Introducing weighted isolated power (wISO)

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 Astros’ Chris 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

This seems a lot messier than it actually is, but due to the nature of the wOBA constants, it is necessary to use the proper constant for each respective season. A home run in the steroid era has a different value than a home run in the pitcher-friendly era of the mid-1960’s (or even today), so it is imperative to use the proper league constants.

The difference between wISO and traditional ISO is not extremely large. The 2014 wOBA-based constant for triples used in the wISO formula is only five percent less than the constant used in the traditional ISO formula, while the 2014 wISO constant for home runs is just 5.6 percent greater than the traditional constant. That’s not drastically different and does not render traditional ISO useless, but why should we choose to accept a lack of precision when a more precise measure is readily available?

wISO isn’t going to overhaul the way we look at power hitters. It’s not going to lead to any recalibrations of the way that power is valued within the game. It is still obvious that Giancarlo Stanton is a good power hitter and Ben Revere is not, but wISO is slightly better at telling us the exact difference between these two players. The constants are no longer arbitrary; rather, they value each event based on its contribution to actual runs being scored, making this a more useful, more precise way to measure the isolated power of players.

. . .

All statistics courtesy of FanGraphs and Sean Lahman's baseball database.

Steven Silverman and Dan Weigel are Featured Writers at Beyond the Box Score. You can follow Steven on Twitter at @Silver_Stats and Dan at @DanWiggles38.