Nelson Cruz and Scarce Power

Nelson Cruz is the kind of free agent that comes with a ton of red flags. He’s heading into his age-33 season, and is reportedly looking for a long term contract after turning down the Rangers qualifying offer of $14 million for 2014. He’s been historically injury prone, having suffered a collection of injuries that tend to reoccur, and has only played in more than 130 games once in his career. Despite playing in a hitter friendly ballpark in Texas, his career on base percentage is .327, and over the last three years, it’s just .319. He’s not a particularly good defensive player, and could very likely have to move to DH in a year or two. Oh, and he’s coming off a 50 game suspension after being connected to the Biogenesis PED scandal.

There are plenty of valid reasons for teams to avoid paying big money to Nelson Cruz, but he didn’t make a mistake in turning down the Rangers offer of arbitration, as he knows that he possesses a skill that is becoming rarer and rarer in today’s game: right-handed power. Over the last three years, only 13 right-handed hitters in the game have hit at least 80 home runs, and Cruz is one of those 13. The growing scarcity of power, especially from the right side of the plate, is going to lead someone to give Cruz a pretty hefty contract. After all, basic economics suggest that the rarer something is, the more it should cost, and Cruz is one of the rare power hitters on the market this winter.

However, I’d like to suggest that baseball teams should not pay a premium to acquire power hitters simply because we’ve moved into an era where offense is harder to come by. Just because home run hitters are now harder to find does not make them significantly more valuable now than they were when everyone could jack 20 bombs a year.

Let’s deal with the scarcity issue first. Yes, there is now a lower supply of home runs than there used to be, and when supply goes down, price usually goes up, assuming demand holds steady. However, a baseball game is not a very good model of economic theory, because the scoring system of baseball is not designed to reward scarcity. If events were valued based on how rare they were, the triple would be baseball’s ultimate hit, as there were 4,661 home runs last year, but only 772 triples. Of course, no one thinks triples are more valuable than home runs just because there are fewer of them, because the currency of baseball is runs, not scarcity of events.

At the end of the day, the only thing that really matters is how many runs a team scored and allowed in a given game. Even over a full season, the standings usually track very consistently with total runs scored and runs allowed. How you score runs does not really matter so long as you do. Home runs certainly help in that regard, but they don’t become exponentially more valuable simply because they become more scarce.

Without boring you too much with heavy math, many of the modern statistical models are based on a concept called Linear Weights. Linear Weights models take every event that happens over the course of a season and assigns an average run value to those events based on the run environment of that season. So, when offensive levels are high and there are lots of baserunners, home runs are more likely to occur with men on base and result in multiple runs scored than solo home runs, so the run value of a home run is higher in offensive booms than it is when pitching is dominating.

This is true of pretty much every offensive event, not just home runs. The value of reaching base goes down when it’s less likely that the guy behind you will drive you in. So, what we really care about are the change in relative values between things like singles and home runs in different run environments. To illustrate these changes, here’s a graph created by my colleague Steve Staude, for a post he wrote earlier this year.


Notice how the blue line for singles and the green line for home runs move in near unison over time, as offense ebbs and flows into and out of baseball. They don’t move in perfect lockstep, but they move very similarly in nearly every era of the game, including the one we’re living in now. There have been times in baseball history where the value of a home run and a single have differed from their norms — specifically, the Dead Ball Era, where no one could score and a home run was one of the few ways you could guarantee some offense — but at anything close to normal levels of run scoring, the relative value of the home run and the single don’t change much at all.

Now, you might wonder why you should care about what Linear Weights has to say about this, because the game is played on the field and not in some spreadsheet, or so I’ve been repeatedly told. While it is certainly true that the game is not played on a spreadsheet, the fact is that models built on Linear Weights have proven to be very accurate estimators of run scoring. If these models built on Linear Weights were undervaluing the effects of home runs, we’d expect teams that hit a lot of home runs to outperform the models expectations.

That is not what we actually find. In 2013, the top 10 teams in home runs combined to underperform their expected runs total by an average of 3.7 runs per team, while the bottom 10 teams in home runs combined to outperform their expected runs total by 9.2 runs per team.

The team with the largest difference between actual runs scored and expected runs scored was the Cardinals, who scored 61 runs more than their linear weights would suggest; the Cardinals finished 27th in the Majors in home runs, with just 125 long balls on the season. Meanwhile, the biggest underachiever in run production was the Tampa Bay Rays, despite finishing 11th in the majors in home runs.

But perhaps no team in baseball offers a more severe warning sign against overvaluing players like Nelson Cruz than last year’s Seattle Mariners. After struggling to score runs for years, the team loaded up on one dimensional power hitters in an effort to boost their offense. Their major off-season acquisitions included trades for Michael Morse and Kendrys Morales and free agent contracts for Raul Ibanez and Jason Bay. They traded defense for offense, and bet big on the value of the home run. It sort of worked, as they hit 188 long balls, more than any other team in baseball besides the Baltimore Orioles.

However, they only scored 624 runs, 22nd most in baseball. They too underperformed their expected runs total based on Linear Weights, even though their offense was relatively prolific at hitting the ball over the fence, as their lack of ability to get on base meant that 63% of their home runs only resulted in a single run, and it takes more than a bunch of solo home runs to win baseball games.

Nelson Cruz will hit home runs for whoever signs him to a big contract this winter, but he won’t do much else, and the reality is that players who hit home runs and do little else to help a team win just aren’t particularly valuable players overall. Rather than focusing on labels like “power hitter”, teams should simply seek to maximize their run differential. Nelson Cruz might do a thing that not many can do any more, but the things he can’t do make him a mediocre player, and unlikely to be worth the contract he’s going to get this winter.

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Dave is a co-founder of and contributes to the Wall Street Journal.

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