Welcome to an interpretation of the extreme from the 2016 Major League Baseball season! I’m going to look into the best and worst performers at several of handpicked statistics from the past season. First, though, let’s go through the statistical ground rules.

I assumed a normal distribution–you know, your basic bell curve–of qualified batters using the FanGraphs leaderboard. To measure how extreme a player’s performance was, I used a statistical measure called a *z-score*. The z-score measures how far a player’s performance was from the mean, expressed in the number of standard deviations (a measure of how much variation there is compared to the mean in a data set). If a player’s performance was x, and the mean was µ, and the standard deviation was σ, the z-score is:

z=(x-µ)/σ

To use a familiar example, the mean of IQ scores is 100 with a standard deviation of 15. Somebody with an IQ if 127 has a z-score of (127 – 100) / 15 = 1.8, meaning that their IQ is 1.8 standard deviations above the mean. The advantage of z-scores is they express a difference relative to the normal amount of variance. For example, in 2016, among batting title qualifiers, the average batting average was .273 and the average percentage of batted balls that were grounders was 43.3%. The standard deviation for batting average was .027 and the standard deviation for ground ball percentage was 6.5%. If a player’s batting average was 20% better than average–.273 x 1.2 = .328–his z-score works out to 2.01, two standard deviations above average. That’s a lot! But a batter whose ground ball percentage is 20% above average (52.0%) has a z-score of just 1.33, since there’s more variance to ground ball percentage than batting average.

In this analysis, I calculated the mean and standard deviation from all qualified batters (3.1 plate appearances per game), rather than from all batters, because I did not want a player who played fewer games to muddy the results.

Here are all the categories so you can play along at home:

HR, Runs, RBI, SB, Walk Rate (BB%), Strikeout Rate (K%),

Isolated Power (ISO), BABIP, OBP, SLG, wOBA,

wRC+, BsR, OFF, DEF, WAR

It may be a piece of cake to guess the leader of each category, but can you guess the worst in each? Remember, this is only among qualified batters, which includes 147 players.

**Home runs**

High z-score: 2.47

Low z-score: -1.90

The high for this category is recently re-signed Mark Trumbo. Trumbo led the major leagues with 47 long balls on the season. Despite the offensive outburst, he was not a sought-after commodity given his lack of defensive ability. Mike Petriello recently argued that to recoup the defensive value, the Orioles should stop attempting to deploy him in the outfield. Trumbo is a first basemen by trade and he will be less detrimental for a team at first base.

The low for home runs is a tie between Ender Inciarte and Adeiny Hechavarria. Both players hit a whopping three home runs on the year. Inciarte added plenty of value to the Atlanta Braves because he has defensive value, while Hechavarria was just above replacement level.

**Runs Scored**

High z-score: 2.47

Low z-score: -2.35

The leader in this category might not be a surprise to many. Mike Trout leads the way with 123 runs scored, but Mookie Betts finished with 122 runs scored.

On the other extreme it is a player who would not have played as long as he did this year if it wasn’t for the necessity at his position and his possible leadership: Alexei Ramirez comes in with a low of 38 runs scored, significantly lower than the next player, Mitch Moreland at 49 runs scored.

**RBI**

High z-score: 2.61

Low z-score: -2.25

RBIs are not a good stat when it comes to predicting ability–some players have far more RBI opportunities than others–but they are a counting stat that are still constantly invoked on broadcasts at every level. Nolan Arenado led the way with 133 RBIs. Part of this number can be contributed to the high offensive numbers he put up in Coors Field, but Arenado defies the mile-high model. He has shown good numbers on the road (116 wRC+ in 2016) in addition to the dazzling home numbers (132 wRC+).

We have our first repeat winner when it comes lowest amount of RBIs among qualified batters. Ender Inciarte takes home the title with only 29 RBIs for the entire 2016 season. In an illustration that home runs and RBIs are not everything, though, Inciarte compiled a 3.6 WAR based on his performance.

