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In Wednesday night's Pirates vs. Diamondbacks game, the Pirates' offense repeatedly bailed out their pitching and defense. Twice, Pirates' hitters overcame deficits that were a product of a combination of poor fielding (four errors) and pitching (eight hits and four walks). We can correctly describe the victory as an offensive win. In other words, the offense deserves the lion's share of the credit for winning the game.
Last night's game got me thinking about how many other games this season we can describe as offensive or defensive wins. There is a statistic that we've used in the past that can help us answer that question, Win Probability Added (WPA). Basically, WPA calculates how much each event in a baseball game adds or subtracts to the probability of winning the game. It then credits the change in probability to the players involved. Here is an example of how WPA works taken directly from Fangraphs.com:
In game 4 of the 2007 World Series, the Win Expectancy for the Rockies started out at 50 percent. When Jacoby Ellsbury doubled off Aaron Cook in the very first at-bat in the game, the Rockies WE declined to 44.2%. The difference or WPA was .058 wins (5.8 percent). Ellsbury was credited +.058 wins and Aaron Cook credited with -.058 wins.
BaseballReference.com tracks each team's aggregate WPA for pitchers and hitters for each game played. For example, last night Pirates' hitters contributed .526 WPA, and the pitchers subtracted -.025 WPA. (WPA is scaled from .5 to -.5. At the end of each game, the winning team will have an aggregate .5 WPA and the losing team a -.5) In other words, the hitters are credited with .526 wins. Moreover, since each game starts with an even win expectancy for both teams, i.e. each team has a 50 percent chance of winning, we can say that the hitters provided an additional 52.6 percent in win expectancy (50 percent at the beginning of the game, plus what the hitters added.) I think this can also be expressed as the Pirates' hitters deserve 103.2 percent of the credit for the win, but I'm not sure of that. I have sent an email to Tom Tango, the inventor of WPA to confirm that interpretation. (On edit: I have not received a email response from Mr.Tango, but this later interpretation is decidedly incorrect. My notion was that since the pitchers supplied all the positive WPA they deserved over 100% of the credit. But that doesn't make much sense. I'll update if I hear back from Tom.)
In order to calculate how many games can be described as pure offensive or pitching/defensive wins, I simply added up the total number or games in which either the offense or pitching/defense scored an aggregate WPA score of .5 or higher. For pure offensive and pitching/defensive losses, I simply added the total number of games in which either the offense or pitching/defense scored an aggregate WPA of -.5 or lower. On the table they are labeled as "Wins" and "Losses".
Additionally, I calculated how many games can be described as "almost completely" offensive or pitching/defensive wins or losses. Everything remains the same as above except that the threshold is lowered to .4 and -.4 respectively. Here are the totals:
As we can see, both the offense and pitching/defense have contributed nine pure wins. The offense has cost the Pirates six pure losses, while the pitching/defense has cost them three games.
In terms of "almost completely" offensive or pitching/defensive wins or losses: the offense has added .4 WPA, 15 times, and has been almost completely to blame for a loss 12 times. The pitching/defense has added .4 WPA 16 times, and has been almost completely to blame for a loss eight times.
Put another way, the offense deserves almost complete credit for 24 percent of the Pirates' wins. They deserve almost total blame for 26 percent of the losses. The pitching/defense deserves almost complete credit for 25 percent of the total number of Pirates' win. They deserve almost total blame for 17 percent of the losses.
Trends
In order to come up with the results I reported above I had to download the WPA scores for both the offense and pitching//defense for each game onto a spreadsheet. That provided me the opportunity to graph the game-by-game WPA scores, and then add trendlines on top of them. The results from that effort are next:
Offensive Game-by-Game WPA
Note the increase in frequency of positive WPA scores after about the 45 game. For the season, the offense has posted 57 positive WPA scores and 53 negative.
(click to enlarge)
Defensive Game-by-Game WPA
Note the relatively consistent distribution of negative and positive WPA scores. For the season, the pitching/defense has posted 60 positive WPA scores and 40 negative.
Offensive and Pitching/Defense Trendlines Compared
Note how the offensive turnaround is reflected in this comparison of trendlines. Red = offense; Blue = pitching/defense
Conclusion
Win Probability Added is a storytelling stat. It quantifies the contribution to wining and losing of each event in a baseball game. As such, it is not a predictive metric. It cannot tell us what to expect in the future.
What it does do is give us a more precise language - let's call it mathematical language - in which to describe the narrative of a season or a game. From these results we can now visualize with more precision what we have seen with our eyes all season; namely, the Pirates pitching has been rarely almost completely responsible for losses. Moreover, by looking at the trendlines, we can see the extent to which the increased production of the offense has directly led to increased winning.
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