Introducing xPA to Project Plate Appearances

I like big rates and I cannot lie. You other readers can't deny. When a rate walks in with an itty PA and an integer in my face, I get sprung...Whoa! Wait just one second, Sir-Mix-A-Nick. Before I go full-Rhymenoceros on everyone, maybe we oughta back the track up a little bit.

What I like are rates according to plate-appearances because they're the simplest way to make adjustments to projections. The final numbers may change from the start of the offseason to the end but it's usually the playing-time components being adjusted, rather than the ones underpinned by assessment of the player's skills.

Imagine that Juan Soto is currently being projected to hit 35 HR at a rate of 0.053 HR/PA but was only projected to hit 32 HR in the previous projections. It's more likely that this is because they now believe Soto will have more opportunities to hit home runs rather than thinking he'll hit them more often. Little in the middle but it's got much back... Let's talk about xPA.

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Basic Methodology

Projecting a player's skill is one thing; figuring out how many times they'll come to the plate is another. Where a player bats is obviously a big driver, on average losing between 0.10 - 0.11 PA/G for every spot dropped in the lineup. That translates to around 16 PA over the course of a 162-game season, or about a 128-PA difference between the leadoff spot and the nine-hole. This is all known. What's not talked about as much is how team runs-scored will affect plate-appearances, in addition to lineup spot. It makes sense to think that the Yankees' leadoff hitter will end with more plate-appearances than his counterpart on the Tigers, no? In order to accurately project plate appearances, both lineup spot and team offense must be considered.

What I've done is use the research previously conducted by Tanner Bell, operator of SmartFantasyBaseball.com and co-author of "The Process", along with the team-offense data from multiple projection systems, to come up with a player's expected plate-appearances, or xPA. This is how many plate-appearances a player will be expected to have, given their expected lineup spot and how many runs their team is projected to score.

Baseball-referance.com has team stats available by lineup spot and what Bell did was take 10 years' worth of data to find the average plate-appearances per lineup spot according to how many runs their team scored. To accomplish this, he grouped the data by team runs scored in 50-run increments, starting with 500-550 runs scored. What he found was that in addition to a player gaining 0.10 PA/G for each spot they move up in the lineup, they also gain around 0.04 PA/G for every additional 50 runs their team scores, or about 5-7 PA over the course of a season.

All in all, Bell ended with a matrix providing average plate-appearances for every lineup spot, according to how many runs a team scored. Batting third on a team that scored 770 runs? It may not always be exact but I'd still bet they averaged around 4.51 PA/G. That comes out to 3.99 PA/G for a player batting seventh on a team that scored 620 runs. And on and on.

With expected PA/G now in hand, we now have one part of the equation but are still lacking the others. To get to xPA, we still need to know where in the lineup the player will bat, how many games he's likely to play, and how many runs his team will score. Let's round them up.

Projected Lineup Spot

Let's start with the most known of the unknowns. In theory, every spot in every lineup of every team can be tenuous. But practically speaking, there are some spots more certain than others and RosterResource on Fangraphs is the go-to source for looking at the current most-likely lineups for each team. As such, their projections will be the ones used in xPA, with adjustments made, as necessary.

This has flaws, as bench players are not given a projected lineup spot and some lineups are more fluid than others. But keep in mind that besides individual player projections, we're also looking to put a proper valuation on each lineup spot, regardless of the person in it.

I copied and sorted this data, making adjustments by hand to players considered fantasy relevant but not currently projected to start. This was as light of touch as I could muster, assigning those bench players a likely primary lineup spot based on known information about how different lineups should look, as well as where players have batted most recently. Imperfect but many of the imperfections will substantially improve in-season as lineup tendencies start sorting themselves out.

Projected Team Runs

I started by looking at six different projections: Steamer, PECOTA, ATC, The BAT, Depth Charts (a combination of Steamer and ZIPs, with playing time adjusted by Fangraphs staff), and Razzball, which is also an adjusted version of Steamer. I then took the average of projected team runs (adjusted to not overweight Steamer-centered systems) and assigned each team a run "bin," with the bins set up in 50-run increments:

Combined with their projected lineup spot, I could now assign every player a code of A2, B1, F5, etc. This tells me where a batter is projected to bat and how many runs their team is projected to score, allowing me to pull their proper average PA/G from Bell's historical matrix.

Projected Games Played

With an expected-PA/G for every player, all I needed was projected games in order to get to xPA. This one was easy, as I just used the average between the same projections systems from above. Take average games played multiplied by xPA/G and you wind up with...

2020 Expected PA

When looking at the overall results, two main trends are clear. In general, xPA projects more plate appearances for top-third batters, particularly on the highest-scoring teams. The projection systems also tend to over-project lower-third batters, especially on lower-scoring teams. Looking at batters with at least a 350 ADP on NFBC, here are the top-15 players that were projected for fewer plate-appearances than what xPA predicts:

Conversely, here are the top-25 players that xPA likes to have more appearances than the average projection system:

Wrapping Up

Using xPA isn't about saying that these are these projections that should be used. While I believe strongly in the historical PA/G averages, xPA is still dependant on projecting the correct amount of team runs and where a batter will spend all of their at-bats. Team projections are often wrong and players don't always bat at the same spot. What xPA is about is giving more context to just how much a lineup spot is worth and what a change can do to a player's value. That added context is helpful for player valuations but is also useful in confronting cognitive biases.

Using myself as an example, I've touted Brandon Nimmo all offseason, believing in the skills but also believing that he'd end up with more plate appearances than what was being projected. My rationale was simple; the Mets announced he'd be their leadoff hitter and I thought he'd be the primary center fielder. Consequentially, I believed he'd be closer to 600 PA, rather than around the 500 PA that other systems called for.

It was nice to see him make the list above but I wasn't happy to see only 552 xPA. He did get a bump for his top-of-the-order slot but xPA gave him far less credit due to the Mets below-average offense. That just goes to show you; never underestimate how much the Mets being the Mets can drag down your projections.

That wraps it up for today, but coming up I'll dive deeper into xPA to root out some more context. Up next, we'll look at players like Victor Robles, Mallex Smith, and others who would benefit from a move up the lineup. Will they improve as much as the fantasy community seems to think? Or will sluggish offenses keep them from earning the high prices they're garnering in drafts?

More 2020 Fantasy Baseball Advice