Missed Connections: How Much Value Could Tulowitzki Have Provided in Pittsburgh?

Tuesday night, just as I was putting the finishing touches on an estimate of Troy Tulowitzki’s potential value to the Pirates, news broke that Tulowitzki would not, in fact, be playing home games in PNC Park in 2019. In spite of being linked to Pittsburgh and San Francisco, Tulowitzki instead opted to stay in the AL East. He signed a one-year deal with the Yankees for the league minimum, per ESPN’s Jeff Passan.

The Pirates were one of several teams rumored to have had considerable interest in the former All-Star after his release from Toronto, and not without reason. Tulowitzki came cheap, he’s a veteran presence in the locker room, and he previously played under Pirates manager Clint Hurdle, who managed the Rockies from 2002-09. Every narrative piece of the puzzle fit perfectly, and with the Pirates looking to bridge the gap between Mercer and a long-term solution at shortstop, be it Kevin Newman, Cole Tucker, or Door #3, Tulowitzki and the Pirates seemed a match made in baseball heaven.

Unfortunately, it wasn’t meant to be. The Pirates still need an upgrade at shortstop and I only narrowly avoided throwing my computer out the window. 2019 has not gotten off to a particularly productive start for either party.

But I like to think value still exists in the exercise. Even if he won’t put on a Pirates uniform this season, it’s worth looking at what might have been, and the risks and rewards the Pirates missed out on.

Offense

Little needs to be said about Tulowitzki’s offensive firepower. At his peak, Tulowitzki was one of the most dangerous hitters in baseball. From 2009 to 2014, his last full season with the Rockies, Tulowitzki posted wRC+ numbers of 132, 140 133, 113, 141, and 170. He was crushing the ball, even when normalizing for the fact that he played in Colorado.

But those numbers mean little to teams today. They’re paying for the current iteration of Tulo: a player who hasn’t played in over a year, and whose production has dipped steeply from his peak seasons. Tulowitzki turned 34 in October; he’s no longer a spring chicken. The question is just how much his age will affect his production at the plate.

Since offensive WAR is built on wRAA, which is, itself, built on wOBA, I took Tulowitzki’s wOBA by season and used Excel to calculate a simple aging curve.

Tulowitzki wOBA Curve

That’s a pretty steep drop-off on the back end. It’s worth noting, though, that Tulowitzki played only 66 games during his last full season, and injuries derailed even those. For optimism’s sake, let’s say that those injuries derailed what would’ve been an otherwise productive season, and that Tulo’s wOBA would’ve been closer to average (.315) rather than the actual .299. Taking those injuries into account, the aging curve looks marginally better, as shown below.

Adjusted wOBA Curve

That’s still a significant drop-off. Per the aging curve, Tulo peaked around age 27 (note: During his outlier age 29 season, Tulo enjoyed a BABIP of .355), and has been on the decline since. Using this curve, based on an age of 34, Tulowitzki would be projected for a wOBA of .239, which is what they call, in scientific terms, “Not Great, Bob.”

Some research suggests, however, that players’ aging curves are slightly flatter. That’s good news for Tulowitzki, whose current segment looks like my stock portfolio over the past two months. The referenced article, which attempts to remove survivorship bias in wOBA aging curves, estimates that players tend to lose about 3 points per season of wOBA after reaching their peak season. A quick look at the wOBA of Ben Zobrist and Derek Jeter, a pair of shortstops who played well into their thirties, supports those numbers.

Derek Jeter and Ben Zobrist wOBA Curves

If you apply that calculation to Tulowitzki, ignoring his injury-shortened 2017 season, you’re looking at a wOBA of around .327 for his age 34 season. Over the last five seasons, the league average wOBA was .315, per FanGraphs, meaning there’s still hope that Tulowitzki could be a plus bat. For reference, Steamer currently projects Tulowitzki to produce a wOBA of .317 in 330 plate appearances in 2019.

Of course, that’s probably the best case scenario. The reality is that Tulo missed the better part of the last two seasons with injuries and just turned 34. It’s possible he hits his ceiling, but it’s also valid to worry about his ability to be productive over a full MLB season.

A more realistic (read: pessimistic) estimate of Tulo’s offense probably lies somewhere in the middle. To estimate that, I took the percentage decrease from peak value per year for Tulowitzki and Jeter and averaged them, then used those numbers to project Tulo’s wOBA for his age 34 season (i.e. seven years from his peak). This returns an estimated wOBA of .288.

Estimating Offensive Runs

Using FanGraphs formula for WAR, which you can find here, we can now use our estimated wOBA of .288 to calculate wRAA and total batting runs. As mentioned above, league average wOBA over the last five years is .315, and the league average wOBA scale was 1.2356.

We also need to estimate plate appearances. Over his last four “healthy” seasons (2013-16), Tulowitzki has averaged 119 games. Let’s assume that Tulo is reasonably healthy, that the time off and surgeries have allowed his body to heal. We’ll estimate he plays 120 games. For his career, Tulo averages 4.2 plate appearances per game, putting him at 504 estimated PA for 2019. Based on a .288 wOBA at 504 PA with an average wOBA and wOBA scale, Tulo would project for a wRAA of -11.19 runs. For reference, that’s slightly worse than Kevin Newman’s Steamer projection of -9.3.

