# Searching for True Power

In the ceaseless quest to identify players with the most raw pop, isolated power, or ISO, is a frequently cited metric, as you’ve probably seen. It’s simply a player’s slugging percentage minus his batting average. The idea is that, by removing single base hits, and measuring just a player’s extra bases per at bat, we can approach a pure measure of a power. I’ve referred to it quite a bit in the past. Like OPS, it’s simple, easy to explain, and easy to calculate in a pinch.

Recently I came across this article by Lewie Pollis from Beyond the Boxscore, wherein he resurrects a metric that had been floating around stat-minded circles in the past — power factor. Power factor is isolated power with one basic change: the denominator is a player’s hits instead of at bats. It can be expressed as isolated power divided by batting average, but what it boils down to is *extra bases earned per hit*. When you phrase it that way, I think the advantage is obvious, but Pollis provided a helpful mental exercise to illustrate how it more effectively approaches a player’s power:

Let’s take two hypothetical players: Tony Stark and Bruce Wayne. Stark hits .350 with a .550 SLG. Wayne hits .200 with a .400 SLG. Both weigh in at a .200 ISO, suggesting their raw power is roughly equal.But that’s not right. If Wayne somehow managed to bring his average up 150 points, would all the extra hits be singles? Stark is clearly a better hitter, and they both produced the same amount of extra bases. But if the two players had similar contact skills, Wayne would undoubtedly be a bigger slugger.

Simply put, a player’s isolated power is still influenced by his batted ball fortune and contact skill, which are not things we want to factor in to our evaluation of power. Measuring extra bases per hit, instead of per at bat, negates these influences. Take the 2011 performances of **Ryan Howard** and **Shane Victorino** as an example. Their ISOs are .236 and .234 respectively, suggesting that their power hitting is roughly equivalent this year. But Howard gets .952 extra bases per hit (his power factor), while Victorino only manages .767. Clearly, if their batted ball luck and contact skills were equal, and Howard were getting as many hits as Victorino, his power as measured by ISO would be superior. That’s what power factor attempts to get at.

Put that aside for a second, and let’s look at another attempt to tweak isolated power for the better. At Fangraphs, Steve Slowinski recently developed a metric he calls Weighted Extra Bases. Instead of using the extra base count of each extra base hit (1 for doubles, 2 for triples, 3 for home runs), Weighted Extra Bases uses their linear weights values (the same ones that go into the calculation of wOBA) in an attempt to represent each hit type’s true value in a power metric. As Slowinski writes, the formula goes:

wXB/AB= [ (1.268 * 2B) + (1.610 * 3B) + (2.086 * HR) ] / AB

ISO= [ (1 * 2B) + (2 * 3B) + (3 * HR) ] / ABWhen you actually weigh extra base hits in proportion to their value, it turns out that ISO is undervaluing doubles, while overvaluing both triples and home runs. This is why a player like

Matt Holliday(33 doubles, 19 home runs) can have the 9th highest wXB/AB in the majors, yet only the 20th highest ISO and 17th highest SLG.

As you can see, doubles have more value than we usually consider, and more than ISO credits them for. The second extra base gained on a triple, on the other hand, is not quite as valuable as ISO calculates it to be. Home runs are similarly overvalued. Using Slowinski’s twist, we can measure a player’s power with a more accurate accounting of the contribution to run scoring that it provides.

So we have two separate variations on isolated power, each resolving a separate issue: Pollis’ use of Power Factor eliminates the influence of contact skills and batted ball luck in measuring a player’s power, and Slowinski’s Weighted Extra Bases paints a clearer picture of the value that each extra base hit type provides, and therefore a clearer picture of the player’s power contribution. Now why not combine them, harvesting the advantages of each? Specifically, let’s take Weighted Extra Bases as our numerator, and hits (rather than at bats) as our denominator. This would allow us to see the true power value that a hitter provides with each hit he collects. Now, Holliday’s doubles are not undervalued, and Victorino’s contact ability and BABIP are not unduly represented. Two birds with one **Randy Johnson** fastball. The new formula is:

**Weighted Extra Bases per Hit** = [ (1.268 * 2B) + (1.610 * 3B) + (2.086 * HR) ] / Hits

Before continuing, let me just point out that this is entirely derivative of Pollis and Slowinski; I’ve contributed nothing new, besides smashing together their separate, clever ideas.

