simple injury formula, and request for data

[ClowntimeIsOver]

Starts missed = 1 / ((62.53/RA) + .0064). R is the injury Rating. A is the number of PAs an ideal player "would" have if he played every inning of every game. (See below.)

A big problem with figuring out each injury rating's "average starts missed per season" is that a full season of PAs varies based on two things: 1) Where the player bats in the line-up; and 2) whether the team is low-scoring or high-scoring. A guy who leads off every game on a very high-scoring team will have a lot more PAs than the #8 or #9 hitter on a low-scoring team. This difference in total full-time potential PAs affects how many starts are missed due to injury (especially for higher injury ratings).

REQUEST FOR DATA: If anybody has had a guy play (almost) every inning of (almost) every game at lead-off on a high-scoring team, I'd be interested in hearing how many PAs he had. Ditto for a guy who batted last in (almost) every game for a low-scoring team.

A while back I posted a complete formula for figuring how many starts would be missed for any injury rating (1 through 6), on average over a full season. The formula allowed for lots of different presumptions to be changed, including the PA question.

Here is a simplified version with some presumptions "built in" (rather than allowing for different presumptions), but still allowing for different PA totals. It's only marginally less accurate.

For a player with fewer than 600 AB+W on his card:

Starts missed = 1 / ((62.53/RA) + .0064). That is, the reciprocal of ((62.53/RA) + .0064). R is the injury Rating. A is the number of PAs an ideal player "would" have if he played every inning of every game.

To account for the "remainder of game" tacked onto each injury (to give the total for "games missed" rather than just "starts missed"), multiply the result by 1.136 (i.e., 13.6% more).

Here's an example of how much difference is made by the range of different "maximum PA" totals:

600: If an ideal every-inning player "would" have 600 PAs in 162 games (e.g., a #9 hitter on a low-scoring team):

injury 1 = 9.00 starts missed
2 = 17.05
3 = 24.29
4 = 30.85
5 = 36.81
6 = 42.25

(multiply all by 1.136 to get total games missed)

800: If an ideal every-inning player "would" have 800 PAs in 162 games (e.g., a lead-off hitter on a high-scoring team):

injury 1 = 11.75 starts missed
2 = 21.91
3 = 30.79
4 = 38.61
5 = 45.54
6 = 51.74

(multiply all by 1.136 to get total games missed)

You can see, it makes a big difference.

I don't have any idea how many PAs would be correct in ANY case, but the above formula allows the number to be adjusted.

(Note: the numbers above are based on a slightly more exact version of the formula. Also, PAs include every plate appearance except sac bunts and hit-and-runs, on which no injury is possible.)

Again:
Starts missed = 1 / ((62.53/RA) + .0064).
Games missed = 13.6% more than starts missed.

[Page2]

Hi,

I know this isn't exactly what you wanted but here are a couple of examples for you:

Bonds on a back to the 90's team. I was second in Runs Bonds hit second.

97 65 .599 7-3 W2 53-28 44-37 37-25 60-40 943 815

http://fantasygames.sportingnews.com/stratomatic/team/team_other.html?user_id=300352

Jeter on a 2009 24 team League hit 1st against LHP and 2nd against RHP I am pretty sure. I was tied for 10th in Runs.

69 93 .426 5-5 W2 35-46 34-47 24-28 45-65 735 788

http://fantasygames.sportingnews.com/stratomatic/team/team_other.html?user_id=290373

Neither player missed a game.

Page2

[ClowntimeIsOver]

Thanks very much, Page2.

So on a team with 943 runs, and batting second, Bonds had AT LEAST 766 PAs. With HBPs, SFs, and whatever else, it would be more.

On a team with 735 runs, and batting first and second, Jeter had AT LEAST 752 PAs, plus HBPs, SFs, etc.

(Note that high-scoring and low-scoring teams are not judged relative to their league -- it doesn't matter if it's a high or low-scoring league.)

Does anybody have a full-time #8 or #9 hitter in their books?

