As the Rangers and Angels play their multi-million dollar game of chicken with Adrian Beltre, I wanted to take a quick minute to address an important issue regarding signing him long-term. Many people have stated that the problem with Beltre is that he is an inconsistent (offensive) player, making it hard to feel confident in a projected performance level for him or giving him a multi-year contract. Variance is an important subject and a point of criticism for many of the projection systems that come out each spring; two players with the same projection can have different value if one has a small projected variance and the other has a much wider range to their projection. In statistical terms, we’re talking about the variance (σ2) and standard deviation (σ) about each mean projection. In general, smaller variance is desired.
I’ve charted Beltre’s wRC+ by year and added Michael Young’s as a comparison. wRC+ is a stat based on wOBA, but is park- and league-adjusted. Similar to OPS+ or ERA+, it is set up so that average is 100 (denoted by the solid line on the chart):
At first glance, it seems that Michael Young’s career wRC+ follows a career arc similar to what we expect for a player, and that Adrian Beltre’s career wRC+ is subject to more variance. The means for Beltre and Young are 110.5 wRC+ and 106.6 wRC+, respectively. Interestingly, the standard deviation (σ) from these means is 22.1 for Beltre and 19.0 for Young.
Furthermore, there is a very important point that becomes clear once you examine Beltre’s seasons in comparison to average (black line): Though Beltre does have significant variance, that variance has not resulted in many bad seasons. In 12 years, he has had five years under 105 wRC+ and just three years under 97 wRC+. The variance in Beltre’s yearly average generally results in a range from average to elite. While not as valuable as a player who is consistently elite every year, that is still more valuable that a player who is consistently average each year.
In my previous article on Beltre, I had projected him to be around 3.5-4.0 WAR player next year and 3.0-3.5 WAR player in 2012, which means he would be providing excess value over his likely $15 million per year contract initially (assuming $5 million per win above replacement) That projection broke down into roughly 10 runs (or 1 WAR) from defense and 20-30 runs (or 2-3 WAR) from offense (average to above-average production for a full season). This projection accounts for the odds that he has one of his below-average seasons by balancing it with the odds that he has an elite season.
Lastly, take a look at how Beltre’s elite glove has helped make him an above-average player for every year of his career except one (solid black line = 2 WAR, or roughly average). Furthermore, the dashed line represents 3 WAR, or the level of production needed to justify a $15 million per year contract. Notice that he has met this standard all but three times in his career: