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# Introducing weighted isolated power (wISO)

Weighted isolated power is a more precise way to measure the power contributions of a hitter.

If it is true that innovation stems from necessity, then consider the new and more precise version of Isolated Power that Steven and I now introduce to be the next in a long line of metrics created to fill a need within the statistical aspect of the game.

I have long been a fan of traditional Isolated Power, as it is an easy rate stat that measures a hitter’s power per se (i.e., isolates it), but this metric is somewhat imprecise. Traditional Isolated Power is computed in its simplest form as SLG-AVG, but can also be written as follows:

Traditional ISO = [(1x2B) + (2x3B) + (3xHR)] / AB

This formula considers only the extra base hits of a player (i.e., power) but uses overly simplistic constants. It seems unlikely that in practice, the difference between a home run and a single is exactly three times as much as the difference between a double and a single.

For this reason, Steven and I created wISO, a new metric that uses the wOBA linear weights instead of the integers found in the traditional ISO formula. As of the time of this publication, the 2014 wOBA linear weights are as follows:

2014 wOBA Linear Weights

w1B = .891

w2B = 1.281

w3B = 1.632

wHR = 2.129

Instead of simply inserting these numbers in the traditional formula, we scaled it to the traditional ISO model. To do this, we found the difference in wOBA linear weights between each extra base hit and a single and then divided the individual results of triples and home runs by the results of doubles. In numerical form, these calculations were as follows:

Weighted ratios = (wHR-w1B)/(w2B-w1B) and (w3B-w1B)/(w2B-w1B)

This gave us the following ratios between doubles, triples, and home runs. As the divisor in the equation, doubles are scaled as 1, hence the changes come in the weight for triples and home runs.

2B = 1

3B = 1.9

HR = 3.17

When entered into the equation, the working formula for 2014 wISO is as follows:

2014 wISO = [(1x2B) + (1.9x3B) + (3.17xHR)] / AB

The benefit of wISO is simple: this formula will value extra base contributions to the degree that they actually lead to scoring runs. Instead of having a home run count as three times as much as a double, the wOBA constants allow us to weight power contributions more accurately with the precise ratios found in game data over a season or multiple seasons.

In practice, wISO functions the same way as traditional ISO. Unsurprisingly, the 2014 and career wISO leaders, shown in the charts below, are largely the players that we would suspect.

Player AB 2B 3B HR wISO
Chris Carter 446 20 1 36 0.305
Edwin Encarnacion 403 24 2 30 0.305
Jose Abreu 487 32 2 33 0.289
Nelson Cruz 534 25 1 39 0.282
Giancarlo Stanton 526 30 1 36 0.278
Mike Trout 543 37 6 32 0.276
David Ortiz 480 25 0 32 0.264
Victor Martinez 496 29 0 30 0.250
Jose Bautista 493 25 0 31 0.250
Paul Goldschmidt 406 39 1 19 0.249

We considered only qualified batters for 2014; career leaders needed at least 2500 AB.

Player AB 2B 3B HR wISO
Babe Ruth 8398 506 136 714 0.354
Mark McGwire 6187 252 6 583 0.335
Barry Bonds 9847 601 77 762 0.316
Ted Williams 7706 525 71 521 0.297
Hank Greenberg 5193 379 71 331 0.297
Lou Gehrig 8001 534 163 493 0.294
Jimmie Foxx 8134 458 125 534 0.287
Albert Pujols 7310 524 15 492 0.285
Jim Thome 8422 451 26 612 0.284
Ryan Howard 4340 220 19 311 0.282

One caveat to note is that wISO is almost always slightly higher than traditional ISO for two reasons. First, the .17 difference in home run ratio between wISO and traditional ISO is larger than the -.10 difference between triples ratio between the two formulas. Second, since home runs are much more frequent than triples, the positive difference in weight for home runs is actualized much more frequently than the negative difference in weight for triples. In 2014, the average player's wISO is 5 points higher than his ISO, so the difference is not drastic.

This means that home run hitters, such as the AstrosChris Carter, will see the biggest increase from traditional ISO to wISO, while players specializing in triples, such as the Dodgers' Dee Gordon, will see their wISO slip, at least relative to the rest of the league. Doubles hitters, such as the Brewers' Jonathan Lucroy, will see less of a difference between their ISO and wISO, as the constant for doubles is the same in both formulas.

With that in mind, the chart below shows the players with the largest positive difference between wISO and traditional ISO. It comes as no surprise that all of the players on this list hit lots of home runs and very few triples (and consequently overlap a lot with the wISO leaders).

Player AB 2B 3B HR wISO Difference
Chris Carter 446 20 1 36 0.305 0.0143
Edwin Encarnacion 403 24 2 30 0.305 0.0123
Nelson Cruz 534 25 1 39 0.282 0.0122
Giancarlo Stanton 526 30 1 36 0.278 0.0119
David Ortiz 480 25 0 32 0.264 0.0117
Jose Abreu 487 32 2 33 0.289 0.0116
Jose Bautista 493 25 0 31 0.250 0.0113
Victor Martinez 496 29 0 30 0.250 0.0105
Lucas Duda 448 22 0 27 0.240 0.0104
Anthony Rizzo 486 23 1 30 0.247 0.0102

Contrarily, the chart below shows the players with the largest negative difference between wISO and traditional ISO (and the smallest positive differences to fill in the table). Unsurprisingly, all of the players on this list hit very few home runs and lots of triples.

Player AB 2B 3B HR wISO Difference
Dee Gordon 543 20 12 2 0.091 -0.0014
Adeiny Hechavarria 464 18 10 1 0.087 -0.0014
Adam Eaton 419 23 8 1 0.099 -0.0013
Ben Revere 517 12 7 2 0.061 -0.0008
Alcides Escobar 497 30 5 2 0.092 -0.0007
Norichika Aoki 415 18 4 1 0.069 -0.0007
Alex Rios 492 30 8 4 0.118 -0.0003
Denard Span 548 36 7 4 0.113 0.0001
Zack Cozart 454 17 4 3 0.075 0.0002
Jean Segura 461 12 6 4 0.078 0.0003

The slight bias toward having a higher wISO is enough that only seven qualified hitters have a lower wISO in 2014, and with the best mark being Alex Rios's 0.118, they aren't exactly a bunch of sluggers, either.

One final technical note: dealing with data over multiple years with varied wOBA linear weights requires an additional step. To find, for example, Mike Trout’s career wISO, one must first take the wISO for each individual season using the wOBA constants for each respective season, multiply by seasonal AB, add all of the seasons together, and finally divide by total at bats during that span.

In numerical form, this calculation appears as follows:

Trout career wISO = [(2011 wISO x 2011 AB) + (2012 wISO x 2012 AB) + (2013 wISO x 2013 AB) + (2014 wISO x 2014 AB)] / Total ABs from 2011 through 2014