The PI and EI: About This Great Game’s Statistical Indexes
Statistics do not lie. They are what they are, and for better or for worse, a baseball player’s career is dependent on the value of the stats he produces. Throughout time, many baseball experts have created numerous, disparate formulae that add, subtract, multiply, divide and trigonometrically decipher the numbers to come up with one big or small number to determine the game’s best players.
They got formulae, we got formulae. At This Great Game, we have developed our own two measures of statistics—the Production Index (PI) and the Efficiency Index (EI)—which takes into account all available critical numbers and, through a comprehensive balance of quality and quantity, determines which players are the most productive in each league, both at the plate and on the mound.
Our Indexes are not replacements for the Most Valuable Player or Cy Young awards. No statistical formula, sabermetric or otherwise, can ever measure a player’s mental focus or clubhouse leadership. The Indexes simply lay it all out as it comes, one at-bat at a time, one batter faced at a time. There are no adjustments within the Indexes; in our view, doing that will simply lead to more endless debate. So lucky you if you hit at Coors Field or bat behind Miguel Cabrera, and tough luck if you pitch at Coors Field or hit in front of the pitcher. We’ll say it again: The stats are what they are.
Here’s a breakdown of how each Index is calculated:
The Hitters. The equation for determining the hitter’s PI is basic. It’s mostly adding and subtracting. Every time you earn a base—whether by a base hit, walk, hit batsman or steal—you add a point to your PI. It’s two points for a double, and so on. If you score or knock in a run, you add another point. If you’re caught stealing or hit into a double play—taking a runner off the bases with you—you deduct a point. Add all this to your batting average—one point for every batting point—and voila, you have your batter’s PI.
The EI does everything the PI does (less the batting average) but rather than add it all up and stop there, it gets divided into the total number of plate appearances (minus sacrifices) to determine the average points per appearance.
Yeah, but: What if you get called up late in the year and earn hits in your only two at-bats? Doesn’t your 1.000 batting average translate to a PI or EI of 1,000 and, suddenly, you’re up there with the league leaders? No. For the PI, your batting average is worth a point per batting point once you’ve amassed 200 at-bats. The worth of your average drops 0.5% with each at-bat under 200. So in the call-up’s case, his 1.000 average is worth only ten points (2 ÷ 200 x 1.000 = 10).
In the case of the EI, we originally deemed ineligible those with less than 3.1 plate appearances per game—much the way baseball sets its eligibility for the batting title. But then we thought: It’s not really fair to deny someone’s EI because they were literally a few plate appearances shy of qualifying. So we’ve introduced some prorating into the process. It goes like this: Say you have a stellar 1.000 EI but only accumulated 452 plate appearances—51 shy of the 503 needed to qualify if your team played 162 games. Since 452 is 90% of 503, you get 90% of the credit for an EI, which in this case would be prorated to .900 (1.000 x .90 = .900). It’s a variation of the Tony Gwynn Rule, named after the Hall-of-Fame hitter who once won a batting title even though he didn’t have enough plate appearances to qualify—but still would have won the crown even had he gone hitless in the few PAs needed to reach the eligibility threshold.
Yeah, but: You don’t give a point to a batter who collects a RBI on a solo home run. Why? We’ll explain by supposing the RBI does count. Let’s say that Rickey Henderson hits a home run. You get four points for the home run (four total bases), one point for the run scored and one for the run knocked in. That’s six points toward the PI. Now let’s say Henderson comes up in his next at-bat, hits a single, steals second, steals third and then steals home. That’s one point for the walk, three points for the three stolen bases, and one point for the run scored. That’s five points total toward the PI. But wait, he’s earned one less point than the solo home run, though he’s basically given his team the same result all by himself. The RBI on the homer suddenly has a redundancy to it. It shouldn’t count toward the PI.
Yeah, but: Why do you give a player the same credit for a single (one point) as an intentional walk? Doesn’t he earn the single more? Yes, but in residual fashion. The hit raises his batting average and is more likely to knock in one or even two runs, which adds to the Index totals. Being hit by a pitch or walking does not, unless of course the bases are loaded. Otherwise, his presence on first base is all the same; a base is a base is base, however you get there.
