Injury Risk & PAs Lost: Using DDope Actuals

The oldtimers around here will remember fondly the days when the indispensible DiamondDope.com posted the actual performance of all the different ATG players at various salary levels. Adrian ultimately took these "Actuals" down because they were hogging server spaced like mad, but they were great while they lasted. Anyway, some time ago (I didn't keep notes on the exact date) I decided to take a count on how the average Plate Appearances (PAs: AB + BB) per season a achieved by a select group of players with different levels of injury risk. I think this study dates back to about ATG5 or ATG6. Adrian may be able to tell us when he took the Actuals down. I've been meaning to share this study for some time, and am spurred on by rburgh's important recent thread about injuries and lost playing time.

A couple of explanatory notes. I decided to look at elite players. I wanted players who might reasonably be used in various different batting order positions since that significantly affects PAs. And I chose to focus on the 100M salary level. This seemed like a way to find players who a manager would want to have in the game every possible minute--there are generally no wacky platoons at the 100M level, but at 100M elite players are more likely to be used than at 80M. I focused first on bulletproof players (either no injury 0 or 680+ PA 1). I see 0 and 1 as identical because although we're told that 680 PA players can have in-game injuries, I've never seen one happen. Next, I looked at 600 PA players: "1". Finally, I looked at players who had less than 600 PA and with injuries on the 1-count. I didn't look at 2-count injury players because I wasn't that interested in them and its tricky to find equivalent players to the elites in the other categories. I chose 7 players for each category and divided each player's total PA by the number of seasons in which they were used. Here's what I got (the year follows the player's name in parentheses, followed by actual average plate appearances per season):

Bulletproof Players:
Ruth (21) 744
Foxx (32) 724
Mays (62) 726
Hornsby (22) 742
Gehrig (27) 718
Hornsby (29) 741
Musial (48) 731
7 Player Avg 732

600 PA Players: inj rating 1. These guys can be injured for a max of 3 games.
Bonds (01) 691
Mantle (56) 706
Mantle (61) 707
Ruth (27) 707
Bonds (93) 693
Charleston(Nel)693
Kiner (49) 680
7 Player Avg 697

On average, 600 PA+ players lose about 35 plate appearances to Bulletproof players (732-697=35). That's 4.8% of total playing time. Or, to make it easy to remember, let's say 5%.

Plate Appearances for 1 inj, players: that is, 1 inj chance with less than 600 real-life Plate Appearances. These guys have a 15 game injury risk.
Gibson (Nel) 673
Bagwell (94) 658
Brett (80) 676
Beckwith (Nel) 666
Dimaggio (39) 652
Griffey, Jr (94) 633
Mauer (09) 662
7 Player Avg 660

So on average, 1 inj (less than 600 PA) players lose about 37 PA to 600 PA+ players, or 053% (again, pretty close to 5%). And on average, 1 inj (less than 600 PA) players lose 72 PA to Bulletproof players. This is almost exactly 10%.

A few observations: even 1 inj players get a pretty high level of playing time, on average. Their 660 PA exceeds the 600 real life cut-off by 60 PA or more. So one might say that to use a sub-600 PA player is not exactly taking a desperate risk. On the other hand, losing a Bagwell or Brett for an average !0% of the season compared to a Bulletproof such as Hornsby (29) or Musial (48) is indeed a real loss. So a salary adjustment of roughly 5% for each injury level (or maybe a tiny bit less, since the scrubs have at least some value) might be appropriate. My guess is that the adjustments the game makes on salary are probably pretty close to these numbers, but it would be hard to know for sure.

Again, I just wanted to share this data after all these years, since I think it might add to our discussion of real impact of different levels of injury risk. I encourage further discussion.

Excellent stuff, Outta Leftfield. Can you post some data for some stud players with 2 and 3 injury chances?

Excellent stuff, Outta Leftfield. Can you post some data for some stud players with 2 and 3 injury chances?

Unfortunantly, when I did the study four or five years ago, I didn't look at 2 or 3 injury chance players, and now the data is gone, since Diamond Dope doesn't provide Actuals any more.