**SB**

High z-score: 5.36

Low z-score: -0.89

This is the highest z-score calculated because of the low average compared to the highest performer in the category. Jonathan Villar led the Brewers and the Major Leagues with 62 stolen bases. The philosophy runs deep with the Brewers, as they led the league with 181 stolen bases compared to the second place team, Cincinnati Reds, who stole 139 bases.

18 players who qualified did not steal a base, earning them a -0.89 z-score. Teams are attempting stolen bases at the lowest rate in 45 years. The added value of stealing a base is thwarted by the negative value when being caught, a mathematical relationship that sabermetrics helped illuminate.

**Walk Rate (BB%)**

High z-score: 2.83

Low z-score: -1.85

Despite a down season compared to his MVP season the year before, Bryce Harper slots in with the highest walk rate in the major leagues. Despite his diminished offensive line last season, pitchers still exercise caution with Harper in the box.

Free swinging is not a positive in contemporary baseball. Walks are almost as valuable as a single and, yet, some players are aggressive outside the zone. No one walked less than Rougned Odor, who walked 19 times in 632 plate appearances.

**Strikeout Rate (K%)**

High z-score: 2.73

Low z-score: -1.93

This is the one metric for which you want to have a negative z-score. The higher your number, the higher your strikeout rate. Chris Davis takes home the title as strikeout rate king with a 32.9 percent rate. Despite the gaudy number, Davis performed well enough to be a positive player for the ever-surprising Baltimore Orioles.

The San Francisco Giants and the Kansas City Royals in the past years have been cited as teams with impressive contact skills. The trend continued in 2016 as Joe Panik only struck out 8.9 percent of his plate appearances. Panik was a first round pick, but he was never the exciting prospect coming up the pipeline. Despite a subpar 2016, Panik has been, over his career, an above-average player on a consistent Giants baseball team.

**Isolated Power (ISO)**

High z-score: 2.39

Low z-score: -2.14

It was a historic final year from David Ortiz. Just when you thought the Dominican slugger was over the hill, he comes back with another incredible year. Ortiz had the largest ISO by a large margin. Brian Dozier was second at .278, but that was nowhere near the .305 that Ortiz put up.

Remember back to the lowest amount of home runs hit this year? Yeah, one of those two players brings up the caboose in ISO as well. Hechavarria is the lucky winner for this category with a .075 ISO. In a full season, Hechavarria has never posted an ISO of .100 or more.

**BABIP**

High z-score: 2.66

Low z-score: -2.37

BABIP is often a skill for speedy runners. Another benefit for players is an expansive outfield. DJ LeMahieu took advantage of the ample dimensions at Coors Field. In the National League last year, .302 was the league average BABIP, and LeMahieu finished 2016 with .388.

On the flip side, BABIP hurts some flyball hitters, as the balls they don’t hit out of the park–which aren’t included in BABIP–are usually caught. No one was hurt more than Todd Frazier, posting a .236 BABIP. Panik is a bit of an outlier with a .245 BABIP given the low strikeout rate. Weak contact could be a large determining factor with these low numbers. Expect a turnaround from Panik in the 2017 season.

**OBP**

High z-score: 3.13

Low z-score: -2.07

OBP might be my personal favorite statistic because my weird fascination with walks. The key to baseball is to make as few outs as possible, right? This number explains that almost entirely. Anyway, Mike Trout is finally atop one of these leaderboards. Trout’s .441 OBP is the highest of his career. We could probably talk about the brilliance and calmness of Trout for post after post, so I’ll keep this short. Trout led all of baseball in avoiding outs, which is one of his more impressive numbers.

It took a while but we see our first Philadelphia Phillie. Freddy Galvis was a poor hitter (74 wRC+), and posting a .274 OBP may get you a job on only a select number of teams and Philadelphia was one of them. What is probably more interesting about Galvis’ 2016 is his career high in home runs, 20. Despite the unproductive year at the plate, Galvis performed exquisitely in the field, recouping some value.

**SLG**

High z-score: 2.78

Low z-score: -2.48

Maybe to no one’s surprise, David Ortiz led in this category as well. With a .620 SLG, Ortiz just demolished the baseball in his last season. 87 extra-base hits came off his bat.

