# Stats with Steven: Turning bbFIP into a Wins Above Replacement metric

Earlier this year I wrote about my favourite pitching metric, bbFIP. bbFIP (or batted ball fielding-independent pitching) is a take on the fielding-independent pitching (FIP) metric that takes into account batted ball type rather than ignoring it—like FIP does. I’ve always felt this shafted groundball pitchers and aided those with flyball tendencies. Since the baseball season ended I’ve concentrated my energies toward attempting to create a Wins Above Replacement metric that incorporates bbFIP.

bbWAR is based upon the FanGraphs model for Wins Above Replacement, which I thought fitting since bbFIP and FIP are calculated in a similar matter, bbFIP just considers more variables of pitcher control.  For a slightly more descriptive explanation you can check out the fangraphs explanation linked above, though I will walk through it as well. Obviously, because bbWAR is based on a pitching metric, it does not (as of yet) account for a win metric for position players—only pitchers.

The first thing I did was separate all relevant data into four categories. These categories were: Home Starting Data, Road Starting Data, Home Relieving Data, and Road Relieving Data.  The separation of these four categories just makes it easier when dealing with differences in replacement level between starting and relieving as well as calculating park adjustments.

To demonstrate the process, let’s take a look at Stephen Strasburg’s 2012 season:

Part One – bbFIP

The first step in bbWAR is, obviously enough, calculating each pitchers bbFIP. For this I will quote directly from the bbFIP primer.

The first part of the formula is the “BIGS”, which is (( unintentional walks + hit by pitch + line drives) – (Strikeouts + Popups)). Then taking that total and dividing it by the number of batters faced.  Lets use the shorthand formula of:

( ( UBB + HBP + LD ) -  ( K + PU) ) / PA.

The next part of the equation is what we call “SMALLS”.  Outfield fly balls and ground balls had similar run expectancy so the second part of the equation is (outfield fly balls – ground balls). Of course we divide this by batters faced as well.  The final equation for “SMALLS” is:

( FB – GB ) / PA

Finally, its time to put it all together as an equation. Doing some fancy math that I won’t bother to get into, we multiply our BIGS/PA by 11 and SMALLS/PA by 3, thus giving ourselves the difference in run expectancy.  Then at the very end of the whole equation we add a simple constant (C) to get bbFIP onto an ERA scale.  In the end our final calculation is:

bbFIP = ( ( ( UBB + HBP + LD ) – ( K + PU ) / PA) ) + ( ( FB – GB ) / PA ) ) + C

Instead of scaling bbFIP to ERA, I’ll scale it to runs allowed per nine innings (RA/9) in order to properly calculate WAR.

Using bbFIP to create a WAR metric leads to some large differences in opinion from fWAR (from FanGraphs), rWAR (from Baseball Reference) or WARP (from Baseball Prospectus), such as Jarrod Parker being worth 1.3 wins in 2012 despite being worth more than 3.7 by both FanGraphs and Baseball-Reference and 1.9 WARP by BP.  It may not look right, but bbWAR just calculates differently due to its batted ball usage.  Using batted ball information does lead to some numbers that just don’t look to add up. For instance, according to bbWAR, Jered Weaver was worth just 1.6 wins and Matt Cain just 2.7 in 2012.  This is due to the way flyballs are classified. As of now, there is no differentiation between a hard-hit flyball and a soft-hit flyball.  Ideally, there would be two types of flyball classifications, but as of right now there is just the one—so bbWAR reflects this issue.

This gives us our first calculation—bbFIP: Strasburg’s 2012 home bbFIP was 3.24, while his bbFIP on the road was 3.00.

Park Adjustment is one of the simpler steps in the process once we have separated all the data. All home data needs to have the park adjustment factored in. Park factors can be found easily over at FanGraphs.

Nationals Park posted a 100 (exactly average) park factor in 2012 meaning that we just multiply his bbFIP 1.00.  But at Coors Field, where the park factor was 113 for 2012, you would multiply by 0.87.  Reaching that number is fairly simple and is calculated like this:

x=[(200 - park factor)/100], were ‘x’ is the park factor variable.

Therefore, Strasburg’s home bbFIP remains at 3.24.

PART 3 – Run Environment

Run Environment is the conversion of runs to wins. To calculate this, we need innings-pitched per game and the home-adjusted bbFIP calculated above. So to get the run environment we use Tom Tango’s formula for runs-to-wins:

Run Environment =|{[(18 - IP/G) * LeagueRA + IP/G * bbFIP] / 18} + 2| * 1.5

Strasburg’s run environment, therefore is 8.92 at home and 8.77 on the road.

PART 4 – Win %, Above Average, Above Replacement

This next part of the calculation has several formulas that are based upon each other. First we have to find out how much better his bbFIP was than league average.  So our first formula in this step is simple:

bbFIP Above Average = League RA/9 – bbFIP (or park adjusted bbFIP).

Using that formula, Strasburg was 1.01 runs above average at home and 1.25 runs above average on the road.

The second part of this step is dividing the R/9 Above Average (R9AA) by the Run Environment (RE).

Win % = (R9AA / RE) + 0.500

This gives a bbFIP-adjusted winning percentage of .613 for Strasburg at home and .643 on the road.

PART 5 – Replacement Level

Through a bunch of fancy math, historical replacement levels have been determined.  Replacement level for starting pitchers is .380 Win % and for Relievers is .470.  The next thing we do is we take the pitchers Win % and subtract replacement level to find “% above replacement).

% Above Replacement = Win % – .380 (or .470 for relievers)

This means Strasburg was .233 above replacement at home and .263 above replacement on the road. Confused yet? It’ll all make sense a few minutes.

PART 6 – Final Calculations

We’re finally at the end of all the gory mathematical details, as Russell Carleton would say. There is just one last calculation to get to bbWAR.  This last calculation factors in Innings pitched and % above replacement.

Wins Above Replacement = ( % Above Replacement * Innings pitched ) / 9

This gives Strasburg a 2.0 bbWAR at home and a 2.4 bbWAR on the road, meaning his total bbWAR for 2012 was 4.4.

And with that, we have reached the end. While not a completely original take on WAR, there are some ideas floating in my mind for experimenting and tinkering with the formula and methodology. I put in a lot of time on this (I do not know how to database unfortunately) and there was a lot of raw number inputting, so there may be the odd calculation error just due to the sheer magnitude of manually calculating data. FanGraphs doesn’t provide Home Start / Home Relief splits so Start / Relieving stats had to be separated manually—so there is an element of error.  If someone with database ability or splits ability is willing to offer some help with this it would be muchly appreciated—comment below.