A batter can be dismissed in ways that give a bowler full credit, partial credit, or none. The allocation is governed by rules that predate any interest in bowling averages.
The modes that credit a bowler
Bowled, caught, leg before wicket, stumped and hit wicket are all charged to the bowler of the delivery. In each, the dismissal is a direct consequence of the ball that was bowled.
The logic is causal rather than proportional. A catch taken at long-on off a full toss counts identically to a batter's off stump being knocked back, because the delivery produced the dismissal either way.
This makes the bowling average a measure of dismissals produced, not of deliveries deserved. A bowler who beats the bat repeatedly without a wicket has nothing to show in the column.
The modes that credit nobody
Run outs are not credited to any bowler. The dismissal arises from a decision made by the batters after the ball has been played, and the bowler's role has ended.
Obstruction, handling the ball, and timed out are treated the same way. They are batter conduct rather than bowling outcomes, so they appear in the team's wicket column with no individual credit.
This creates a permanent asymmetry between team wickets and the sum of bowlers' wickets. A team can lose ten and the bowling analysis can account for seven of them.
What this does to fielding-side statistics
Fielders receive credit for catches and for run out involvements, but the accounting is much looser. A run out effected by a direct hit and one completed after a relay may be recorded identically.
Some scoring systems record the thrower and the receiver separately, and some record only the player who broke the stumps. There is no universal convention, which makes fielding data hard to compare.
Baseball's error and assist conventions offer an instructive contrast. Those categories were standardized early, and cricket never developed an equivalent for the field.
Why caught behind and stumped separate
Both dismissals involve a wicketkeeper and a batter beaten by the delivery, but only one requires the batter to have left the crease. The distinction determines which is recorded.
It matters statistically because stumpings cluster against spin and catches behind against pace. Reading a keeper's dismissal split tells you about the attack he kept to, not only about his hands.
The bowler receives full credit in both cases. The difference lives entirely in the fielding record, which is another reason those two columns are read separately.
Where the rules distort the picture
A bowler's average is sensitive to catching. A spell that produces five chances and two catches records two wickets, and the record never mentions the other three.
Attempts to correct this with expected-dismissal models exist, but they are analytical constructions rather than official record. The scorecard remains a count of outcomes and says nothing about deserving.
That is a reasonable design for a legal document. It becomes a problem only when a count of outcomes is read as a ranking of ability.