Also, a full-time #5 hitter would be interesting as the middle of the pack. Or, for that matter, ANY 162-or-almost game players who always/almost always batted in the same spot.

[george barnard]

Here's Ethier from SOM 2007 (MLB 2006) 161 games always in the fifth spot.

[url]http://fantasygames.sportingnews.com/baseball/stratomatic/2007/team/team_other.html?user_id=45249&stats=sim[/url]

Bill

[Knerrpool]

Here is Vizquel from a 2009 team - 159 games batting in either the 8th or 9th spot. Pretty bad statistics (even for Petco) but amazingly this team won the championship.

[url]http://fantasygames.sportingnews.com/stratomatic/team/team_other.html?user_id=292763[/url]

[ClowntimeIsOver]

Great! Thanks!

So a #5 guy on a team with 805 runs had at least 668 PAs, pro-rated (162 games for 161) to 672, plus HBP etc.

A #8/#9 guy on a team with 683 runs had at least 573 PAs, pro-rated (162 games for 159) to 584, plus HBP etc.

A #2 guy on a team with 943 runs had at least 766 PAs, plus HBP etc.

A #1/#2 guy on a team with 735 runs had at least 752 PAs, plus HBP etc.

Look at the range in the above four numbers! As is obvious, but shown more accurately by looking at the 600/800 comparison in the first post, this has a significant impact on injury averages, particularly for higher injury ratings.

(If it seems confusing to use "ideal 162-game every-inning" PAs to figure injuries for guys who miss a lot of games, I should explain: The formula is based on a maximum ideal season, which is then "discounted" based on the injury rating.)

[Page2]

Hi,

Another one for you.

89 73 .549 - 7-3 L1 44-37 45-36 31-13 58-60 779 736

Jeter from a 2009 team he hit leadoff against both RHP & LHP pitching and played in all 162.

http://fantasygames.sportingnews.com/stratomatic/team/team_other.html?user_id=268464

Page2

[AeroDave10]

I guess the real question is, with an average number of runs scored, how many PAs can you expect a player with injury rating "R" to have over the course of a season?

I tried to input about 300 or so players worth of 2009 SOM game data on PAs (AB + BB), assuming they played as much as they could when healthy (no platoons). Most of the data came from my own teams, but then I started to supplement it a bit with some of the opposing teams, too. Very time consuming, but I thought I'd share what I have so far. I broke it down by injury categories:

680+ (39 player-seasons) = 694 PAs
600-679 (92 player-seasons) = 658 PAs
R=1 (88 player-seasons) = 606 PAs
R=2 (28 player-seasons) = 578 PAs
R=3 (17 player-seasons) = 563 PAs
R=4 (17 player-seasons) = 518 PAs
R=5 (11 player-seasons) = 527 PAs

Obviously, the R=3, 4, and 5 data are not that reliable because of the low sample size, and R=2 isn't great either. A lot of injury prone guys get used in platoons, and/or there aren't enough quality ones that warrant such players being inserted in the lineup every day. However, the data for the top 3 injury categories are pretty reliable, I think.

Anyone else have any numbers on this kind of stuff, or share any thoughts or opinions?

[ClowntimeIsOver]

Thanks, AeroDave -- I just want to repeat what I said above: "The formula is based on a maximum ideal season, which is then 'discounted' based on the injury rating."

So, for me, the relevant data are the "maximum" PAs someone would have if he played every inning. Once you have that, the formula will give a very accurate average of starts missed and games missed PER 162 games. To get PAs for different injuries (as you're mentioning), "games missed" can be multiplied by some number of average PAs per game and subtracted from the "maximum number." But I'm looking at starts missed and games missed (rather than total PAs) per injury rating (though the two are equatable).

Page2 -- so always leading off, Jeter had at least 754 PAs, plus HBP, SF, etc, on a team that scored 759 runs.

Compare this to:

A #2 guy on a team with 943 runs had at least 766 PAs, plus HBP etc.

A #1/#2 guy on a team with 735 runs had at least 752 PAs, plus HBP etc.