What we lost... what we "gained"

I'm here bored in my office, such is the life of an intern who works where they didn't have enough work for him to do in the first place.  I was thinking about our predicament and the current arguments, whether this is poor managing or injuries or both or what have you.  One post caught my mind, yes we're 2nd in the league in runs scored, but how many more or less would we have if the guys we had to start the season had finished it?

Further more I thought, how would that impact our expected wins?  So after some work and number crunching this is what I've found.

First off, the method:

This is based off of wOBA, weighted on base average which is a pretty good measure of offensive impact.  This year according to fangraphs (the home of most of this data) the league wOBA is .337, which also happens to be the same as the league OBP, wOBA is scaled so league average OBP is equal to league average wOBA.  The method I found to turn wOBA into runs is to find runs above average.  This is done with the following formula:

( (player wOBA - league wOBA) / 1.15 ) * Plate appearances

I don't know how this was discovered but it's the formula I found.

I then went about calculating what our starters contributed this season until they were hurt and what they would have contributed if they had played out the season (scaled to their typical amount of PAs a year).  In Ellsbury's case his year's wOBA was affected by his injury so I used last year's number as more representative of what a healthy Ellsbury would be.  the difference between these numbers was calculated then.  I then calculated what each of the players who have seen decent starting time in their place has contributed this season.   The difference between the replacement production and what was lost is a rough indication of how many runs more or less we would have scored under a full season with these players healthy. 

This was then put into the pythagorean formula for winning percentage:

winning% = RunsScored^2 / (RunsScored^2 + RunsAllowed ^2)

To see what our expected winning percentage is. 

This is where I admit the first of several weak points in the study.  Given a poor selection of defensive statistics I think it would be inappropriate to calculate the defensive change in Runs Allowed over this time.  I would expect that our runs allowed would be much lower given more time played by our starters but small sample sizes diminish the ability to calculate the difference.

Onto the numbers:

-What we lost

Dustin Pedroia - in 351 PAs he racked up a .377 wOBA and was worth 12.2 runs above average.  Over a typical season length for him he would have been good for 24.3 runs above average.

The difference: 12.1 runs

Kevin Youkilis - in 435 PAs he had an amazing .419 wOBA, worth 31 runs above average.  His expected output over 620 PAs was 44.2.

The difference: 13.2 runs

Jacoby Ellsbury - in 84 PAs he posted a horrible .237 wOBA, good for -7.3 runs.  Last season's .354 wOBA would have been good for 10.3 runs above average over 700 PAs.

The difference: 17.6 runs

Mike Cameron - this year in 180 PAs he posted a .321 wOBA worth -2.5 runs.  Also having played hurt I used the same method as Ellsbury, last year's wOBA, coincidentally tied with his career number.   This produces 6.5 runs above average.

The difference: 9 runs

Victor Martinez - This season he has produced 2.7 runs above average with his .343 wOBA.  Projected over a season where he doesn't miss a month he is worth 3.4 runs.

The difference: .7 runs

Jason Varitek - in half the season he was thriving given more rest to the tune of a .365 wOBA worth 2.6 runs above average (our catchers were doing very well).  He only gained a game or two more than Martinez since he too soon fell to injury, I'm guessing this was roughly half his expected at bats.  Over a season he would have been worth 5.2 runs.

The difference: 2.6 runs.

Total difference in offense lost: 55.2 runs

-What we gained

Jed Lowrie - has pitched in with a .364 wOBA since his return from mono.  He certainly has the look of someone who could be a starting SS or 3B next year.

Contributed: 2.7 runs

Bill Hall - has done decently since he joined us, he doesn't get on base much but pounded the ball for a high slugging percentage, bringing his wOBA to an above average .343.

Contributed: 1.7 runs

Mike Lowell - he has been a ghost of himself this year, hitting for a .294 wOBA.

Contributed: -7.4 runs

Daniel Nava - lit the league on fire early but has slumped hard lately, bringing his year's wOBA down to .321.

Contributed: -2.0 runs

Darnell McDonald - a pleasant surprise when I did these calculations, he has a slightly above average wOBA of .343 to go along with his good corner OF defense.