Yeah, but: Doesn’t a batter get credit for a sacrifice hit or fly? Only if he knocks in a run. Otherwise, everything cancels out; it doesn’t affect his batting average (there’s no official at-bat given to a SH or SF), and he doesn’t get a base. You might say he deserves something for moving the runner(s) forward, but he gave an out—he sacrificed—in order to do it.
So you know: Historically, statistics for walks include those given intentionally—even as they’re listed next to the number of free passes given. We think this is confusing. So for thisgreatgame.com, walks are purely separate from intentional walks, or at least in those years where such statistics are available. So while many sites officially list Barry Bonds’ collection of walks and intentional walks from 2004 as, respectively, 232 and 120, we actually list them as 112 and 120.
The Pitchers. The differences between the pitcher PI and EI are more stark; whereas core pitching stats such as wins, winning percentage, saves and earned run average are pivotal toward a pitcher’s PI, they are of no consequence to the EI—which essentially goes through the same process as the hitter EI, taking a pitcher’s accumulation of total bases, walks, runs, etc. allowed and dividing it into the total number of batters faced. The pitcher EI does not discriminate on the basis of wins, losses and run support—the latter of which the pitcher has no control over and leads to some often misleading records. So the EI may sometimes become the best friend for a pitcher like Felix Hernandez, who in 2010 easily had the best EI despite an unspectacular 13-12 record thanks to lousy offensive support from his Seattle teammates.
For the pitcher PI, there are similarities to the hitter PI in that the pitcher can add or deduct single points from one batter faced to the next, just as the hitter can facing the pitcher. Men on the mound get a point for every out they make (or every third of an inning you pitch), but then there’s deductions for total bases, earned runs, walks, intentional walks, hit batsmen, balks, wild pitches and stolen bases allowed. Points are returned for opposing players caught stealing, picked off or grounding into double plays. Then the formulaic fun begins, as shown at in the example box at left.
Incredibly, while pitching stats have forever included batting average and on-base percentage against, they have not included slugging percentage against—in large part because there are no official records of doubles or triples allowed through a large chunk of the 20th Century. This robs historians of knowing for sure how many total bases a pitcher allowed from year to year. This glaring omission makes the pitcher Indexes slightly incomplete through the early 1950s, when total bases are finally and duly noted. Thanks to the wonderful research from the good folks at www.retrosheet.org, this oversight is being overcome, and the hope is that in the near future complete pitcher Indexes from much earlier years in baseball annals will be realized.
Yeah, but: With the pitcher PI, you penalize closers for blown saves, but not starters for losses. What’s up with that? A few things. One, the average starter has, historically, roughly a 30% chance of winning the game when he takes the mound. The average closer has an 80% chance of earning the save, because all he has to do is pitch anywhere from one-third to two innings with a lead of one-to-three runs. Also consider this: Closers sometimes get credit for the “accidental win”—gaining credit for victory after blowing a save when his teammates bail him out with a winning rally. (Some believe this allows the closer to benefit from the pitcher PI in a faulty way, but trust us—the points for the win is more than offset by the damage done being tagged not only with the blown save but also with the hits, runs, etc. he suffered in doing so.)
Yeah, but: We almost never see a closer become eligible for the pitcher EI. Why? Like the hitter EI—where one typically needs 3.1 plate appearances per game to qualify—the pitcher EI uses the same eligibility requirement to qualify for the earned run average title: At least one inning pitched per game over a full season, or roughly 162 innings. Again, as explained above with the hitter EI, you can qualify through a prorated figure; say you pitch 146 innings—or roughly 90% of 162—you earn credit for a prorated EI that’s 90% of full value. This provides an in for relievers and closers to qualify, though it’s still a tall wall to climb. This may seem unfair to closers as far as the final rankings are concerned, but starting pitchers have had their own teeth to gnash every time a closer takes the Cy Young Award—and for good reason.
Yeah, but: You don’t give the pitcher any points for strikeouts. Why should we? The strikeout, like beauty, is only skin-deep. Whether the batter whiffs or flies out to deep center, it’s an out all the same.
So you know: Because the concept of blown saves as a statistic wasn’t even realized until its official entry in 1969, there is no such prior recording of it—and thus, the pitcher PI grants eight points per save before 1969 (instead of the ten points given afterward), since it’s generally regarded that the average closer will save 80% of all opportunities.
All Statistics for thisgreatgame.com are complied through www.retrosheet.org.
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