Rolls on Hitter's card vs Rolls on Pitcher's Card

I know there's been debate over the years as to the relevance of Run Differential, however, I wonder if anyone has ever explored the relevance of discrepancies regarding Die Rolls on the pitcher's card vs Die Rolls on the hitter's card?

What happens, say, if I'm -50 on both sides: I roll 50 times more on my opponents pitching card and 50 times less on my own hitter's card? What happens if I'm -100 on both sides? etc...?

Is there any way to quantify this?

I have files of pbp records from 3 seasons of ATG9, 80m, no dh and 3 seasons of ATG9, 100m, dh. So that's 2,916 games per set. From them I calculate that the average runs per roll above average by card are:

80m no dh
hitter: .067
pitcher: -.068
specialty(h&r, bsac, sqz): .002

100m dh
hitter: .108
pitcher: -.111
specialty(h&r, sac, sqz): .023

So, going by this, for 80m no dh, if you roll 50 more times on your opponents pitcher card you would score 3.4 runs below average
If you roll 50 more times on your opponents hitter card, they would score 3.35 runs above average.

For 100m dh, if you roll 50 more times on your opponents pitcher card you would score 5.4 runs below average
If you roll 50 more times on your opponents hitter card, they would score 5.55 runs above average.

Did I understand your question correctly?

I think so barmorris.

How did you do this however: "From them I calculate that the average runs per roll above average by card are:"?

That's a long and nerdy answer:

There are 24 possible (runners, outs) combinations at the beginning of an at-bat (beginning state), and 25 (runner, outs) at the end (end state) (the original 24 plus 1 for 3-outs). From the data I calculate the transition probabilities between beginning and ending states. From those, I simulate half-innings to develop a run-expectancy(re) matrix for the 24 beginning states. This re matrix tells me what the expected number of runs are for the remaining portion of an inning given a specific beginning state. Then I can tag all of the pbp entries with a value. That value is runs scored on the play plus the change in re (re.end - re.beginning).

With all of the pbp entries tagged with a value, I can calculate the average value for entries that have a pitcher's card roll and the average value for entries that have a hitter's card roll.

Don't worry, I didn't do all of this to answer your question. My first purpose was to determine the average value of a single, double, etc. rather than use the formula in Diamond Dope.

That's a long and nerdy answer:

There are 24 possible (runners, outs) combinations at the beginning of an at-bat (beginning state), and 25 (runner, outs) at the end (end state) (the original 24 plus 1 for 3-outs). From the data I calculate the transition probabilities between beginning and ending states. From those, I simulate half-innings to develop a run-expectancy(re) matrix for the 24 beginning states. This re matrix tells me what the expected number of runs are for the remaining portion of an inning given a specific beginning state. Then I can tag all of the pbp entries with a value. That value is runs scored on the play plus the change in re (re.end - re.beginning).

With all of the pbp entries tagged with a value, I can calculate the average value for entries that have a pitcher's card roll and the average value for entries that have a hitter's card roll.

Don't worry, I didn't do all of this to answer your question. My first purpose was to determine the average value of a single, double, etc. rather than use the formula in Diamond Dope.

i've always thought (hoped) i was at least ahead of some or a lot of the pack, but that comment above Barr shows me I am a blind, deaf, and dumb guppy in a tank full of barracudas, piranhas, and hammerheads

sheesh, im playing with tiddlywinks and u guys are using ballistic missile codes ;- )

respect, more respect, and even more respect

Thanks, but analytics isn't the only successful approach. There are many managers in 365 that are better than me using more traditional baseball knowledge/strategy. Just like in real baseball, there are managers that do well with analytics and managers that do well with experience.

Don't worry, I didn't do all of this to answer your question. My first purpose was to determine the average value of a single, double, etc. rather than use the formula in Diamond Dope.

Barr: Great Stuff! First, I am personally jealous of your 'retiree' status that allows you to delve into such an interesting topic. Second, the old rule of thumb (James? Palmer?) is that 10 extra runs are needed for a win. If true, that means your value of 3.4 extra runs for a 50-roll advantage does not even equate to one win. But, I may not be comparing apples-to-apples here (need to ponder it). My question, has your analysis derived a number of runs that equate to a win? Seems like that would be an interesting comparison. Thanks, -Toady

Yes, retirement is great.

I suspect the rule of thumb comes from the Pythagorean expectation formula. If you start with a team that scores 850 runs and allows 850 runs (expected wins =81) and add 10 runs to runs scored you get an expectation of 82 wins - which is one extra game (but 2 games above .500).

I haven't tried to come up with another way of converting runs to wins.

In looking at the numbers I posted, earlier I'd focus on the 100m dh set of numbers. With no dh, there are more times (compared to dh) when the offense wants the roll to be on the pitcher's card. But I agree, the idea that a 50 roll advantage would only get you .5 extra games (1 game above .500) seems small.

Barr, Thank you for the response. That all makes sense. It occurs that I believe we are discussing a team, correct. Since there are 6,000-6,500 rolls in a season for each of batters and pitchers, it is logical that being off by only 50 rolls would only be a slight variation such as 0.5-1.0 win.

Yes, in general it is better to get rolls on your cards, but I would also look at the individual players.

If Bonds is -10 and Crosetti is +10, the team's rolls are even. But it probably cost you a few runs.

Sometimes, I will notice my first 6 batters roll on the pitcher's card and then 7-8-9 roll on the hitter's card.
That isn't much better than having all 9 on the pitcher's card.