I didn't look at the higher injury players in part because it would have been hard to find seven equivalent players to the superstars in my other groups. They would mostly be 6M or 7M catchers and such, and that might leave a lot of noise in the data, especially since these players are going to be batting lower in the order, and they might be platooned, etc..
Even so, if I had it to do over again, I'd run at least the 2 injury chance, but the stats I drew from are now gone. Sorry about that.

My educated guess, based on the existing stats, is that a 2 injury chance player might lose an additional 5 to 7% over a 1 injury chance (sub 600 PA) player, because the 2 injury slightly more than doubles the chance of an injury over a 1 injury chance (since we have to considered that the 600+ PA guy also has some injury risk, but we also have to consider that when a player is injured, they can't be injured again). I think 7% is likely about right--it can't be off by more than a point or two either way.

If we take the 7% figure, then a 2 injury chance player might lose about 17% of PA over a bulletproof player. This might work out to about 608 PA (83% of 732 PA), on average. This is assuming a true stud hitter who would be batting somewhere in the 1 to 5 slots, and thus generating an average of 732 PA. My guess is that most 2 inj players are lower batting order guys, however, and would have fewer PA (players lose an average of 15 PA for each slot they drop).

For what is worth, I created formulas for the expected number of missed PAs. The way I did my formulas, I need to insert the expected number of at-bats for a player with no injury, so I'll assume that 732 AB is indeed the correct number for all-stars playing in a 100M league. The formulas then calculate the missed at-bats for all the categories of players.

OuttaLeftfield says that he never saw a player with bold 1 (1+rest of the game only) have an injury. I believe I did see those players having an injury in 20XX leagues, so unless we're told the rules for injuries are different in ATG, I'll assume that it can also happen in ATG.

Players with no injury: 732 PA (assumed)
1+rest of the game : 726 PA; 6 PA missed.
1+max 3 games : 700 PA; 32 PA missed.
1+max 15 games : 677 PA; 55 PA missed.
2+max 15 games : 629 PA; 103 PA missed, 48 more than the preceding level.
3+max 15 games : 588 PA; 144 PA missed, 41 more than the preceding level.
4+max 15 games : 552 PA; 181 PA missed, 37 more than the preceding level.
5+max 15 games : 519 PA; 213 PA missed, 32 more than the preceding level.
6+max 15 games : 491 PA; 241 PA missed, 28 more than the preceding level.

Of course, these formulas work only if we assume that the players hit at the same rank. If some of the players Outtaleftfield put in the "1+injury" have a greater chance to hit lower in the offensive lineup than the players in the "no injury" set, then of course the number of PAs outtaleftfield has for the first group will be artificially lower than the expected number of missed PA. And I think this explains the gap between my numbers and outtaleftfield's numbers. I have 677 PA for regular 1-injury-rated player whereas outtaleftfield has 660 PA. Griffey, for one, has much less PA than the other players, and I think it's precisely because Griffey is more likely to hit lower in the lineup, especially vs lhp. In any case, he's an outlier in the set. If we pull him out, the mean PAs of the other allstars inlcuded by outtaleftfield is 667. But of course, the gap might come from a miscalculation in my formulas.

For the record, 732 AB for players with no injury is quite higher than I got from regular 20XX seasons, which is more around 680 AB-700 AB. But of course, there is much less offense in regular 20XX (and therefore less at-bats per game). In 20XX, for players rated 1 with potential 15 games injury, I have an expected missed PA around 49 instead of 55. So just a reminder that the exact number of PAs is likely to differ for each environment, and the more offense, the more PA you're expected to miss from higher injury rated players.

Marc (a.k.a. "Luckyman"),

I learned this rule of thumb from you or one of the others years ago as expected games missed:

1+max 15 games : 11 games missed
2+max 15 games : 11+10=21 games missed
3+max 15 games : 588 PA; 11+10+9=30 games missed
4+max 15 games : 552 PA; 11+10+9+8=38 games missed
5+max 15 games : 519 PA; 11+10+9+8+7=45 games missed
6+max 15 games : 491 PA; 11+10+9+8+7+6=51 games missed

I think this is pretty similar to your expected PA missed above.

I agree with OuttaLeftfield that I've never seen an instant of a 680+ PA guy ever being in injured. I've never seen an example of such an injury in ATG or 20xx