## AN Mailbag #5: Which Home Runs Mattered?

We’ve gotten a question about how home runs affected game outcomes in 2012. Here it is, edited for grammar and brevity:

Home runs -- they can win games, or they can just add insult to injury. Looking at the A's stats this year, they finally delivered the long ball. BUT, how many of those home runs actually gave them a win?

I'm looking at Reddick, Carter and Moss, who put up great numbers. How many of those home runs could be removed from the box score and still give the A's a win?

A lot of factors have to come into play. Like was the pitcher removed after the fact? Did it put them in the lead, or did it cause the other team to simply give up? Was it a walk-off? What was the pitcher who gave up the home run's rate of giving up HRs? Was it a cruddy bullpen? How many of those home runs really helped?

Look at the Boston game, how many runs in that game really mattered?

First, let's rewind a little and talk about sabermetric theory. One of the core tenets is that player performance, at its core, translates to runs that a player contributes above his replacement sitting in AAA right now. Not actual runs scored, necessarily, but runs that an average team would add to its season total. Roughly 10 runs equals one win. This is a very crude description of the concept of "runs above replacement level."

That doesn't take into account context, though (and is one thing that rankles some about sabermetric theory). There is a counting statistic, however, that can help with that a little. Win Probability Added (WPA) measures the change in Win Expectancy (WE%) per play, excluding defense effects. So, if Yoenis Cespedes singles with no one on the 5th inning of a game in which the A's are winning 10-0, he's not adding much to the percent chance that the A's will win that game. Similarly, he's not subtracting from it if he strikes out instead. Now, let's change the context: it's the bottom of the 14th inning, one out and one on, and the A's are down by 2 runs (Sound familiar?). Whether he K's or gets a hit, the percent chance that the A's win or lose changes dramatically. Indeed, his HR that day gave him a 0.475 WPA on that play alone (+47.5% change in WE), tied for the 2nd highest WPA of any home run the A's hit in 2012 with Josh Donaldson's HR in the 9th against the Mariners on 9/29.

Armed with this information, we can then make some conclusions about how HRs affected the A's 2012 season and answer some of the questions posed.

• If we add up all the +WPA of HRs, they contributed 25.488 wins to the season.
• If we just look at Chris Carter, Brandon Moss, and Josh Reddick, we can see that their HR contributed 7.345 wins to that 25.488 number.
• In the Boston massacre game on 8/31 (I assume this is one the questioner is referring to), Reddick's grand slam and George Kottaras' 8th inning HR literally did not change the game's Win Expectancy, and therefore did not add anything to their season WPA totals. These were two of the three WPA neutral HRs the A's hit in 2012, the third being Carter's HR in the 7/25 game in Toronto that the A's won 16-0.

Some other fun HR-by-WPA trivia:

• The HR with the highest WPA was Derek Norris' walk-off against the Giants on 6/24, at 0.833
• If you take out players who hit less than 5 HR last year, Jonny Gomes provided the most "meaningful" HRs on average, with an average of 0.193 WPA/HR. (This basically eliminates Brandon Hicks' walkoff from skewing these data. Honorable mention goes to Eric Sogard, who hit 2 HR on the year for 0.252 and 0.187 WPA, respectively. Not bad.) Naturally, these data skew towards power hitters in general, because the more HR a player hits, the more likely he is to hit one in a high-leverage situation.

Remember, though, that EVERYTHING in a game contributes to WPA, not just HRs. Any hit, or out made, contributes a positive or negative number to WPA. So, it's really hard with HRs, and just in general with baseball, to start going into what-if scenarios. We can really only measure the contribution of what happened on the pitching and offensive side of the ball. For example, take Brandon Inge's walk-off grand slam on 5/8. Yes, it was an exciting way to end the game, but there were many other ways he could have ended it. A walk, HBP, non-HR hit, or sacrifice fly would have sufficed. Given that there was one out at the time, even if he had failed, the A's would have had one more chance to end the game. For that reason, Inge's WPA was only 0.168 on that grand slam. What would have happened if Francisco Cordero would have been replaced with a reliever who was HR-prone? Or one who is groundball prone? Did John Farrell give up, or did he think Cordero was really the guy best suited to get Inge out? There are infinite possibilities that can take a fan down a what-if rathole, and not really provide any clarity to the situation. That's not even taking into account defense, which is another story altogether. Those defensive data need to be far more robust before they can become useful.

All data taken from Baseball-Reference. The play index HR log is a beautiful thing. Fangraphs calculates WPA slightly differently, but has some excellent explanations of Win Probabilities in their glossary

Please continue to submit questions to the mailbag: athleticsnationmailbag [at] gmail [dot] com. We welcome any and all questions!

### In This StoryStream

##### Athletics Nation Mailbag
1. Dec 10 6 comments
##### 2013 Offseason Mailbag # 6: Infield Musical Chairs, Cespedes Extension, and more
2. Dec 16 74 comments
##### AN Mailbag #5: Which Home Runs Mattered?
3. Dec 11 95 comments

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