Quote:
...it's not the lower of the new score vs. the old score because the old score is based on the 10 lowest hits.
...you have to take the lower of ... the refired target or the old target, but scored using the 10 highest hits.

Right, it's not exactly the lower of the two scores.
At the bottom of the post, I've quoted the entire section on dealing with more bullet holes than should be present.
Here's how it shakes out. I did this mostly to work it all out for myself and figured others might get something out of how I laid it out so I could see things clearly.
1. You can take the target as scored according to section (b). That means that holes are eliminated, starting with the highest scored hits until you're down to the proper number and then the remaining hits are scored and summed for your total score.
2. You can refire as long as:
A. ...all the shots on the original target don't score exactly the same. That's according to section (a). In other words, if you shoot 10 shots and have 11 hits on target, but all 11 of them score the same, you can't ask for a refire. That's because whether they delete the highest or the lowest scoring hits, it will result in the same final score.
B. ...you didn't fire too few shots on target. According to section (c), if you fired too few shots on target and ended up with more hits than than you fired, the target is scored using the highest scoring hits for as many shots as are fired. The rest of the hits are disregarded and you will be scored misses for them. In other words, if you were supposed to fire 10 and only fired 6, but there were more than 6 holes in the target, then you would get credit for the 6 highest scoring hits on the target and you would be scored with 4 misses.
C. ...you didn't fire more shots than you should have. According to section (d), if that happens then you get the target scored with the lowest scoring hits. So if you fire 11 shots when you should have fired 10, they eliminate the highest scoring hit and sum the scores for the remaining 10 hits and that's your score. You don't get a refire because the extra holes are your own fault.
IF you choose to refire, and your refire score is HIGHER than the score on the original target
when the original target is scored using the HIGHEST scoring hits (instead of the lowest hits) then you will get the score of your
original target scored using the highest scoring hits by eliminating the lowest scoring hits. That's section (e).
Example 1:
So let's say you fire the requisite number of shots and your original target has 11 hits but should have 10. Nine of them are 9s, one is an 8 and one is a 10. If you choose not to refire, your score is a 89 (9x9 + 8)they would drop the 10.
Now you refire and end up with all 10s, for a refire score of 100. They would now look back at your original target but this time they would score it by eliminating the lowest hitthe 8. That would give you a reference score of 91 (9x9 + 10). Since your refire score is higher than 91, you would get the score of 91 and wouldn't get the refire score.
If you refired and ended up with a refire score of 91 or less then you would get your refire score.
So, for this particular example, it probably wouldn't make a lot of sense to refire because you can only improve your score by 2 points (from 89 to 91) since 91 is the maximum score you would be allowed on your refire. And, of course, you could end up with a much lower score if you botch the refire.
Example 2:
Let's run through it again with different numbers. You fire the requisite number of shots and your original target has 13 hits instead of 10. Nine of them are 9s, one is a 10, and the remaining three hits are 5s. Now your original target would be scored as (3x5 + 7x9) = 78.
You choose to refire and get all 10s for a score of 100. They score your original target by dropping the lowest hits and get 91 (9x9 + 10). So you can't get higher than 91 and that's what you get.
But in this case, refiring makes more sense (assuming you are pretty sure the 5s aren't your hits) because you can potentially improve your score from 78 to 91.
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http://www.nrahq.org/compete/RuleBoo...ol/pstw14.pdf
14.10 Excessive Hits  If more than the required number of hits appear on the target, any shot which can be identified by the appearance of the bullet hole as having been fired by some competitor, other than the competitor assigned to that target, or as having been fired in a previous string, will be pasted and will not be scored. If more than the required number of hits then remain on the target a complete new score will be fired and the original score will be disregarded, except:
(a) If all hits are of equal value, the score will be recorded as the required number of hits of that value.
(b) The competitor shall be allowed to accept a score equal to the required number of hits of lowest value.
(c) If a competitor fires fewer than the prescribed number of shots through the competitors own fault, and there should be more hits on the target than the shots fired, the competitor will be scored the number of shots of highest value equal to the number fired, and will be given a miss for each unfired cartridge.
(d) If a competitor, by mistake, fires more than the required number of shots, the required number of hits of lowest value will be scored. This shall not be considered a refire as outlined in Rule 9.14.
(e) If the competitor refires, the original target with excessive hits shall be retained by the designated range official and on refiring, the competitor may not receive a score higher than the required number of hits of highest value on the original target. If the score on the refired target is higher than the required number of hits of highest value on the original target, then the original target shall be scored using the appropriate hits of highest value; but if the score on the refired target is not higher, then such refired score will be
recorded.