*Re-post from last year.  Haven’t made any changes to the formula.  The example used represents a scheduled game from last season.

I’ve been saying to myself and others, that the exerted effort necessary to complete a worthy and sufficient formula for integrating the variable of the bullpen into creating an MLB game moneyline is not proportional to the degree of change in moneyline.  For some reason I was under the impression it wouldn’t make that much of a difference, for most bullpens hover around a 4 ERA (3.5 to 5 at the most), and the ratio of innings pitched to that of a starter in any given game for both teams is such that any projected runs allowed would not see a consequential increased when subjected to the mark of a bullpen.

However, I now realize that I was absurdly wrong on so many levels.  After having finally found the proper formula concoction to conduct a bullpen variance, the bullpen adjusted line and the original created line (calculations explained here with changes discussed here), often sees a 40 cent line differential.  So let me explain as best I can how I was able to add a satisfactory number to project the impact a team’s bullpen may have on any one particular game.

The created line as it previously stood, was a 162 game projection using ZiPS, CHONE, or actual data, of the starting pitchers’ projected runs allowed of 9IP per game, and a team’s projected runs scored over the season.  This gives a nice standard number of runs scored vs runs allowed, used to measure the Pythagorean winning percentage.

How would I add starting pitcher determinant bullpen factor?  What I thought best was to take the projected innings pitched by the listed starting pitcher, divided by the number of games projected to start (projections are for now, CHONE, and ZiPS in season projections that is updated regularly).  Then use that number as a percentage of 9.  Multiply the resulting percentage by the number of runs projected to allow over 162 games, and you get a total number of runs surrendered by that starting pitcher over an entire regular season.  Now you still have a certain percentage left over to use as the normalizer of the two dimensional bullpen projection (bullpen ERA * 162) using the YTD statistics as ERA.  Multiply this two dimensional projection of the bullpen by what percentage is left over from the starter’s predicted innings pitched per start, and you have bullpen runs allowed over an entire regular season if that particular starting pitcher pitched every game.  Add the two numbers, and this should equate to a solid indicator of how a bullpen might regulate the expected team’s pitching performance.

Here is an example of a calculation using Randy Wolf (listed 4/22 vs Nationals):

Projected Runs allowed = Runs / IP  * 1460 (allows for randomness)

Runs allowed = (87 / 183.3) * 1460 = 692.96

Adding Bullpen Variable:

IP / GS = IP per game

IP per game = 183.3 / 31 = 5.91

IP per game / 9 = Percentage of IP per game

Percentage of IP per game = 5.91 / 9 = 66%

Projected runs per 162 games = 66% * 692.96 = 457.36

1-Percentage of IP per game  * 9= Projected Bullpen IP per Randy Wolf start

1-66% * 9  = 34% * 9 = 3.09 Bullpen IP/g

ERA * 162 = Runs allowed (Flat projection over 162 game season)

Bullpen runs allowed = 5.85 * 162 = 947.7

Runs allowed * Project Bullpen IP per Randy Wolf start

Runs projected per 162 Randy Wolf games started = 947.7 * 33% = 325.07

Randy Wolf projected runs per 162 games + Bullpen Runs projected over 162 Randy Wolf games started

Total expected runs allowed per 162 games = 457.36 + 325.07 = 782.43

782.43 runs allowed is the bullpen adjusted runs per 162 Randy Wolf games started

Let’s compare the numbers, by use of words, and look for proportional reciprocality to ensure a consistent method of calculation.

Randy Wolf’s ERA being 4.27 is considerably lower than Milwaukee’s current bullpen performance, which is a dreadful 5.85 runs per game.  The two being separated by about 1.6 runs per game, would leave a reasonable person to assume that Milwaukee’s bullpen will have a negative effect on games started by Randy Wolf.  And the resulting numbers show as much.

We projected Randy Wolf to pitch roughly 5.91IP per start.  Using this number, his adjusted runs allowed (692.96) is now appropriated to his IP per start, and the result is 457.36.  With Milwaukee’s bullpen ERA being considerably higher than Randy Wolf’s ERA, we would now expect the bullpen variant to have a negative impact on runs scored, meaning a consequential increase.  Milwaukee’s bullpen has a two dimensional projection value of 947.7 runs allowed per 162 game.  And adjusting to Randy Wolf being the listed starter and the number of total runs allowed (782.43) should be higher than the starting pitcher exclusive runs allowed (692.96).

All the variables and determinants appear to line up with rational expectation.

Now using the framework in place, a team with a solid bullpen with an ERA better than that of the listed starting pitcher’s ERA, would correlate to a higher advantage in projected runs allowed if that respective starter is expected to pitch lesser and lesser innings by degree.  One problem with that theory, of course, bullpen ERA is not uniformly distributed from reliever to reliever.  The more the bullpen is expended, and the earlier it is called on for relief, the more the level of performance regresses to mediocrity.

For now this is the best method I can come up with.  If you want the updated excel MLB linemaker, now with a column for starting pitcher predicted line, and bullpen adjusted line, comment here, email or twitter me.