Intro to BP Stats Using Blue Jays Players: True Average (TAv)

This Toronto Blue Jays based site for Baseball Propsectus is still in its infancy. While the articles here have shown a distinct professionalism and belonging, we’re still a rookie in the BP Family. We’re a bit like Trevor Story; showing that we belong here in a small sample, but really striving for sustained excellence and respect.

As readers, you may have noticed some new statistics and acronyms that you don’t always see on other Blue Jays blogs. A few examples include WARP, Tav, and DRA. Explanations of those stats can sometimes be long, difficult to find, and even harder to parse. That’s why this series will undertake explaining the (possibly) new-to-you stats you’ll see regularly on the site. However, it won’t just explain the math; you can find that elsewhere and that’s no fun. Instead, I’ll put it into context using Blue Jays players.

Today’s undertaking will be True Average or TAv for short, which is arguably the most important statistic on Baseball Prospectus, it is certainly the most important stat for evaluating a hitter. It’s goal is to consolidate all of a player’s batting value into one number, scaled to look like batting average. Straight from the BP glossary, True Average is adjusted, “for park and league quality.” Therefore, every player’s bench mark is the same. In short, there’s no need to be weary of numbers at Coors Field, or inflate numbers at Petco Park; that work is done for you. The league average mark is set at .260. It’s worth noting though, that True Average doesn’t incorporate a player’s contributions on the basepaths.

For the math-inclined folk, it’s a pretty simple premise. You take a player’s runs above average (RAA) — which is dependent on the situation of each plate appearance. Then, make it a rate stat by dividing by the player’s plate appearances and multiply by a constant to adjust to the league average. Then, just add your baseline to make it look like batting average. The formula, then, looks a bit like this: 0.260 + (RAA/PA) x 0.9.

To better understand how RAA works, think of it like this: with a home run in one plate appearance, a player can produce anywhere between one (a solo shot) and four (a grand slam) runs. By R/PA, a grand slam is worth four, no matter how many outs there already are. However, depending on the situation of the game (the base-out state to be more precise), the run expectancy changes. So, by RAA/PA, a home run with nobody out and the bases loaded is worth 1.718 runs as your team was technically ‘expected’ to score 2.282 runs in that situation anyways (4 – 2.282 = 1.718). It’s a bit more complicated than that though, as the base-out state immediately returns to nobody on-base, nobody out. In that situation, the team is expected to score 0.461 runs. So, the player contributed four actual runs, the chance to add 0.461 more runs, all in a situation that was supposed to garner 2.282 runs. Therefore, the player who hit the grand slam actually contributed 2.179 runs (4 + 0.461 – 2.282 = 2.179).

Now that you are well-equipped to start calculating your own TAv while sitting right at the bar, lets use some Blue Jays examples for some context.

The Above Average

For sample size purposes, we’re going to stick with the 2015 stats for now.

There was a dead-heat for the best hitter of the Blue Jays 2015 season, and it actually ended up a tie. Both Edwin Encarnacion AND Josh Donaldson had a .324 TAv, and placed ninth among all hitters in baseball with at least 400 plate appearances. That’s .064 higher than league average.

Here’s where TAv gets most useful: Encarnacion and Donaldson line up comparably despite getting there by slightly different means. While the home run tallies were nearly identical (39 and 41 respectively), Donaldson had 58 more total bases than Encarnacion. That could, however, be attributable to the 87 fewer plate appearances that Encarnacion had. Despite fewer plate appearances, Encarnacion took slightly more walks and struck out 35 fewer times.

Despite lining up nearly identically in TAv, the routes taken there are independent. We can look at this two ways. First, TAv gives us a means to equate player value across multiple avenues; not just simple counting stats that don’t line up. Second, TAv fails to tell the entire story. I would caution against the second opinion, since no statistic tells the full story anyways, but we’ll revisit that on the WARP explainer at another time.

The Average

The Blue Jays didn’t actually have a player who was perfectly average last season. However, the closest — believe it or not — was Kevin Pillar at .257. That being said, that is well within one standard deviation of the average .260 mark.

Pillar isn’t considered by many to be a league average hitter. However, in 2015 he was. And you can say so with confidence as long as you have TAv on your side. For posterity, Pillar is sandwiched between Johnny Giavotella and Brock ‘All-Star’ Holt on the TAv leaderboard.

It is worth noting at this time that league average does not denote ‘replacement level.’ Replacement level is another set-point, quite a bit lower than league average. For instance, if you could ‘replace’ all your bad players with league average players, your team would be excellent. Instead, ‘replacement level’ is a player that could be picked up on waivers, promoted from Triple-A, or signed as a free agent. From his TAv and base-running, Pillar contributed 22.3 VORP to the Blue Jays in 2015. If held by itself (without his defense), that would contribute roughly 2.2 WARP.

The Below Average

Poor Ryan Goins. At .238 TAv last year, he was the worst Blue Jays hitter with at least 400 plate appearances.

Sure, Goins is a below average hitter, but he still contributed half a win by WARP last year. It’s important to keep in mind then that when TAv is being used, the author is only evaluating hitting value. While some authors value offense more greatly, it is fallacious to pass TAv off as a player’s one contribution to the game. Therefore, TAv is extremely useful in assembling a batting order, but useless at figuring out where to place your fielders.

If you’re curious, Jose Reyes was barely better at .241 TAv.

There you have it. Not only can you scribble your calculations on the napkins and coasters of the Loose Moose, but you know what TAv actually looks like now — it’s personified.

Lead Photo: Kim Klement-USA TODAY Sports

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