Many commentators have said something in the last 24 hours about how Shohei Ohtani's 6-for-6 historic day was the best offensive performance ever. As it happens, I think the arctex fractional R stat is the best way to answer this question. Let me walk through the calculation play by play, calculating ACR, R, and ACW step by step, using the bb-erd tool.

There are some preliminaries. The current ballpark code for Miami is MAR.0. Looking in bwp-tab, the home team win rate is 440 / 913 for end of 2023 or 0.481927710843373. To set up bb-erd properly (OK, this will be a little easier in a future release), I enter: 

> V MAR.0
> Z 0.481927710843373
> T
erv: MAR.0
score difference: -1
Z: -0.197
> E 0 0
0.4561
> E 0 1
0.2381
> E 0 2
0.0872

Those last 3 numbers are the ERV table values for the R calculation below.

The first double:

0 out, 0-0, 0p2000, nPNO=2

In bb-erd: 

> 0p2000
0.7243
> We 0 0 0
0.4819
> We 0 2 0
0.4049
So we have:

ACRc += 0.7243

For R, we have

R += 0.7243 + ( 0.4561 - 0.2381 ) * (1/2) = 0.8333

ACWc += log( 1 - 0.4049 ) - log( 1 - 0.4819 ) = 0.138561184830064

The first stolen base:

1 out, 0-0, 3n6110 

> 3n6110
0.4586
> We 1 3 0
0.4342
> We 1 6 0
0.3879

ACRc += 0.4586 * (1/2) = 0.9536

R += 0.4586 * (1/2) = 1.0626

ACWc += ( log( 1 - 0.3879 ) - log( 1 - 0.4342 ) ) * (1/2) = 0.177888689324842

In this case, the factor of (1/2) is because there are two baseruners.

The single:

8 out, 0-1, 3p5221, nPNO=3 

> 3p5221
1.0297
> We 8 3 -1
0.3509
> We 8 5 -2
0.2591

ACRc += 1.0297 = 1.9833

R += 1.0297 + ( 0.0872 - 0 ) * (1/3) = 2.121366666666667

ACWc += log( 1 - 0.2591 ) - log( 1 - 0.3509 ) = 0.310167564708031

The second stolen base:

8 out, 0-2, 5n6220 

> 5n6220
0.1247
> We 8 5 -2
0.2591
> We 8 6 -2
0.2503

ACRc += 0.1247 = 2.108

R += 0.1247 = 2.246066666666667

ACWc += log( 1 - 0.2503 ) - log( 1 - 0.2591 ) = 0.321975027794436

The double out at third - that makes him 5 for 6 in arctex:

14 out, 1-5, 5p0232, nPNO=1 

> 5p0232
1.5495
> We 14 5 -4
0.1516
> We 15 0 -6
0.1114

ACRc += 1.5495 = 3.6575

R += 1.5495 + ( 0.0872 - 0 ) = 3.882766666666667

ACWc += log( 1 - 0.1114 ) - log( 1 - 0.1516 ) = 0.368269995605717

The first home run:

31 out, 3-7, 2p0112, nPNO=2 

 2p0112
 1.5491
 > We 31 2 -4
 0.0995
 > We 31 0 -6
 0.0744

ACRc += 1.5491 = 5.2066

R += 1.5491 + ( 0.2381 - 0.0872 ) * (1/2) = 5.507316666666667

ACWc += log( 1 - 0.0744 ) - log( 1 - 0.0995 ) = 0.395762006869173

The second home run:

38 out, 3-12, 4p0222, nPNO=2 

> 4p0222
1.7164
> We 38 4 -9
0.0362
> We 38 0 -11
0.0304

ACRc += 1.7164 = 6.923

R += 1.7164 + ( 0.0872 - 0 ) * (1/2) = 7.267316666666667

ACWc += log( 1 - 0.0304 ) - log( 1 - 0.0362 ) = 0.40176181797799

The third home run:

50 out, 3-14, 3p0223, nPNO=9 

> 3p0223
2.6664
> We 50 3 -11
0.0122
> We 50 0 -14
0.0098

ACRc += 2.6664 = 9.5894

R += 2.6664 + ( 0.0872 - 0 ) * (1/9) = 9.943405555555556

ACWc += log( 1 - 0.0098 ) - log( 1 - 0.0122 ) = 0.404188512798789

Finally,

ACRr = ACRc / 6 = 1.598233333333333

ACWr = ACWc / 6 = 0.067364752133131

ACRa = ACRr * PAPG = 6.800371231551082

ACWa = ACWr * 10 * PAPG = 2.866323163660185

R = 9.943405555555556

There will be a little variation from the eventual "official" stats due to a number of factors including rounding errors and the updating of the ballpark tables and home win rate for next year. All that said, at the end of 2023 in the retrosheet database, the highest fractional R value assigned to a player in one game was:

9.9562 for Mark Whiten (whitm001) in game CIN199309072

So Shohei has one superior, and it turns out the only one. What did Whiten of the Cardinals do in that game? First at bat, a two out grand slam. That always helps. A flyout to start an inning, then a 3-run homer with nobody out. Then a third 3-run homer with 2 out, and a 2-run homer with one out just to finish things up. ACRa 8.132 and ACWa 4.147. That's a hell of a game. Third place behind Ohtani is Phil Weintraub of the Giants in 1944 with 9.6072, and then fourth is Anthony Rendon of the Nationals in 2017 with 9.5265. If I made any errors, Ohtani could wind up on top. It's very close.

Incidentally, these are nowhere close to the record in ACW or ACR, as those are averages not totals. That goes to David Bote for a pinch-hit walkoff grand slam in 2018, which was worth 132.857722066 in ACWa, and good for an ACRa of 14.193170574020237. The maximum ACR for a game is hard to determine with the current version of the software, but that's pretty close to it. The maximum possible was 14.684456685878146 in RFK stadium, but no pinch hitters did that. There have been 5 pinch-hit occurrences of the code 7q0224, which is worth 14.329753832534507.

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