Formulas for expected singles, doubles, triples, and HR

[Curtis]

I'm assuming the reason for that is because that's the way they were displayed in the 2006 version, when the game was changed. The usage of Contact and BABIP have changed from 2006 to 2007, but maybe changing the display is either complex or a low priority.

[injury log]

I think it makes more sense to display Contact, which is directly linked to batting average and expected hits, than it does to have the user try to figure it out from Avoid K, Power and BABIP. So I expect it's a design decision, and not something one should expect will be changed in a future version.

And while Avoid K is already incorporated into the Contact rating, it may be useful for some people to see, since at least it predicts how many strikeouts a player will get.

[RonCo]

Originally Posted by jar2574

Yeah, but two guys with the same contact rating are going to have the same number of "expected hits", right? So while contact rating is made up of component parts, it allows us to see how many hits we should expect.

Yes. Contact is an attempt to provide the user with an idea of expected batting average. Markus went this way (rather than directly exposing the BABIP rating) because he felt users would be more comfortable with a value that meant "batting average" in the traditional way.

[MrHaroldG]

Originally Posted by injury log

BABIP: 100
Avoid K: 100
Power: 1
Resulting Contact: 90

BABIP: 100
Avoid K: 100
Power: 100
Resulting Contact: 101

BABIP: 100
Avoid K: 100
Power: 200
Resulting Contact: 144

That being said, do you know if there is a formula for calculating a player's resulting contact?

[injury log]

Originally Posted by MrHaroldG

That being said, do you know if there is a formula for calculating a player's resulting contact?

There is a formula, certainly. I expect what the game does is work out expected batting average first, using Power, BABIP and Avoid K, then converts that batting average into a Contact rating. So from what I've posted above, about how batting average is determined, and how Contact is linked to average, one could produce a formula for Contact. It will be a messy equation, though. I might derive it later today, after I've had some coffee.

[injury log]

Okay, I've worked out a formula for Contact from the other ratings. It's not too difficult to generate the formula, but it looks like a train wreck, only because it combines several different quantities into one equation. The formula is at the bottom of this post, but I'll walk through my steps in case anyone wants to verify the work, or finds a mistake:

All of the ratings-stats functions are piecewise linear functions, with a single slope change at rating = 100. Put more simply, if you increase, say, Avoid K by 10 points, you'd expect 10 fewer strikeouts per 550 ABs when Avoid K is less than 100, but a decrease of only 8 strikeouts per 550 ABs when Avoid K is more than 100.

I can write these equations in a single line by using a Maximum function, which chooses the larger of two values. So, for example, the Avoid K (AK) rating predicts the number of Ks per 550 at bats as follows:

K = 200 - AK + 0.2*Max[0, AK-100]

That Max term is zero when AK < 100, and corrects for the slope change in the AK-strikeouts function when AK > 100.

Contact is similar; 1 point of contact corresponds to 2 points of batting average when Contact < 100, but only 1 point of batting average when Contact is > 100. If we know batting average (BA), we get Contact as follows:

CON = 500*(BA - .065) + 500*Max[0, BA - .265]

To find BA, we need to use Avoid K, the BABIP rating and Power. Normalizing everything to 550 ABs:

K = 200 - AK + 0.2*Max[0, AK-100]

HR = 0.16*POW + 0.18*Max[0, POW -100]

% of balls in play that are hits = 0.1 + 0.002*BABIP - 0.001*Max[0, BABIP - 100]

no. of balls in play per 550 AB = 550 - K - HR

no. of hits = HRs + the percentage of balls in play that are hits times the number of balls in play

BA = hits/550

I'll use P for Power, B for BABIP and A for Avoid K to save space:

Batting Avg = [0.16*P + 0.34*Max[0, P -100] + (0.1 + 0.002*B - 0.001*Max[0, B - 100])*(550 - [200 - A + 0.2*Max[0, A-100]] - ( 0.16 * P + 0.34*Max[0, P -100])]/550

and finally...

Contact = 500*([0.16*P + 0.34*Max[0, P -100] + (0.1 + 0.002*B - 0.001*Max[0, B - 100])*(550 - [200 - A + 0.2*Max[0, A-100]] - (0.16*P + 0.34*Max[0, P -100])]/550 - .065) + 500*Max[0, [0.16*P + 0.34*Max[0, P -100] + (0.1 + 0.002*B - 0.001*Max[0, B - 100])*(550 - [200 - A + 0.2*Max[0, A-100]] - ( 0.16 * P + 0.34*Max[0, P -100])]/550 - .265]

There are some obvious simplifications that I'm not going to bother to make. The Max functions account for most of the mess in the equation above. When Power, BABIP and Avoid K are all less than 100, the formula is much simpler:

Contact = (1/11)*(1.44P + 350 + A + 7B + 0.02*B*A - 0.0032*B*P) - 32.5

One could generate 8 separate formulae, each about as 'clean' as this one, for the 8 possible combinations of BABIP, Power and Avoid K (all less than 100, all more than 100, AK < 100 and the rest > 100, etc). I'm not planning to do that, however.