Contributed: 2.4 runs

Ryan Kalish - hasn't made that jump yet in production posting just a .312 wOBA.

Contributed: -2.2 runs

Eric Patterson - has posted a .316 wOBA in a too many 185 PAs.

Contributed: -3.8 runs

Kevin Cash - was an offensive butcher this year as our primary starter for a month, hitting to a .230 wOBA over 123 PAs.

Contributed: -11.4 runs

Jeremy Hermida - over a 171 PA sample size he hit with a .269 wOBA.

Contributed: -10.1 runs

Total offense gained: -30.1 runs

This is where I point out a second flaw.  I've projected the starters to the end of the season but have only calculated current contributions by the replacements.  However, the number shouldn't change much given the little time left and that players like Hall, Lowrie and McDonald can offset the damage done by Lowell, Nava and Kalish, mostly anyway, if anything I would guess that the number becomes even more negative with contributions by rookie September callups.

But to recap:

We've lost 55.2 runs due to injury this year by my estimation.  The replacements for these players have contributed -30.1 runs.  Leading to a total difference in offense of about 85.3 runs.  A third admission.  Some of these players were going to play anyway, Hermida, Hall and Lowrie would have found playing time whether the starters were healthy or not.  If Youkilis was here and Tek was still injured, Cash would likely have recieved starts anyway.  There are some positives and there are some negatives so it would mostly even out. 

Now onto wins.

Our current winning percentage is .558, leading to an expected record of about 90-72, maybe less if you consider that we've been closer to .500 lately.  We've currently scored 694 runs and allowed 626.  This gives an expected winning percentage of .551 or a record of 89-73, about identical to what our actual winning percentage suggests.

What if we scored 85 more runs?

Time to scale to a 162 game season.  694 runs scales out to 814 runs, plus 85 more, assuming consistent contributions for the last 24 games, gives us 899 runs scored for the year.  More than last year for the record.  For runs scored, 626 runs scales out to 735 runs allowed. 

The pythagorean expected winning percentage: .599, or a record of 97-65.

That says a lot.  According to expected outcomes we're losing 7-8 extra games this year based entirely on a loss of offense.

Of course there are many more things to consider beyond just offense and there are certainly some shortcomings in my logic that you are more than welcome to point out but this was only meant to be a rough gauge of performance.  To get a full look, defense must be taken into account.  Youkilis, Pedrioa and Cameron were all very strong defensive players, Ellsbury in LF had shown he could be strong there.  McDonald as a replacement showed strong play in the corners, as does Kalish who can also play center.  Hall is a defensively liability everywhere, as is Lowell at first.  Lowrie is a bit of an unknown, there isn't enough data to know but the eyeball test shows he's been average at worst.  Overall there has been a decline in defense, that is for sure.  An increased defense would reduce the runs scored number a good bit and push our winning total closer to 100.

Also a lot can be said about the pitching in terms of the run scored number.  That is even more difficult to determine though.  Wakefield was not good in his time as a starter this year.  On the flip side.  Beckett has not been good as a starter this year.  However, his peripherals suggest a MUCH lower ERA than the one he is currently sporting, FIP has him a 4.17, xFIP at 3.87, compared to his 5.91 ERA.  If Beckett had the time to fit a whole season in, it wouldn't be a stretch to imagine that he would have contributed an extra win or two over the contribution of Wakefield.  Doubront was decent in his time too.  Daisuke missed a few starts with various ailments this year and despite appearances has put together a decent season with his 4.29 ERA which should be higher or lower determining whether you suscribe to xFIP or FIP respectively.  We also missed a start or two of Clay Buchholz and his near Cy Young worthy season. 

According to the expected record of 97-65 we would be one game behind the rays and four behind the Yankees.  That's before taking into account defense and pitching which would put us much closer to the divisional lead and in what was expected by most pundits to be a down year, well it would have been rather surprising.  I'll sign off saying this, no team plays healthy all season.  The Rays have seen a few starters get hurt, the Yankees have been dealing with a gimpy Alex Rodriguez and the loss of their DH all season in Nick Johnson.  But like I said, this isn't perfect, just a guesstimate.