We also need to adjust for park factors and non-pitcher wRC. I won’t bore you with the calculations, save to say that I calculated this based on Pittsburgh’s park factor for obvious reasons. Based on historical averages from FanGraphs, Tulo projects for 1.46 runs for the park adjustment and -2.52 runs for a league adjustment. This brings his total estimated batting runs for WAR to -12.25 runs.

Offensive runs also includes base running runs. Tulowitzki has never been particularly skilled at base running. He’s been a negative on the bases most of his career, sometimes to the tune of -4 runs. There’s no Steamer projection for base running, so I simply estimated -3 runs, bringing Tulo’s total offensive runs to -15.25.

Defensive Runs

One of the biggest arguments for Pittsburgh adding Tulowitzki was his skill with the glove. Outside of his rookie season, Tulo has been a positive in the field, accumulating 97.4 runs over replacement during the course of his career. In seasons where he’s played over 1,000 defensive innings, he’s averaged over six defensive runs. Jordy Mercer, in contrast, never posted a defensive runs over replacement of higher than 2. That’s an enormous difference that Tulo could’ve made in the field, especially if Newman isn’t ready to take over the position full time.

Unsurprisingly, defensive runs are highly correlated with defensive innings played. Using Excel, you can graph his historical defensive runs against defensive innings and fit it to a quadratic formula. This yields an r-squared value of .6876.

But what if you wanted to factor age into the equation? It turns out, if you use Tulo’s defensive innings divided by age as your variable, then fit the defensive runs using a cubic function, the r-squared increases to .7136. Below is the chart, with the trendline included.

Fielding Runs by Defensive Innings/Age

Tulowitzki has averaged 8.5 defensive innings per game. With our estimate of 120 games, that puts him at 1,020 defensive innings, or 30 dINN/Age.

(Note: I plan on testing this on multiple players in the near future to see how well this formula holds. For now, I’m assuming the assumption is a safe one since the cubic function actually provides a more conservative estimate–2.88 to 3.31.)

Since Tulo only plays shortstop, the positional adjustment calculation is simple. Simply multiply the shortstop positional value of 7.5 by estimated innings (1,020) over 1,458 (the total defensive innings in a 162-game season). Tulo receives 5.25 runs, for a total defensive runs above replacement of 8.13.

League Adjustment and Replacement Runs

The last two pieces of the WAR estimate are fairly simple. Both league adjustment and replacement runs are highly correlated to plate appearances, as you can clearly see in Tulo’s historical graphs.

League Adjustment (NL only)

Replacement Runs

Replacement runs has an r-squared of nearly one, meaning they’re very nearly perfectly correlated with plate appearances. If you know the plate appearances, you can guess the replacement runs pretty easily. League adjustment (which excludes Tulowitzki’s years with the Blue Jays in the AL) still highly correlates to plate appearances, but not quite so closely.

Based on our estimated plate appearances of 504, Tulowitzki projects for a league adjustment of .937 runs and 15.02 replacement runs.

Estimated WAR and Player Value

Here’s a summary of my projected WAR for Tulowitzki as a Pirate, broken down by component:

• Batting Runs: -12.25
• Base Running Runs: -3.0
• Fielding Runs: 2.88
• Positional Adjustment: 5.25
• League Adjustment: .937
• Replacement Runs: 15.02

That’s a total of 8.84 runs. At a rate of 9.73 runs per win (what I used for calculating surplus value), Tulo would’ve been worth 0.91 wins above replacement in Pittsburgh. Assuming $8.5 million per win, Tulowitzki would’ve provided a value of $7.72 million to the Pirates.

Of course, Tulo signed for the veteran minimum of $555,000. That means based on 120 games, 504 plate appearances, and 1,020 defensive innings, I would’ve expected Tulowitzki to provide $7.17 million of surplus value. For a team looking to find bang for their buck, that’s an excellent value. Unfortunately, that option is no longer available.

Downside Risk

Obviously, the biggest question surrounding Tulo was risk. He’s missed the better part of the last two seasons with injuries. What if injuries continued to rob him of playing time? What if his aging curve wasn’t as flat as hoped and his offensive prowess vanished into the ether?

Let’s answer the second question first. Outside of a major injury, Tulowitzki’s bat will be the biggest factor in determining his value. Holding all other factors constant, I charted Tulo’s estimated WAR based on different wOBA levels.

If everything else is constant (games played, defensive innings, etc.), Tulowitzki would’ve needed to hit for a wOBA of over .266 to reach replacement level in Pittsburgh. That’s not out of the question based on his age curve, but given his wOBA even during his injury-shortened 2017, I’d feel decent about him hitting those marks.

As for health, here’s Tulo’s projected WAR based on number of games played, holding wOBA constant at .288.

As you can see, the defensive runs simply don’t produce the same effect as a similar change in wOBA. In other words, as long as Tulowitzki’s offense doesn’t fall off a cliff, there’s a good chance he’s a plus player.

Sadly, that plus player will not be in Pittsburgh this year. Instead, the Pirates will be counting on a breakout season from Newman, or they’ll have to look elsewhere for safer, albeit more expensive, options.