Paraball Win Share: A New Win Expectancy Tool
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Watching the Wild Card Series the last few days, I’ve found myself thinking of win expectancy tools. Baseball has a long history of using empirical formulas to estimate a team's expected win total based on run differentials. This practice dates back to the days of the Bill James Pythagorean Theorem and has undergone refinement over the years. While run differential remains a powerful tool for assessing a team's quality independently of their win-loss record, it's not without limitations.
One notable flaw with the use of run differential is the consideration of blowout games. Every season there are teams that have many more blowout wins than losses, and teams that have many more blowout losses than wins. As a result, these teams have a skewed run differential and a skewed win expectancy. Not all runs should be treated equally; when a position player gives up 6 runs in the 9th to extend his team’s deficit to 16, those runs should be devalued.
Consider this scenario: a nail-biting 1-1 game that ends in a dramatic walkoff grand slam, resulting in a final score of 5-1. This outcome shares the run differential and final score of a less competitive game in which one team quickly establishes a 5-0 lead in the first inning and then concedes a single run in the ninth to win 5-1.
This leads me to ask the question: Is there a better way to estimate win expectancy?
I’ve developed a new win expectancy tool that shifts its focus away from run differentials and instead focuses on in-game win probabilities - I’ll refer to it as the Paraball Win Share. To illustrate the tool's effectiveness, I've gathered data from Fangraphs Live Scoreboards, and for my inaugural analysis, I'll use it to evaluate the first set of Wild Card games that took place on Tuesday, October 3rd.
Figure 1: Fangraphs win probability charts for the first set of Wild Card games on October 3rd. The green lines are independent of team strength and the grey lines are adjusted for team strength. The x-axis illustrates the inning
My approach involves using Riemann Sums to calculate the integral of the grey win probability graph (team strength adjusted); the combined areas above and below this graph add to 1. For example, in the Blue Jays Twins game, illustrated in the top-left section in Figure 1, the area above the graph sums to the Blue Jays' Paraball Win Share, while the area below sums the Twins' Paraball Win Share.
Paraball Win Share shows that the closest game on Tuesday was the Diamondbacks win over the Brewers game and the most dominant wins belonged to the Twins over the Blue Jays and the Phillies over the Marlins, as presented in Table 1 below.
Table 1: Wild Card Game 1 Paraball Win Shares calculated using Riemann Sum integral on in-game win probability graphs
To provide a more detailed explanation of the novelty of Paraball Win Share, let's revisit a critical moment in the Diamondbacks Brewers game: In the bottom of the 5th inning, with the Brewers trailing 4-3, they found themselves in a promising situation with the bases loaded and no outs. However, they were unable to capitalize on this opportunity and failed to score a run. A strikeout followed by a line drive that turned into a double play saw their win probability plummet from 71% to 43%, as seen in the top-right section of Figure 1. Failing to score in that situation, and leaving 11 runners on base to the Diamondbacks’ 8 runners left on base, ultimately resulted in their Game 1 loss, despite a very competitive performance. The Brewers’ Paraball Win Share of 0.497 reflects the tight competition better than the 6-3 final score and their -3 run differential.
The Phillies, on other hand, consistently applied pressure to the Marlins throughout the game. They had runners on second and third with no outs in the 1st inning and failed to score, before breaking through for their first run in the bottom of the 3rd and then extending their lead to 3 in the 4th inning. Their offensive performance was strong, amassing a total of 11 hits, and every member of the starting lineup contributed at least one hit. Additionally ace Zach Wheeler effectively shut down the Marlins' offense. Their Paraball Win Share of 0.808 is much more indicative of their dominance than the final score of 4-1 and their run differential of +3.
Similarly, the Twins wasted no time in taking the lead against the Blue Jays. A home run by Royce Lewis in the first inning gave them a 2-0 advantage, and another blast by Lewis in the 3rd inning extended their lead to 3 runs. The Blue Jays' offense struggled to make an impact against Twins' ace Pablo Lopez and the Twins’ formidable bullpen, led by closer Jhoan Duran, whose fastball topped out at a blazing 102.9 mph (Duran led the majors with an average 4-seam velocity of 101.8 mph). In this case, the Twins' Paraball Win Share of 0.819 provides a more accurate reflection of their victory than the final score of 3-1 and their run differential of +2.
The Potential of Paraball Win Share
Paraball Win Share has the flexibility to reward higher win share to the losing team in a particular game, if that team led for most of the game but gave up the lead late. The tool emphasizes the importance of early scoring and protecting the lead.
My aspiration is that tools and concepts like this will continue to challenge the conventional strategies in baseball and other sports. For instance, is it optimal to deploy your top reliever as the first pitcher out of the bullpen with runners on base in the 5th or 6th inning of a closely contested playoff game? While it may be a viable strategy, it's rarely seen in practice. Paraball Win Share can serve as a tool to assess teams more accurately and assist in improving managerial decisions.
