Batting Average Variation & the Waiver Wire by Jeff Zimmerman September 29, 2021 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 Brad Miller .225 .227 .002 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 Harrison Bader .228 .270 .042 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.