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I am calculating penalty success rates of soccer players. For example, let's say we have 3 players.

Player 1: Success - 20 out of 100 tries

Player 2: Success - 2 out of 100 tries

Player 3: Success - 1 out of 1 try

Success rates for above players are 0.2, 0.02 and 1. Just looking at the success rates, player 3 seems like the best performer. But looking at the absolute scores, player 1 seems like the winner as player 3 only tried once.

I need to create a metric which captures the success of each player and also the number of tries. So for a player like player 3, the score should be lower as compared to player 1 since this player hasn't played a lot of penalties.

Anish Gupta
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    I don't think anyone can answer this as it is, because it's a bit subjective, so lots of different functions would fit your bill. You need to give more examples of how you want the end results ordered for close cases to come close to a meaningful function. – Suzu Hirose Jun 09 '22 at 23:52
  • YOU define the metric that is of value to your study. One metric might be "the player who is most likely to score on the next penalty kick." Another metic might be "the player who draws so many fouls that he gets the most points in a season." Another metric might be ... Well, you get the idea. – David G. Stork Jun 09 '22 at 23:59

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The basic answer is, as given a comment, that you are trying to rank players, so you decide the way that makes sense to you. There cannot be one definite answer to this question. However a couple of points may be useful.

First: why are you trying to rank players? Presumably, in order to predict future behaviour. In that case, it makes sense to have a scoring system which works the way you want for present, past and hypothetical behaviour. So you need a large number of examples (real or made up, possibly doesn't matter much), you need to decide how you would rank them intuitively, and you need a scoring system which reflects this reasonably accurately. Don't expect it to work perfectly, a method which reduces various aspects of play to a single number is unlikely to do that.

Second: you need to decide what factors are important to you. From your post it appears that you are interested in two factors: the penalty conversion rate, call it $r$, and the number of penalties attempted, call it $p$. It seems you view both of these as being numbers which should be increased to give a better score. This suggests a scoring $$\hbox{score}=r^ap^b$$ for certain positive numbers $a,b$. If you think about it a little, you can see that if you take any power of this score, then, although the actual scores will change, the relative ranking of players (which is what you are interested in) will remain the same. So, may as well take $a=1$ for simplicity and try $$\hbox{score}=rp^b\ .$$ You will now need to experiment with various values of $b$ and find one which gives you the results you want, as described in my previous paragraph. Note that if $b=1$ you end up with the score being exactly the number of successful penalties, which probably is not what you want. So I would suggest trying values with $0<b<1$.

There are no doubt more sophisticated scoring functions which could be used, but keep it simple for a start.

David
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