NOTE: I think I ran into a dead-end in my thinking here but I decided to publish anyway. For posterity, of course.
Sometimes it helps to break baseball down into its simplest, most obvious truths. All runners can advance bases simultaneously. But there's only one ball; the defense can only get one runner out at a time.
In 1869 the baseball stats world charged the out to the batter or runner who was actually put out. After 1869 outs gradually fell out of favor as a batting stat. The batter is mostly responsible for most outs and so you could estimate his outs by his hitless at-bats if you wanted to, and add in other outs like times caught stealing, GIDPs, and sacrifices if you had them available.
The foundation of the ORA system is that the batter is responsible for the average outcome of his batting event, if it comes to pass. If the outcome is exceeded, the runner who made the out or the exceptional advance gets blame or credit for the excess. Interpreting this principle in a logical and coherent manner is where it gets tricky.
In my first version of ORA, I used the average outcome for each baserunner, for runs and outs. In 2022, when the batter hit a groundball that wasn't a base hit or a successful sacrifice with runners on 1st and 2nd and one out, the batter was out 63% of the time, the runner on 1st was out 69% of the time, and the runner on 2nd was out just 7% of the time. So if the runner on 2nd is put out he is on the hook for 93% of his out (1 minus .07), even though that out has almost nothing to do with his own baserunning ability and everything to do with the batter hitting a sharp grounder to the 3rd baseman who was playing near the bag. If the batter grounds into a 5-4 double play, he gets charged just 0.76 outs (0.07 for the runner on 2nd and 0.69 for the runner on 1st), less than the 0.93 the runner on 2nd gets charged for being forced out. Similarly, the runner on 1st has a very low out percentage on pop-ups, which means he has to eat almost all of his out if an infielder lets the ball drop and forces him at 2nd.
George Wright wouldn't have had a problem with that but I think we can do better. I'm not going to check, but I'd bet if I just fed runs scored and putouts 1869-style into ORA that Barry Bonds, 2004 would still hold the single-season record (depending on how often he got forced out after those 232 walks). What I'm saying is that it doesn't prove anything that Barry does hold the single-season and career records (for the last 47+ years) in my first version of ORA. He holds the record in every metric. I should still strive to make ORA as logically consistent as is reasonably possible.
Adding what position fielded the ball to the base/out/event type matrix might help. Then we'd have groundballs fielded by the 3rd baseman with runners on 1st and 2nd and one out separate from groundballs fielded by the shortstop in the same base/out state and groundballs fielded by the second baseman and so on. That's a lot of added complexity and clunkiness with a questionable amount of benefit.
So let's simplify instead. The defense can only make one out at a time, so instead of the average outs made by each batter/runner, let's look at the overall out expectancy for the play. 1.39 outs were recorded, on average, when batters hit a groundball non-hit, non-sac bunt with runners on 1st and 2nd and one out in 2022. This means if only one out is recorded then the batter is responsible for all of it. Okay. That swings things back to the post-1870 view that the batter gets 100% of the blame for a forceout. That's much better than him only getting a little of the blame. But what if it's a double play? Do we just split the remaining 0.61 evenly between the two runners who were put out? This isn't a terrible solution but I think we can still tweak it a little more. Here goes.
If no outs were recorded on a play, then no one gets charged any outs. Any runner put out on a non-batting play (such as a pickoff or caught stealing) is responsible for 100% of his out. (So far this is the same as my original method.)
If one out and only one out was recorded on a batting play, the batter's share isn't the average number of outs made on that event type, it's the percentage of times that at least one out was recorded. These numbers will be the same if the bases are empty and/or there are two outs, but will be different if more than one out is possible - if there are runners on with less than two outs.
Batters hit groundballs (that weren't hits or sac bunts) with runners on 1st and 2nd and one out 1,015 times in 2022. Of those 1,015 events, 55 resulted in no outs, 510 resulted in one out, and 450 resulted in two outs. That's 1,410 total outs (510 + 450*2 = 1,410) and 1,410 / 1,015 = 1.39 outs per event. But the number of events where at least one out was recorded was 510 + 450 = 960, which was 960 / 1,015 = 95% of events.
If the batter hits a groundball non-hit, non-sac bunt with runners on 1st and 2nd and one out, and only one out is made on the play, then the batter is responsible for 95% of that out. The runner actually put out is responsible for the other 5% of it.
Let's go through the first inning of the Astros/Angels game of April 7th, 2022 mostly because it comprises the first eight or so rows of my event files spreadsheet.
ASTROS 1ST: Altuve was called out on strikes. Altuve earns .998 Outs for the called third strike and .002 Outs for being put out.
Brantley singled to left. No outs on the play.
Bregman forced Brantley (shortstop to second) [Bregman to first]. Bregman earns .96 Outs for hitting a groundball that wasn't a hit or a sac bunt. Brantley earns .04 Outs for being put out.
Alvarez walked [Bregman to second]. No outs on the play.
Gurriel popped to first. Gurriel earns the full out for popping up (because an out was made 100% of the time batters hit pop-ups that weren't hits with runners on 1st and 2nd and two outs in 2022).
Here's a table of events for the top of the 1st. "OutsBat" is batting Outs, the outs caused by the batter just having the type of batting event that he did. "OutsBR" is baserunning Outs, what the runner (including the batter as a runner) alone was responsible for.
So far I've covered all events where less than two outs were recorded, which was 98% of all events in 2022, and demonstrated with the Astros' first five plate appearances of the year. That leaves the other 2%: double plays and triple plays.
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