That being said, let’s look at some of the things this metric tells us. For starters, here are the top 15 wXB/H seasons in the history of baseball, minimum 300 At Bats:

Season | Player | wXB/H |
---|---|---|

2001 | Barry Bonds |
1.257 |

1998 | Mark McGwire | 1.136 |

1999 | Mark McGwire | 1.13 |

1995 | Mark McGwire | 1.125 |

2010 | Jose Bautista |
1.094 |

2009 | Carlos Pena |
1.087 |

1999 | Barry Bonds | 1.07 |

1973 | Dave Kingman | 1.038 |

1996 | Mark McGwire | 1.023 |

2003 | Jim Edmonds |
1.017 |

1920 | Babe Ruth | 1.005 |

1921 | Babe Ruth | 1.003 |

1995 | Albert Belle | 0.993 |

2004 | Barry Bonds | 0.985 |

1969 | Reggie Jackson | 0.984 |

The names aren’t surprising, but this looks quite a bit different from the best 15 ISO seasons using the same criteria. McGwire appears with the same frequency, but players held up by high contact skills, such as Babe Ruth, Lou Gehrig, Jimmie Foxx, are bumped down a bit. And players who did a lot with the ball when they *did* hit it, like Jose Bautista and Carlos Pena, are given their proper due. Players who appear on the Power Factor leaderboard for the same criteria but are boosted by overvalued hit types, like **Adam Dunn**, Harmon Killebrew, and **Sammy Sosa**, are also bumped down in the wXB/H metric.

Now for the career leaders. Who, according to wXB/H, provided the most value with their power every time they logged a hit? Unsurprisingly, it turns out to be McGwire, and by a wide margin at that (minimum: 3000 At Bats):

Player | wXB/H |
---|---|

Mark McGwire | .950 |

Adam Dunn | .876 |

Barry Bonds | .843 |

Ryan Howard | .837 |

Carlos Pena | .837 |

Jim Thome |
.818 |

Babe Ruth | .818 |

Gorman Thomas | .808 |

Rob Deer | .807 |

Dave Kingman | .804 |

David Ortiz |
.801 |

Carlos Delgado |
.799 |

Hank Greenberg | .790 |

Mike Schmidt | .786 |

Steve Balboni | .779 |

Darryl Strawberry | .774 |

Richie Sexson |
.774 |

Greg Vaughn | .771 |

Harmon Killebrew | .768 |

Troy Glaus |
.767 |

I know what you’re thinking now: Gorman Thomas? Steve Balboni? The former spent 13 years in the majors, from 1973-1986, hitting decently above average (114 OPS+), which was not bad for a guy who was a full time centerfielder for most of his career. But he’s not exactly the stuff of legends, and he certainly doesn’t come to mind if you were asked to rattle off some of the great power hitters in history. His slugging percentage only cracked .500 twice. This is mostly because he didn’t have very good contact skills — his career batting average was just .225. But when he *did* get a hit, it turned out to be an extra-base hit 47% of the time. The league average for that figure is 29%, and only a handful of other players have sustained a better rate than him for the amount of time he did. The same can be said for Steve Balboni. He was a league average hitter (101 OPS+) for 11 seasons, batting only .229 for his career, but 45% of his hits went for extra bases. Our all-time leader McGwire, by the way, turned 52% of his hits into extra base knocks.

How about the Phillies? Here are the top 20 wXB/H seasons in franchise history:

Season | Player | wXB/H |
---|---|---|

1979 | Mike Schmidt | .964 |

2007 | Ryan Howard | .923 |

1980 | Mike Schmidt | .922 |

2003 | Jim Thome | .915 |

2008 | Ryan Howard | .912 |

1975 | Mike Schmidt | .909 |

2004 | Jim Thome | .897 |

1977 | Mike Schmidt | .880 |

2008 | Pat Burrell |
.862 |

2009 | Ryan Howard | .856 |

2009 | Raul Ibanez |
.855 |

2006 | Ryan Howard | .848 |

1956 | Stan Lopata | .838 |

1949 | Andy Seminick | .830 |

2003 | Pat Burrell | .822 |

1981 | Mike Schmidt | .821 |

1976 | Mike Schmidt | .817 |

1978 | Greg Luzinski | .816 |

1983 | Mike Schmidt | .810 |

1999 | Scott Rolen |
.808 |

Nothing groundbreaking. Mike Schmidt appears seven times. His top ranking season, 1979, was only his 6th best by OPS+, but he posted a .564 slugging percentage while hitting just .253. He homered in 6.7% of his plate appearances (league average that year was 2.1%), and his hits went for extra bases 54% of the time. Almost all of Ryan Howard’s career is represented. It’s interesting, though, that Howard’s best offensive season, 2006, ranks the lowest of his other seasons on this list. Both his SLG and ISO that year were, by far, the highest of his career thus far. But again, we’re seeing the effect of eliminating contact factors; Howard’s batting average and BABIP were much higher in 2006 than in subsequent years, and when he connected with the ball from 2007-2009, it went for extra bases more frequently.

Finally, the top 20 Phillie careers, minimum 2000 at-bats:

Player | wXB/H |
---|---|

Ryan Howard | .837 |

Mike Schmidt | .786 |

Pat Burrell | .744 |

Dick Allen | .689 |

Scott Rolen | .689 |

Stan Lopata | .655 |

Chase Utley |
.653 |

Darren Daulton | .648 |

Greg Luzinski | .631 |

Bobby Abreu |
.621 |

Gavvy Cravath | .609 |

Chuck Klein | .608 |

Johnny Callison | .596 |

Juan Samuel | .593 |

Andy Seminick | .586 |

Mike Lieberthal |
.574 |

Del Ennis | .573 |

Jimmy Rollins |
.550 |

Don Hurst | .543 |

Cy Williams | .536 |

There are perhaps some surprising names (hello Cy Williams), and you could quibble about the order, but the top dogs are as you might expect. For all the intra-fanbase battles about Howard’s value, his power is undeniable, and will be his legacy as a Phillie. There is a wide gap separating him, Schmidt, and Burrell from the rest. By wXB/H, at least, they represent the top tier of raw pop in Phillies history.

It’s an interesting metric to play around with, and I think it gets at some aspects of a player’s hitting that might not necessarily be represented by slugging percentage or isolated power. I certainly would not go bandying it about in overall player evaluations, but raw power is one of those fundamental things that draw us to baseball, and that make it fun to watch, and it’s not as easy to quantify as it might seem on its face. As a postscript, here are the values for the 2011 qualified Phillies:

## Fantusta @Fantusta

September 04, 2011 09:07 AM

I spent this whole article looking forward to what John Yayberry’s wXB/H would be…

## JF

September 04, 2011 09:15 AM

I enjoyed the article, Ryan.

Just for fun, what is John Mayberry Jr’s wXB/H for 2011 so far? I’ve got a feeling it will be up there with Howard.

How much regression do you expect from Mayberry, assuming he gets a lot more plate appearances in 2012?

## JF

September 04, 2011 09:16 AM

Fantusta, you beat me to it!

## Nick

September 04, 2011 09:36 AM

Using the formula Ryan gave, Mayberry is at .830

## Phylan @Phylan

September 04, 2011 11:06 AM

Sorry guys, I really should have included that

## Tony No-Dad

September 04, 2011 11:32 AM

Hey Ryan, nice article, but could you explain where the weighted numbers come from for wOBA? I can’t find a good explanation for them.

## Chris

September 04, 2011 12:22 PM

The weights for wOBA are based on the run expectancy for each event, relative to an average out.

sports.yahoo.com/mlb/blog/big_league_stew/post/Everything-you-always-wanted-to-know-about-wOBA?urn=mlb-208135

www.insidethebook.com/ee/index.php/site/comments/run_values_of_events/

## Rich

September 04, 2011 01:14 PM

I’d love to see the all-time Phillies lists bounced off ballpark factors to see how the Vet & CBP influence the numbers.

## Marty

September 04, 2011 01:27 PM

I loved the article. One of the most crisp explanations I’ve seen of a new complicated-looking statistic that really isn’t so complicated.

Heads up, the rest of this comment does nothing but do a simple subtraction and add a factor – this stat belongs to Pollis, Slowinski and Ryan – I just decided to use the subject to write a sample article to submit to Fangraphs with a job application 🙂 … and I didn’t see any reason why not to share it in full. ….

