Expanding on Four Factors- Fun- With Mat

Posted by Melissa Underwood on October 18th, 2017

I seem like my Four Factors series, that has covered a few interesting hitters, went over well here. It seemed like it could be more, however, and I believe Ive taken the first step into which makes it more than a simple tool or guideline. The followingis more of a reference post than an analytical post, and because the title suggests, there will Mike Miller Jersey be some math involved here. What I put forth here also suggests a po sible inclusion of a fifth (or sixth) factor, albeit one (or two) that are significantly le s important compared to other four.

For the 4 factors to have more use besides being an at-a-glance hitter evaluation tool, it might have to mean something in terms of runs. For hitting, which means wOBA. A bridge between your Four Factors and wOBA indicates we could find how meaningful it's that Ryan Howard has witne sed his strikeouts drop if his power returns to previous form, or just how much better my boy George Kottaras could be with a respectable BABIP instead of his current .195 mark.

Of course, BB% and K% can provide us raw (or, even better, per plate appearance) numbers for walks and strikeouts. Working to figure out another four events 1B, 2B, 3B, and HR would give us a functional estimate of wOBA. This can be done with the use of POWH (XB/H), the form of Isolated Energy that only looks at slugging percentage on hits, and BABIP (H/BIP), another two factors. These four relatively isolated hitting skills can almost completely account for a players overall line.

The tricky part includes estimating home runs, because of the four stats we have, only two of them deal with contact, and of those, one deals with balls in play, excluding home runs. But Andrew Luck Jersey we are able to solve for home runs the following. Follow the jump for that math.

POWH*BABIP = (XB/H)*((H-HR)/BIP) where BIP = PA-BB-SO-HR, or balls in play. Now, its time for you to apply certain fancy algebra, meaning lots of steps. Note that rather than using PA, I personally use 1, as rather than calculating raw PA totals, I prefer per plate appearance totals for that results.

Expanding:POWH*BABIP = (XB/H)*(H/BIP)-(XB/H)(HR/BIP)

Cancelling:POWH*BABIP = (XB/BIP)-(XB/H)(HR/BIP)

Simplifying:POWH*BABIP = (XB/BIP)-(POWH)(HR/BIP)

Expanding the XB term:POWH*BABIP = (2B+2*3B+3*HR)/BIP (POWH)(HR/BIP)

Combining like terms:POWH*BABIP = (2B+2*3B+(3-POWH)*HR)/BIP

Expanding the BIP term:POWH*BABIP = (2B+2*3B+(3-POWH)*HR)/(1-BB-SO-HR)

Multiply each side by expanded BIP term:POWH*BABIP*(1-BB-SO-HR) = (2B+2*3B+(3-POWH)*HR)

Distribute on left side (note that (1-BB-SO) may be the percentage of PAs ending in touch):POWH*BABIP*(1-BB-SO)-POWH*BABIP*HR = (2B+2*3B+(3-POWH)*HR

Add POWH*BABIP*HR to each side:POWH*BABIP*(1-BB-SO) = 2B + 2*3B + (3-POWH)*HR + POWH*BABIP*HR

Now were stuck. But we can use two more leaguewide factors to allow us to get round the fact that we've one equation with three variables (2B,3B,HR). We can make use of the leaguewide rates of 2B/HR (call this X) and 3B/HR (refer to this Clayton Geathers Jersey as Y) to reduce this equation to a solvable form, which limits us to a suming the same rates of XBH for every hitter, which causes some i sues at the margins. These i sues, however, are usually relatively small. Our equation now reads the following:

POWH*BABIP*(1-BB-SO) = X*HR + 2*Y*HR + (3-POWH)*HR + POWH*BABIP*HR

Factor out HR:POWH*BABIP*(1-BB-SO) = HR*(X+2Y+(3-POWH)+POWH*BABIP)

Divide off right-hand side:HR = (POWH*BABIP*(1-BB-SO))/(X+2Y+(3-POWH)+POWH*BABIP)

With HR figured out, all of those other events fall under place. Since X = 2B/HR and Y = 3B/HR,2B = HR*X and3B = HR*YFinally, 1B = BABIP*(1-BB-SO-HR)-2B-3B. This is the remaining in-play hits after 2B and 3B.

There it's. For that 2009 hitters with at least 50 plate appearances, this formula is on average within .0001 points of wOBA with a standard devation of .010 that means that 68% of players are projected within 10 wOBA points simply using league-wide XBH distribution, and 95% are projected within 20 points. What that informs me is that there really is a 5th factor (or 5th and 6th?), XBH distribution, which would be enough to make sure total accuracy naturally, because this would just Jabaal Sheard Jersey be estimating wOBA from their overall line. XBH distribution seems to be by far le s important than the other four factors.

What are the uses of this? Ideally, as above, its to isolate these factors and to describe the way a change in one of these factors could impact a players production while at bat. Perhaps there are more; perhaps this really is limited being used. Heres a spreadsheet with the players from 2009 as well as their full Four Factors lines you can play around with it, and please let me know of any suggestions within the comments.

Later this afternoon, well take a look at some examples of how I think this could be useful.