It is not surprising that ISO and SLG show the same highest and lowest performers. Hechavarria posted a .311 SLG, lower than 12 players’ *batting average* in 2016.

**wOBA**

High z-score: 2.52

Low z-score: -2.70

David Ortiz. Again. With a .419 wOBA, Ortiz narrowly beat out Mike Trout with a .418 wOBA. These two players were the top offensive players in 2016 and they are close to or at the top of nearly every category listed so far.

This may be getting redundant. Adeiny Hechavarria posted the lowest wOBA in 2016, .256. He was not a good player for the Miami Marlins, but he’s definitely better than you or I, so can we really be that harsh on him?

**wRC+**

High z-score: 2.88

Low z-score: -2.71

No one new is at the top of the wRC+ leaderboard, as Mike Trout takes it again. Since his rookie season in 2012, Trout has been no worse than tied for third in wRC+ in any season. Trout’s play is so incredible that the Hall of Fame could already be within reach.

Yes, you guessed it. Hechavarria is the lowest performer based on wRC+. Unfortunately this post has taken a turn for the worse for Hechavarria. A seemingly lighthearted look back on the 2016 season has turned malicious. My condolences, Adeiny. We’re almost done picking on you.

**BsR**

High z-score: 2.52

Low z-score: -2.99

BsR is an all-encompassing stat that takes into account all aspects of baserunning. This includes stolen bases, avoiding double plays, taking extra bases, and other factors. For the first time we see Mookie Betts emerge from Trout’s shadow to lead a category. FanGraphs pegs Betts at a 9.8 BsR, .5 better than Trout. Wil Myers is surprisingly in fourth place in BsR. The San Diego Padres first basemen/outfielder is the main attraction for years to come given his extension and the parting of the Chargers from San Diego. The other extreme is Victor Martinez, whose bounceback season with the Tigers (120 wRC+ in 2016 vs. 78 in 2015) was not accomplished by way of baserunning, as his -11.4 BsR was lowest in the majors.

**OFF **

High z-score: 3.58

Low z-score: -2.31

Off gives a more refined landscape than wRC+ or wOBA, as it incorporates ability on the bases in addition to hitting skill. With that in mind, we have a runaway winner with none other than Mike Trout. Trout posted a 67.7 Off and Kris Bryant, the other MVP, was a distant second at 49.1. Quite a difference, eh?

I thought a positive BsR would keep Adeiny Hechavarria away, but that is just not the case. Yes, let’s welcome Hechavarria back into the limelight with a -27.8 Off. The only way to go from here is up?

**DEF**

High z-score: 2.64

Low z-score: -1.98

Def has two parts: fielding runs and positional adjustment. Positional adjustment refines a player’s raw fielding numbers for the difficulty of his position, giving extra weight to more difficult positions such as shortstop and center field compared to first base and left field. The leader in Def is Brandon Crawford with a 28.0. This is Crawford’s best defensive season in his immaculate defensive career.

J.D. Martinez makes his first appearance with an atrocious -22.6 Def. His defensive performance dropped considerably compared to the last two seasons in the outfield.

**WAR**

High z-score: 3.25

Low z-score: -2.71

The all-encompassing statistic has the leader you all expect. Mike Trout posted a 9.4 WAR, the third best WAR of his career. He is simply the best and I think we all hope for a long and amazing career to marvel over like the career of Barry Bonds.

While Adeiny Hechavarria has garnered most of the titles here, Alexei Ramirez comes back with the worst WAR of the season at -2.4. Ramirez is over the hill as a shortstop, but the Cuban put together solid years mainly due to his defensive prowess. In 2016, the defense fell along with the offense and, at 35, there doesn’t appear to be much left in the tank.

This has been a fun exercise, but it is not over. I added all the z-scores by player to calculate a winner (and loser), accumulating all z-scores for each individual player:

Mike Trout ran away with the z-score title with a 31.43 combined score, Alexei Ramirez brought up the rear with a -24.52.

This was not a completely exhaustive list of statistics that can be retooled as z-scores. If there is interest, then I will gladly widen what’s already been done. A viewable version of the spreadsheet used for this post is available.

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