I've calculated the exact number of games per season that a player will miss, depending on whether his injury rating is 1, 2, 3, 4, 5, or 6 (for less than 600 AB+W) or 1 or 2 (for 600 or more AB+W).

By "exact number," I mean the average over an infinite number of 162 game seasons (no post-season games), where a player would have 700 PAs if played in every inning of all 162 games.

Of course, that 700 PAs number is an estimate, so the "exact" figures would have to be adjusted slightly up or down if someone knew the actual average of full-season PAs (ignoring bunts, H&Rs, and other SOM exceptions); until someone figures out that actual average over a big sample of every-inning-every-game players, 700 will have to do. With a slight error (because the formula doesn't allow a simple pro-rated substitution for 700), a different number can be pro-rated to 700.

The "exact" number reflects the fact that a player who gets injured will have fewer PAs than the 700 figure. In other words, if it were calculated as just "per 700 PAs," it would show the number of missed games over MORE than one season, because it would take more than one season for a player who ever got injured to have that many PAs. This problem was fixed by "solving for x", where x is the number of missed games and is also the number of games subtracted from 162 to adjust the 700 PA number downwards.

One problem: the table below does not account for injuries that are shortened because the season ends. For example, a 6-game injury in game 158 ends up being a 4-game injury. Therefore, the average numbers have to be slightly lowered. I'll try to fix this eventually. (The problem is minor for 600+ PA guys, small for injury-1 ratings, and increases in importance up to injury-6 ratings.)

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INJURY TABLE (ASSUMING 700 PAs = 162 FULL GAMES)

inj rating = average number of missed starts AND missed games (respectively) per season

(As explained below, "remainder of game" is counted as "one-half missed game," so e.g. a 3-game injury is 3.5 missed games but only 3 missed starts.)

The result for "less than 600 AB+W" players:

inj 1 = 10.883 missed starts and 12.003 missed games

inj 2 = 20.396 and 22.349

inj 3 = 28.782 and 31.361

inj 4 = 36.230 and 39.280

inj 5 = 42.890 and 46.293

inj 6 = 48.879 and 52.549

The result for "600 or more AB+W" players:

inj 1 = 5.932 and 7.126

inj 2 = 11.445 and 13.651

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EXPLANATION:

The 20-side roll for "number of games missed" works out to an average of 3.6 starts missed and 4 games missed per injury (for "less than 600 AB+W" players) or 1.9 starts missed and 2.3 games missed per injury (for "600 or more AB+W" players).

This is a simple thing to figure: you just add up the number of games or starts missed for each 20-side roll (anywhere from zero to 15.5), and divide by 20. The result is the average number of games missed per injury. NOTE: I counted "remainder of game" as equaling one-half of one game, which in fact in the long run is the correct average for non-platoon starters. For example, a 15-game injury is counted as 15.5 missed games (but only 15 missed starts) because it's "remainder of game plus 15." However, this means that "missed games" is slightly exaggerated for bench players and platoon players, because they'll get injured in pinch-hits and late-game substitutions where they miss only an inning or two in the "remainder of game," rather than an average of half a game (but, again, "half a game" is accurate in the long run for non-platoon starters, slightly excepting guys who get pulled for defensive subs). Note that the "bench and platoon" difference is really negligible for longer injuries, because the "remainder of game" part is such a small proportion.

This is how I got the results:

Since injury ratings are per 216 PAs, the relevant numbers are 216; 700 (estimated average full-year PAs for an every-inning 162-game player); 700/162 (average PAs per game); the injury rating (1 through 6); and 4 (average number of games missed per injury). The last number is changed to 3.6 for missed starts; for 600+ guys, the number is 2.3 games or 1.9 starts.

700 minus (x times (700/162)) = number of PAs per season, where "x" is the number of missed games.

Divide this number by 216 to get the number of times a "one" chance will occur (i.e., a roll that occurs 1/216 times).

Multiply the result by the injury rating (to change 1/216 to 2/216 or 3/216 or etc.).

Multiply the result by 4 (games per injury), or one of the other options.

The result is "x" (number of games missed per season). But because "x" is already part of the formula (see the beginning, above), it has to be moved out of one side of the equation to the other.

I may have done something wrong, but I think it ends up being this:

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x equals

4 times the injury rating times 700/216

divided by

1 plus (700/(216 times 162) times 4 times the injury rating)

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That last part involves the number 700/(216 times 162), which is .020004572, so the formula is easier to read as

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x equals

4 times the injury rating times 700/216

divided by

1 plus (.020004572 times 4 times the injury rating)

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[Again, "4" is changed to 3.6, 1.9, or 2.3, depending on which part of the above table is being solved.]