# Batting Average Variation & the Waiver Wire

Yesterday, I wrote about the replacement level hitters in the NFBC 12-team Online Championship (OC) and the 15-team Main Event (ME). In the comments, Joe Wilkey asked:

There are a couple of good questions here, so it’s time to start working through them. I’ll start with “Is batting average unpredictable?” Yes, with any given player’s actual range being unacceptable for a fantasy manager. Looking back at Steamer Projections (2010 Steamer to 2021), I found the standard deviation for the difference between the projected and actual batting average.

The Standard Deviation in Batting Average at Various Plate Appearances
Proj and Act PA Std Dev
>= 100 0.0308
>= 200 0.0274
>= 300 0.0252
>= 400 0.0240
>= 500 0.0236
>= 600 0.0219

With smaller plate appearance sample sizes, the variation is high. As a hitter gets more and more plate appearances, the variation shrinks. The deal is that assuming a hitter is projected for a .250 AVG and 500 PA and gets 500 PA 68% of the time the hitter’s final AVG will be between .226 and .274 and 90% of the time between .202 and .298. That range is tough to plan a fantasy team around.

The deal is that there isn’t just one hitter contributing to the overall batting average, it is 14 of them. Some final values will be above the projection and others below but with a large enough sample, the actual results will merge with the projections. I found out that Central Limit Theorem defines this overall variation using the following formula:

(Std Dev on Indiv Samples)/(sqrt(# of samples))=Final Value Standard Deviation

In this instance (14 players with a 0.236 standard deviation), the final standard deviation is .0063. For 14 hitters projected for a .250 AVG, the batting average range is .244 to .256 for 68% of the time or .236 to .263 for 90% of the time. The increase in sample size helps to limit the overall variation.

The final step is to look at how the expected range can be predictive in the final outcome. Here are the average finishes from 2019 for the Online Championship and the Main Event.

Average Batting Average Finish in the OC and ME
Rank OC ME
1 .277 .275
2 .273 .271
3 .271 .269
4 .269 .268
5 .268 .266
6 .266 .265
7 .264 .263
8 .263 .262
9 .261 .261
10 .259 .260
11 .257 .259
12 .254 .258
13 .255
14 .253
15 .249

With a range of +/- 6 points, I would aim for a projection of around .265 in the ME and .267 in the OC. The value keeps me off the bottom if everything goes south, but I won’t waste any production pushing for first place if everything clicks. Also knowing the variance, aiming for the middle would be another reasonable option. In the absolute worst-case scenario, I’d like to have a projection over .260. Batting average does have some extreme variation, but since several hitters are involved, the variation gets cut into almost a quarter of a single player.

Onto the next question, “Were these players cut because they were underperforming?” To find out, I compared the hitter’s projection to the results so far this season in both leagues.

Replacement Hitter in the NFBC Main Event
Name Proj AVG Actual AVG Act – Proj
Chas McCormick .240 .255 .015
Edward Olivares .247 .238 -.009
Elvis Andrus .252 .243 -.009
Ji-Man Choi .244 .229 -.015
Jose Iglesias .285 .268 -.017
Kevin Kiermaier .232 .255 .023
Kevin Pillar .247 .226 -.021
Leury Garcia .261 .268 .007
Nick Ahmed .250 .221 -.029
Niko Goodrum .228 .211 -.017
Rowdy Tellez .259 .241 -.018
Wilmer Flores .277 .261 -.016
Yandy Diaz .273 .258 -.015
Yonathan Daza .293 .283 -.010
Average .254 .246 -.009
Median .250 .243 -.015

Replacement Hitter in the NFBC Online Championship
Name Proj AVG Actual AVG Act – Proj
Bobby Dalbec .228 .242 .014
Brandon Belt .248 .274 .026
Colin Moran .260 .267 .007
Enrique Hernandez .246 .251 .005
Evan Longoria .247 .278 .031
Garrett Cooper .261 .284 .023
Gregory Polanco .222 .208 -.014
Jed Lowrie .234 .245 .011
Jon Berti .241 .210 -.031
Josh Harrison .247 .282 .035
Lorenzo Cain .270 .257 -.013
Luis Arraez .312 .282 -.030
Miguel Rojas .270 .265 -.005
Nico Hoerner .269 .302 .033
Average .252 .261 .009
Median .247 .267 .011

For these 15 hitters, their batting average didn’t differ that much from their projections. I expected values closer to the .023 value calculate above. A couple of interesting points stick out. The first is that in the Online Championship, the hitters who are available are outperforming their projections while in the Main Event they are underperforming. This divergence is happening with similar projections.

Also, the combined average ranks differently in the respective leagues. In the Online Championship, the average results come in ninth with the median between fifth and sixth. In the Main Event, the average and median results come in dead last. The replacement level player was likely a batting average sink.

So were the players cut for the low batting average, probably, but the options on the waiver are so slim, other managers felt compelled to add these black holes. These hitters were bouncing on and off the waiver wire. The hitters that stayed on the wire were the ones whose AVG dropped 20, 30, 50 points (e.g. Eugenio Suarez) based on expectations.

The preceding work makes me feel more sure of my original comment about the Main Event.

“Throughout the entire draft, it might be best to focus on batting average knowing it’ll be difficult to find during the season.”

As for the Online Championship, at least some league-average batting average can be found on waivers so some chances can be taken while adding speed and power. In the original article, both leagues provided the same amount of home run contributions. In the Online Championship, it would be wiser to focus a bit more on those home runs during a draft.

Both league types have nearly the same rules, the player pool determines which stats are harder to find on the wire.

Jeff, one of the authors of the fantasy baseball guide,The Process, writes for RotoGraphs, The Hardball Times, Rotowire, Baseball America, and BaseballHQ. He has been nominated for two SABR Analytics Research Award for Contemporary Analysis and won it in 2013 in tandem with Bill Petti. He has won four FSWA Awards including on for his Mining the News series. He's won Tout Wars three times, LABR once, and got his first NFBC Main Event win in 2021. Follow him on Twitter @jeffwzimmerman.