ERV Scoring, Deluxe Edition

Based on the fine comments to this post on my ERV scoring system, I've thought some more about it and came up with an idea for a "Deluxe Edition" of ERV (you don't need to use it, but it makes you cooler if you do) that might address the main concerns raised in the comments.

The main criticism of the ERV Standard Edition is that it is good at valuing actions relative to the inning, but not relative to the game, in that it values the game winning single the same as the single that makes the score 12-1 instead of 12-0. A related criticism was that it sometimes did not adequately value the batter who actually caused a run to occur -- I call this the "Cabrera Problem" after my example from the earlier post, where Cabrera hits a sac fly to score a runner from third but gets a 0 RV. I think the Deluxe Edition takes care of both problems. And most importanly, I think it does so meeting the strict, paramount, external constraint on the ERV system -- it must be something I can compute on paper with a dog in one hand and few beers consumed

I started with the notion that you can analyze the "state of the game" with ERV just as you analyze the "state of the inning". ERV tells us that the average team scores 0.5 runs per inning, or 4.5 runs per game. Thus, at any point you can calculate what the expected runs per game is for each team, and thus which team will win if the averages play out. For example, at the first batter of the game, each team is expected to score 4.5 runs, so the game is tied.

Now, let's assume the Visitors score 1 run in the top of the first. According to ERV, they will score 5 runs in this game (the 1 they just scored, then 0.5 for each of the remaining 8 innings, or 4.0 more, for a total of 5). Now, what about the Home team's chances of winning? If they just score the ERV average, they will lose 5.0 to 4.5. They need to make up the 1 run to avoid a loss. So, instead of 0.5 runs per inning, they need to score 0.556 runs per inning (5 runs divided by 9), or an additional 0.056 runs per inning. Let's round that off to 0.1 run per inning, or 1 RV.

What about later innings, like the 7th, for example? Let's say a game is scoreless until the top of the seventh, when the Visitors score 1 run. ERV says they will score 2 runs that game (the 1 they have scored, plus 0.5 for each of the 2 remaining innings, or 1, for a total of 2.) Now, ERV says the Home team will score 1.5 in its remaining at bats, but they need to score 2 to avoid a loss, so they need to score 0.67 runs per inning at least, or 0.17 extra runs per inning, which we can round off to 2 RV extra per run.

Why only go-ahead or lead-building runs? These are the only types of runs that make the opponents job of avoiding a loss harder. If my team is winning 7-2, and the other guys score 2 runs, according to ERV we'll each score the same for the rest of the game and I win by 3 runs without doing any extra work. So, it is key to remember that the Deluxe Edition requires a new approach only for those runs that create a lead or add to a lead. This is why it is relatively simple to implement.

Simple? After all this explanation? Yes. Because I've done the work for you. I have calculated the Win Value (as I call it) of each run for each inning for Home and Visitors, in the table below:

Team	1	2	3	4	5	6	7	8	9	10
Visitors	1	1	1	1	1	1	2	3	5	5
Home	1	1	2	2	3	3	5	10	10	10

These values can be easily added to the ERV scoresheet, at the top next to each Inning number for Visitors and Home.

What do you use these numbers for? Remember that in Basic ERV, when a run is scored, you add 10 to the normal comparison of states to account for the run that crossed the plate. Now, in ERV Deluxe, if a go-ahead or lead-building run is scored, you add the corresponding Win Value above to the 10 RV, based on the inning you are in.

Here's a good (but heart-breaking for me) example, from the top of the eighth inning in Game 4 of the 1993 World Series between Toronto and the Phils. Going into the inning, the Phils were winning 14-9. The Win Value for the Top of the Eighth is 3.

Larry Andersen pitching for the Phils
Alomar grounds out, -2 RV
Carter singles +2 RV, (runner on 1st, 1 out)
Olerud walks, +5 RV, (1st & 2d, 1 out)
Molitor doubles, run scores, 14-10 Phils, +15 RV (2d & 3d, 1 out) (Note: he gets 5 RV for moving the state from 12-/1 to -23/1, and 10 RV for the run scoring. No WV is applied, because they still trail 14-10)
Mitch Williams comes in to pitch (pit forms in my stomach, even today)
Fernandez singles, run scores, 14-11 Phils, +7 RV (1st & 3d, 1 out) (Note: he gets -3 RV for moving the state from -23/1 to 1-3/1, plus 10 RV for the run, but again no WV as they still trail)
Borders walks, +4 RV (bases loaded, 1 out)
Sprague strikes out, -8 RV (bases loaded, 2 outs)
Henderson singles, two runs score, 14-13 Phils, +17 RV (1st & 2d, 2 outs) (Note: he gets -3 RV for moving the state from 123/2 to 12-/2, but plus 20 RV for the runs scoring. Again, no WV applied)
White triples, two runs score, 15-14 Toronto, +22 RV (3d, 2 outs). (Note: He gets -1 RV for moving the state from 12-/2 to --3/2, but gets plus 20 for the two runs, plus 3 for Win Value, as he knocked in the go-ahead run worth +3 in the 8th inning).
Alomar grounds out, -4 RV

Totals: 55 RV, 3 WV for the Blue Jays. Mitch Williams has a -38 RV for 6 batters faced.

Note that if Morandini had walked and Lenny Dykstra had hit a home run in the bottom of the Eighth to take the lead again, it would have been worth 28 RV for Dykstra (20 for the two runs, 10 for the one WV, -2 for the change in states). Alas, they both struck out.

This solves the Cabrera problem because if Cabrera's sac fly scored a go-ahead run, then he would get a WV added to it, which in his case (Top of Fourth) he would get a +1 RV.

I think this accurately accounts for game situation in ERV without a lot of extra work. I'd be grateful for any comments or suggestions, especially those picking up something I missed. One question I'm not sure on is excluding game-tying runs from any WV adjustment. My rationale is that a tying run does make it harder for the opponent to avoid a loss, so it should not get credit, since the WV are calculated based on the extra runs needed to avoid a loss. Any thoughts on that issue would also be helpful.