Strikeout Rate’s Link to WHIP

I’m still in disbelief from a recent finding I made. It started with this comment in a recent article I wrote about STUFF:

How much WHIP changed in the two “Stuff” models was almost too good to be true. In both cases, the walk rate increased as a pitcher’s stuff got better, but the hit suppression was so large that the WHIP declined.

Well I was wrong about the hit suppression. I went back and found no link to BABIP. The difference was because WHIP is on an innings denominator and a strikeout removes the chance for a Hit and Walk. An out comes down to the random chance of a batted ball. I know it’s confusing so here is an example assuming a pitcher with a 9 K/9, 3 BB/9, and .300 BABIP and throws 6 IP/GS.

Of the 18 outs he gets, 6 will be from strikeouts. Then 12 outs will need to come from batted balls. Assuming perfect distribution, there will be 3.6 hits (12 * .300) and 8.4 outs. The pitcher still need the 3.6 outs so with the runners on base he’ll face batters after the first round of hits and will allow 1.1 Hits (.300 * 3.6) the second time. Finally, assume he gets the final out with no more hits. In all, the inputs to WHIP are 2 BB and 4.7 H in 6 IP or a 1.12 WHIP (6.7 BB+H/6 IP).

Now assume his strikeout rate jumps to 12 K/9 and keeps the 3 BB/9, 6 IP/GS, and a .300 BABIP).

Of the 18 outs he gets, 8 will be from strikeouts. Then 10 outs will need to come from batted balls. Assuming perfect distribution, there will be 3.0 hits (10 * .300) and 9.0 outs. The pitcher still need the 3.0 outs so with the runners on base he’ll face batters after the first round of hits and will allow 1.0 Hits (.300 * 3.0) the second time. Finally, assume he gets the final out with no more hits. In all, the inputs to WHIP are 2 BB and 4.0 H in 6 IP or a 1.00 WHIP (6.7 BB+H/6 IP).

The strikeouts help to keep the random luck of hits coming into play.

So with this relationship now known, I found how much a change walk and strikeout rate has on WHIP. I took all the pitchers (min 30 IP) from 2021 and 2022 found the linear regression equation to estimate WHIP knowing just BB/9 and K/9.

WHIP = (BB/9 * .127) + (-0.055 * K/9) + 1.33
r-squared = .587

Obviously, walks have more of a weight on WHIP but the effect from strikeouts is about half the amount from walks. And to help the few readers who have made this far and hate math (or those who skipped over the explanation, here is table with the strikeout rate going down the left and walk rate across the top. I color red any WHIP over 1.40 (~ last place in my 15-team leagues) and between 1.25 and 1.40 yellow (between middle of the pack and last place).