I did a little work and last year the 5 pitchers anticipated to be our starting rotation averaged 6.84 K/9, so without looking at relievers and to use whole #s for simplicity let’s say we average 7 Ks a game leaving 20 POs between IFs and OFs outside of Ks.

Then I averaged their FB/GB rates (just last season again) and came up with 1.484 so there is about 1 1/2 GB for every FB so if we apply that over 20 POs we get 12 IF PO and 8 OF PO. (Not accounting for infield flies but this is really rough so if anyone can refine this, by all means please do) So say the IF misses 20% (arbitrary # for a really bad D) of their reasonable PO chances and we’ll say they miss about 2 1/2 a game.

We’d then reapply the % so there is about a 25% chance we get a K, about a 45% chance we get another GB and about a 30% chance of a FB. So on the whole if an IF missed 20% of it’s reasonable chances, and the OF converts all it’s reasonable chances it would turn into a little less than an out a game.

But here is where the GB/FB tendencies might make a difference. Let’s look just at Washburn from last year. He struck out a little over 5 a game so we’ll say his starts leave 22 POs avail. He had a .84 GB rate so over 22 POs that would work out to about 12 OF POs and 10 IF POs. So the IF has a little less chance to screw up in the first place, so at a 20% error rate they miss 2 a game. Wash then has about an 18% chance that turns into a K, only a 37% chance of a GB, leaving about a 45% chance of an FB. Which with the lower # of opportunities it still is a little closer to 1 a game but still a less than 1 whole out shifted a game. So in reality since the FB pitcher is giving less opportunities to the IF it doesn’t really make a huge difference in how many of their missed IF POs turn into OF POs contrary to what I thought, although there is a small variation.

So I guess that would add up over a whole season, but I wouldn’t say it is a huge factor in the # of OF POs generated. And as I mentioned earlier you would need to decrease the total # of OF POs because some of those FB outs are going to be caught by an IF.

Also I have no idea what the normal % of GBs turned into outs is compared to FBs so that could skew the #s as this formula implies that an exactly proportionate % of GB/FB allowed turns into outs. IIRC I think a higher % of GBs are turned into outs so that would further decrease the # of missed IF POs that turn into OF POs because even if the next batter does hit a FB it is less likely to be converted to an out, again IIRC. Well that’s the longest post I’ve ever written but I hope at least one other person finds it interesting.

Someone correct me if I mess up math or do something I shouldn’t here, but I’ll try to figure out what that would look like here. Assuming 1:1 ratio and 50% IF and OF PO efficiency, for convenience (eliminating K’s and BB’s as well). I think the easiest way would be to look at it like a probability tree. For any at-bat, there is a 25% chance of a IF PO, missed IF PO, OF PO, or missed OF PO. So for each at-bat, we assume .25 of each, correct? We need to accrue 27 outs through this, and since each at-bat yields half an out that’s 54 at-bats per game, totalling 13.5 IF PO and 13.5 OF PO. If we knock down the IF PO efficiency to 25% but leave the 1:1 ratio the same, each at-bat is now worth .25 OF PO, .25 missed OF PO, .125 IF PO, and .375 missed IF PO. Still needing to amount to 27 outs we now have to raise the number of at-bats up to 72, and end up with 18 OF PO and 9 IF PO.

Even though the numbers I used are completey ridiculous, it looks pretty apparent after doing all that the an inferior IF defense WILL increase OF PO, and vice versa. Using the same logic you’d have to assume that K’s wouldn’t stay constant either, and would actually increase as the defense gets worse. Counterintuitive at first, but I guess it makes sense.

In order to figure out how MUCH an increase/decrease in IF or OF PO efficiency changes the other (and K’s too) you’d have to plug in the actual numbers.

I think your examples sum it up though in that there are certain situations where a missed IF PO does lead to decrease in total IF POs but also there are situations where it just turns into a different IF PO. Which is why I concluded the GB tendencies of the pitching staff might have a bigger impact on how often a missed IF PO is then turned into an OF PO.

I guess where I need to go from here is some kind of formula based on % of FBs GBs and missed opportunity, which I’m probably not smart enough to figure out on my own.

Would bad IF defense really have that much of an increase in OF POs?

Take it to the extreme. If you had no infielders, literally no one, OF putouts and K’s would go up. They will eventually get 27 outs per game (or 24 losing on the road). Likewise, if you had no fielders, pitchers K’s would go up. They’d K approx 3/IP (minus popups to P and C). Now per plate appearance they wouldn’t change much, but per IP they have to go up.

OFPO+IFPO+K=Total outs
or
OFPO+IFPO=Total outs-K

Assuming Total outs and Strikeouts remain constant, a decrease in IF PO would HAVE to lead to an increase in OF PO.

You’re looking at it in an at-bat by at-bat sequence – I’m looking at the final tallies. I’ll run through two short example inning to try to explain better:
Groundout to SS
Flyout to CF
Grounder to 3B, but Sexson bumbles the catch and the runner reaches on an error
Fielder’s choice to 2B

Groundout to SS
Flyout to CF
Grounder to 3B, but Sexson bumbles the catch and the runner reaches on an error
Flyout to CF

In the first one, there are 2 IF PO and 1 OF PO. You’re right in the sense that the missed opportunity for a PO doesn’t directly lead to an increased chance for an OF PO. But, there were still 2 IF PO recorded, and only 1 OF PO. In the second example, there is only 1 IF PO, therefor there must be a 2 OF PO to make up for it (assuming no K’s).

I’m looking at the final stat line, and putting it into the equation above. An decrease in the FINAL TALLY of IF PO must mean that either K or OF PO increased (assuming a constant number of Total Outs).

If this is the wrong way to be looking at it though someone please let me know, I’m just trying to sort my way through and rationalize the possible meanings of the graph.