With a runner on 1st and no outs, the batter draws a walk, moving the runner to 2nd. How many runs did the batter create?
According to Tom Tango et al. in The Book, about 0.62 runs above what the average plate appearance is worth (usually a little over 0.1 runs). This is because in the run environment of 1999-2002, a team with a runner on 1st and no outs could expect to score 0.953 runs through the end of the inning, and a team with runners on 1st and 2nd and no outs could expect to score 1.573 runs through the end of the inning. Therefore the batter increased the number of runs his team could expect to score by 0.62 runs, and so the run value of his walk was 0.62 runs above the average plate appearance.
I can test this on my 2022 event files spreadsheet. Teams scored an average of 0.872 runs through the end of the inning when they had a runner on 1st and no outs, and 1.445 runs through the end of the inning when they had runners on 1st and 2nd with no outs. So the batter's walk increased his team's run expectancy by 0.573 runs above an average plate appearance. (The run environment of 2022 was a little lower than at the height of the Steroid Era.) Add in the 0.114 runs/PA average for 2022, and the batter created 0.687 runs with his walk.
No runs have been scored yet, even though any team that has two runners on with none out is feeling pretty good about its chances. But if the inning ends with those two runners stranded, that means the batters that followed combined for 1.445 runs below average - because the team's run expectancy was 1.445, and then three outs later its run expectancy is zero with zero runs scored.
To build a Runs Created system based on Run Expectancy, batters who increase their team's chances of scoring earn positive runs (even if no runs actually score), and batters who decrease their team's chances of scoring earn negative runs.
Run Expectancy for the team is great because when the batter walked, not only did he put himself on base and move the runner closer to home, but he avoided making an out, which increases the chances that the batters on deck and in the hole will score that inning.
But we can also look at the run expectancy for each runner, including the batter. With a runner on 1st and no outs, the batter's run expectancy was 16.6% and the runner's run expectancy was 37.4%. With runners on 1st and 2nd and no outs, the runner on 1st's run expectancy was 36.9% and the runner on 2nd's run expectancy was 59.8%. So by drawing a walk, the batter increased the runner's run expectancy by 0.224 (0.598 - 0.374) and his own run expectancy by 0.202 (0.369 - 0.166), an improvement of 0.426 runs total. Add in the 0.166 the batter was expected to score when he came to bat and he has 0.593 runs he created with his walk. Or does the runner on 1st deserve some or all of that 0.166 for getting on base and not making an out? After all, batters who came up with the bases empty and one out only scored 10.5% of the time.
The reasons I avoided Run Expectancy when I built the ORA system are two-fold and related: I don't like negative Runs, and I don't like theoretical Runs. If you award credit for theoretical Runs when no runs actually scored, then you're forced to penalize the players who lowered their teams' chances of scoring with negative Runs. And I don't want negative Runs because batters and runners are already penalized for their failures with Outs.
The solution of course is to only award Runs when a batter or runner advances who is destined to score. But a runner's Run Expectancy, just like his team's, goes down if someone else make an out. Suppose the destined-to-score leadoff hitter gets to 1st. We give him 0.374 runs - his chance of scoring with no outs - but then the next batter strikes out, and then the third batter draws a walk. The lead runner's chances of scoring have only improved from 37.4% to 40.8% - 0.033 runs. But the batter who walked actually improved the runner's chances by 0.153 runs, because after the second batter struck out, his run expectancy was down to 25.5%. If the fourth batter of the inning also strikes out, the lead runner's run expectancy is back down to 22.3% - lower than it was when he was on 1st with one out. If the fifth batter finally drives him in with a double, that's about 1.3 total Runs created (0.374 for the runner getting to 1st, 0.153 for the batter who walked, and 0.777 for the batter who doubled), even though exactly 1 run scored.
So since I don't like negative Runs for outs, I should just ignore outs altogether. With a runner on 1st, the runner has a 23.9% chance of scoring. With runners on 1st and 2nd, the runner on 2nd has a 36.5% chance. So the runner earned 0.239 runs getting himself to 1st, the batter who walked earned 0.126 runs (0.365 - 0.239) for getting him to 2nd, and getting him from 2nd to home was worth 0.635 runs (1 - 0.365). I thought using Run Expectancy would make ORA kinder to table-setters, but when I remove outs from the base/out context, that's definitely not the case.
Here's how ORA currently works: when batters walked with a runner on 1st and no outs in 2022, the batter and the runner on 1st each averaged exactly one base. One base advanced is a quarter of the way to home, so it's worth a quarter of a run. So if the runner and the batter both go on to score, the batter earned half a run for his walk: 0.25 for the runner and 0.25 for himself. If only the runner goes on to score, the batter earns a quarter of a run for advancing him to 2nd. And if neither of them score, the walk isn't worth any runs. It's not a bad system, if I do say so myself.
I modified how Outs work because my old system was unfair to runners when they get forced out, especially when multiple runners are on base. I'm only rethinking Runs because I already had to reimagine Outs, and I'll keep looking for ways to improve how Runs are allocated. But it's possible that the system I'll like best is the one I already have.
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