcher’s ERA, and the park factor and league ERA. To interpret ERA, there is a handy chart, again courtesy of Fangraphs:Note 4

Interpretation  ERA-
Excellent 70
Great 80
Above Average 90
Average 100
Below Average 110
Poor 115
Awful 125

It is worthwhile to mention that ERA- is somewhat unique in that the factors it accounts for (average ERA and park factor) are not universal. That is, the park factor only applies the home stadium of the pitcher (so roughly 1/2 of his starts) and the league average only takes AL/NL into consideration rather than the entirety of MLB. While this does not affect the comparison ability of the statistic, it does mean that it isn’t perfect.

A final note on ERA- (seen on Fangraphs): while it is the same idea as ERA+ (seen on Baseball Reference), the calculation of the two is fundamentally different. A very well-written article describing the difference between the two (and the superiority of ERA-) can be found at Beyond the Box Score.

Looking at Clayton Kershaw’s 2015 numbers one final time for purposes of calculation, he had an ERA of 2.13 at a home stadium with park factor 96, in a league with average ERA of 3.90. Calculating ERA- produces:

$\textrm{ERA-} = \frac{(2.13) + (2.13 -2.13 \cdot 0.96)}{3.90} \cdot 100 = 57$

Once again, we see that Kershaw had one of the truly legendary seasons amongst pitchers in 2015. His ERA- of 57 is 43(!) percentage points better than the average NL pitcher and 13 percentage points better than what we could objectively call a “great” season by a pitcher. Few are able to produce at the rate Kershaw has, and it is why he is such a decorated pitcher.

## Rounding Second: Sabermetric Hitting Stats and Player Valuation

This article in conjunction with the Basic Pitcher Statistics provides a thorough basis of the statistics used to measure pitchers today. With this and an understanding of the Advanced Hitter Statistics, participation in the sabermetric community is fully possible, especially here at SaberBallBlog. The knew-found knowledge can be used to engage in our discussions of players and teams. To elevate your knowledge even further, read up on WAR and Player Evaluation.  This will explain the determination of a player’s all-around ability and his worth to a team, particularly when it comes time to negotiate a contract.

1The FanGraphs explanation of the FIP constant can be found here. Essentially, the constant is the league average ERA minus the first term from the FIP equation, using league averages for HR, BB, and K.

2You can find Dave Studeman of The Hardball Times’ article here.

3Fangraphs explains some of the regression to .300 here.

4Fangraphs ERA- interpretation.