My only question is whether or not we should subtract the value of singles from each extra-base hit, the key innovation of ISO. If I understand you correctly when you write that the stat we’re trying to create is “the true power value that a hitter provides with each hit he collects,” then we want to see how much value his power adds to a pop-less single.

Subtracting .89 (the best singles value I could easily find) from each xBH give us weights of:

1.27 – .89 = 0.38 * 2B

1.61 – .89 = 0.72 * 3B

2.09 – .89 = 1.20 * HR

Now our metric both properly weights power and isolates it, all with a new maddening name:

wISOXB/H = [ (0.38 * 2B) + (0.72 * 3B) + (1.20 * HR) ] / Hits

It turns out that the power that goes into Holliday’s doubles doesn’t add all that much relative value to our singles-hitter baseline (+0.38 runs per double) – the power in a homer gives you three times as many runs.

*Note: This does NOT mean that home runs are three times more valuable than doubles, it means that home run power is three times more valuable than doubles power, assuming, as Ryan stressed, that contact and BABIP is the same for both hitters.

Power factor, then, even using the simplistic ISO as its basis, comes surprisingly close to getting the actual relative values of extra-base hits correct. The surprising conclusion? An extra base is worth almost exactly .4 runs, with the tweak that extending a double into a triple only nets you .3 runs.

This gives us a statistic that has an exceptional set of properties:

Its construction is very simple to explain;

It is very easy to calculate;

It is very accurate;

And the output is an actual substantive value: The number of extra runs provided by a hitter’s power, per hit.

Simplified and appropriately scaled, that Frankenstat, wISOXB/H, becomes weighted Power Factor:

wPF = .4 * [ 2B + (1.75 * 3B) + (3 * HR) ] / Hits

As a final note on the potential popular appeal of this statistic, we can use the *1, *1.75, *3 coefficients to create a superb counting statistic, as well. Even traditional statistics never merged or compared doubles, triples, and homers, but with or without the .4 scalar, this framework provides just the simple formula we need to start counting power. We could also use *2, *3.5, and *6 to make the counting even easier (and change the scalar to .2), or we could go the whole nine yards and go with *4, *7, and *12, all over 10 (although the coefficients get less intuitive at this point). What do you think?

It’s a funny course that power factor has taken. It was taken for granted as a nice, quick statistic to look at, but considered insufficiently rigorous to try to develop into the kind of powerfully analytical statistic that we statheads concoct all huddled around our caldrons under the full moon. But the whole time PF was only a tweak and a factor away from giving us a highly accurate measuring stick for the value of power.

## Jesse

September 04, 2011 02:48 PM

It’s great that I’m not the only one who thought this article would just be a big run-up to showing how great at XBH JMJ has been this year… alas…

## The Howling Fantods

September 04, 2011 03:39 PM

This is a great topic, and one that I had been kicking around in my head for a while as well.

Also, if I’m calculating it correctly, Mayberry is at .830 for the year. Right in the middle of the top seasons for a Phillies player, but probably won’t qualify with AB at 211.

## Richard

September 04, 2011 07:34 PM

Hi – I’d read the two articles you cite, and I enjoyed your take on it. One thought. You write: “Simply put, a player’s isolated power is still influenced by his batted ball fortune and contact skill, which are not things we want to factor in to our evaluation of power.”

I wonder if there’d be a useful way to combine FB % with these metrics? That would seem to me to be the one “batted ball fortune” that would be relevant to the question of a batter’s power. (Does he leave a lot of balls at the warning track? For example.) I’m not sure how you’d do it though.

## EHW

September 04, 2011 09:27 PM

That wXB/H number for Pence is for the whole season, correct? Cause I calculated him for just his time with the Phillies and I’ve got him at .582, which sounds about right given the power spike that he’s had since he came here (SSS acknowledged). That would have him right in front of Utley and behind Howard, Shane, and Raul, whereas his ISO since joining would have him only behind Shane and Howard. (and, in both instances, Mayberry)

Great article.

## Bob

September 06, 2011 09:14 PM

Great article. My question is that alot of Victorino’s hits are extended because of his speed (e.g, singles into doubles, doubles into triples). How does this account for that? Is there a stat for power that incorporates this already?