Mathematically speaking, the 9 doesn't contribute any meaningful information. The same information would be encoded in the ERA using Earned Runs/Innings Pitched
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1ER/IP gives a scoring rate per actual innings. ER/IP × 9 gives a scoring rate per theoretical game. They do not give the same information.– Nij ♦Commented Aug 27, 2019 at 5:28
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They do give the same information. 1 inch is the same as 2.54 cm. The use of a conversion factor doesn't change what information is encoded.– kadCommented Aug 31, 2019 at 15:33
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If a conversion factor is needed, that is a separate piece of information, therefore the original number cannot convey all the information of both.– Nij ♦Commented Aug 31, 2019 at 21:52
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1 Answer
ERA stands for Earned Run Average and to put it in other words, the average number of runs given up per game. Earned runs divided by innings pitched gives you the average number of runs per inning, which isn't particularly meaningful or easily understood. Multiple by 9, though, and now it becomes easy to grasp.
For example, at the start of the season Pitcher A pitches a complete 9 inning game win and gives up 2 runs in the game. ERA is (2/9)x9 which gives you 2. One complete game, two runs, and the ERA makes sense and is easy to understand. If you report ERA as .222 (or 22.2) that doesn't make any sense to how that works out in terms of evaluating pitcher effectiveness overall.
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Reporting the ERA as .222 means they gave up .222 runs per inning. Any ratio quantity has a physical meaning. Just like you can multiple by 162 * 9 and get a season ERA. The fact of the matter is, whether you multiple by 9, 1458, or any constant quantity, you're just scaling the value.– kadCommented Aug 31, 2019 at 15:32
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Like I said, 2.00 is much easier to understand. An ERA of two means you give up an average of 2 runs a game (for a starter who goes deep). An ERA of .222, you give up a fifth of a run an inning? That's not nearly as easy. Commented Sep 3, 2019 at 11:04
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It would make just as much sense as a batting average of .333 says you get 1/3 of a hit per at-bat. It's an arbitrary scaling factor, though a defensible one. Once upon a time, at least, it was common for a pitcher to throw 9 innings in a game (far more common than being lifted early for a reliever or pitching into extra innings), where there was no equivalent "expected" number of at bats in a game.– chepnerCommented Sep 27, 2019 at 18:52