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i noticed that if a batter reaches on error it is counted as an at bat but he does not get a hit so that has an effect of lowering his batting avg. why is this so?

Short answer. Because that is the rule and how it is done.

Longer answer
1. That is the rule.
By definition reach on error is an "official at bat".
By definition average = total hits/ official at bats.
Only a very few specific situations for when an at bat is not an official at bat. (Eg walk and sac bunt).
See mlb rule citations below.


2. Why this makes sense?
B/c, the batter should have been out. He failed to hit safely. As such He does not get credit for a hit. The official scorer by giving the error has determined batter should have been out had fielder made a routine play.

Side note.
The assignment of hit/error can have a very significant impact on pitcher era and fielder stats too, and as such assignment of errors should not be taken lightly and done appropriately... There are extensive guidelines and rules around errors that an official scorer shpuld be up to speed on and apply consistently.....

Also
Note. batter stats gets same treatment if batter reaches on a fielders choice, ie an official at bat but not a hit and lowers his batting average .


Hope this helps...


Relevant MLB rule citations below...
(all other official leqgues i have seen follow this too)

10.02 Official Score Report
The official score report prepared by the official scorer shall be in a form prescribed by the league and shall include:
(a) The following records for each batter and runner:
(1) Number of times batted, except that no time at bat shall be charged when a player
(i) hits a sacrifice bunt or sacrifice fly;
(ii) is awarded first base on four called balls;
(iii) is hit by a pitched ball; or
(iv) is awarded first base because of interference or obstruction;

And
10.21 Determining Percentage Records
To compute
.....
(b) Batting average, divide the total number of safe hits (not the total bases on hits) by the total times at bat, as defined in Rule 10.02(a);
(c) Slugging percentage, divide the total bases of all safe hits by the total times at bat, as defined in Rule 10.02(a);
(f) On-base percentage, divide the sum of hits, bases on balls and times hit by pitch by the sum of at-bats, bases on balls, times hit by pitch and sacrifice flies.

extremely helpful... thanks!

That's also why the pitcher is not penalized in his ERA because if the runner scored, it's unearned. It's not the pitcher's fault, he didn't do anything wrong to let them score.