Formulas for expected singles, doubles, triples, and HR

[jar2574]

Here are formulas to calculate expected singles, doubles, triples and HR.

I am now working on a formula for expected walks.

When I am finished I should be able to calculate expected Runs Created, which is the purpose of my whole exercise.

Each category is based on 1000 at bats. If you want to figure out expected chances based on fewer at bats, or even in any given at bat, then adjust accordingly. I used 1000 at bats to help solve rounding calculations problems.

I will use the symbol "#" to show where you plug in the rating being discussed. I will use * to show multiplication.

Expected hits.
Hits are derived from Contact Rating.
For Contact ratings 1 to 10:
(# * 20) + 65 = expected hits in 1000 at bats. A person with 1 as a contact rating is expected to get 85 hits in 1000 at bats. A person with a 10 contact rating is expected get 265 hits.

For Contact ratings 11 to 25:
((# - 10) * 10) + 265 = expected hits in 1000 at bats. A person with 11 as a contact rating is expected to get 275 hits in 1000 at bats. A person with a 25 contact rating is expected to get 415 hits.

Doubles and Triples.
Doubles and Triples are derived from Gap Rating and the proportion of doubles to triples is affected by Running Speed Rating.
For all Gap ratings:
# * 5.2 = expected doubles & triples in 1000 at bats.

This formula is off by one extra base hit for the Gap Ratings 2, 3, 8, 9, 13, 14, 18, 19, and 23.

Unfortunately, for some numbers it needed to be adjusted up and for others the expected number needed to be adjusted down. So I could not figure out a more accurate multiplier than taking Gap Rating * 5.2. Any help would be appreciated. I'm really not a math guy. In any event, the calculation was always accurate within one extra base hit, and that's good enough for me, for now.

Next, to calculate total bases from these extra base hits we need to use Running Speed Rating. Running speed does not seem to meaningfully affect the number of extra base hits, but it does affect how many triples a batter gets from among his extra base hits.

As mentioned, I am trying to eventually reach an expected runs created formula, so with doubles and triples I am only concerned with how many total bases a runner reaches based on his Gap Rating and his Running Speed Rating.

To calculate the total base value from among your extra base hits:
For Running Speed ratings 1-8:
(expected doubles + expected triples) * 2.077 = total bases from doubles and triples.

For Running Speed ratings 9-12
(expected doubles + expected triples) * 2.146 = total bases from doubles and triples.

For Running Speed ratings 13-17
(expected doubles + expected triples) *2.170 = total bases from doubles and triples.

For Running Speed ratings 18-22
(expected doubles + expected triples) *2.200 = total bases from doubles and triples.

For Running Speed ratings 23-25
(expected doubles + expected triples) *2.248 = total bases from doubles and triples.

Home Runs
Home Runs are derived from Power Rating.
For Power Ratings 1-10
# * 2.9 = expected home runs in 1000 at bats. A person with a 1 power rating is expected to hit 3 home runs in 1000 at bats (if we round 2.9 up to 3.) A person with a 10 power rating is expected to hit 29 HR in 1000 at bats.

For Power Ratings 11-25
(# - 10) * 6.2 + 29 = expected home runs in 1000 at bats.
From 11 Power Rating onward, instead of increasing by 2.9 per one rating increase the expected HR value increases by 6.2 per rating increase.

A person with a 11 Power rating is expected to hit 29 home runs in 1000 at bats. A 15 Power rating is expected to result in 54 home runs. A 25 Power rating is expected to result in 122 home runs in 1000 at bats.

Walks
Walks are derived from Eye / Plate Disipline Rating
For Eye Ratings from 1 to 10:
# * 9.09 = walks per 1000 at bats

For Eye Ratings from 11 to 25:
((#-10) * 18.17) + 91 = walks per 1000 at bats


I hope these formulas might add to your enjoyment of the game, or at least help you in drafting. I am working on an excel spreadsheet that will use these formulas to calculate Expected Runs Created. That will make my draft day and trade decisions much easier.

A lot of these multipliers may be off by a few hundreths or tenths. I got things as close as I could. I didn't want to spend several days on this, just one afternoon. So these are good enough for me, and accurate within one double, or one walk, etc. in 1000 at bats.

Now for the spreadsheet....

[injury log]

If you're interested in the same for pitching ratings, I worked out the formulas here:

Resulting Stats (based on a neutral, modern Major League environment)

Again, individual ratings largely affect a single projected stat, independent of the others (Stuff- Ks; Movement- HRs; Control- BBs). One caveat- based on his research into the statistical outpout of the game, RonCo has warned, in the thread above and elsewhere, against reading too much into the stats projections provided in the editor.

[Charlie Hough]

What about other rating scales? I imagine it would be pointless to try to compute this for a 1-10 rating scale, because the results would probably vary too much. But I play with the 1-10 scale, and it would be interesting to know.

[jar2574]

Originally Posted by injury log

If you're interested in the same for pitching ratings, I worked out the formulas here:

www.ootpdevelopments.com/board/showthread.php?t=149681

Again, individual ratings largely affect a single projected stat, independent of the others (Stuff- Ks; Movement- HRs; Control- BBs). One caveat- based on his research into the statistical outpout of the game, RonCo has warned, in the thread above and elsewhere, against reading too much into the stats projections provided in the editor.

Thanks!

I wasn't going to even try it for pitchers, given that I was worried about movement and stuff both affecting the data.

Batting was easy in comparison, methinks.

Nice work on that stuff. Maybe I'll be able to put it in a spreadsheet as well, and then I could have expected runs and expected runs given up.

I know the values don't always work as expected, but I've played the 1947 season about 3 or 4 times, and the results were generally close to what these expected results.

[jar2574]

Originally Posted by Charlie Hough

What about other rating scales? I imagine it would be pointless to try to compute this for a 1-10 rating scale, because the results would probably vary too much. But I play with the 1-10 scale, and it would be interesting to know.

I don't know. When I edited the rankings in the player editor, they were on a 1-250 scale (corresponding to the 1-25 scale.)

So I'm not even sure how I'd go about calculating it for the 1-10 scale.

[injury log]

jar,

Before you get too far on the spreadsheet, I think there might be a problem with your equations involving Contact. The Contact rating in the editor combines BABIP, Avoid Ks, and Power (small influence), and determines the number of projected hits, not the number of projected singles. Perhaps you have the right equation, but described it incorrectly above? I'm working it out now, in any case.

And to amplify my earlier comment about the unreliability of the editor projections, with a 1 Contact and a 250 Gap, the game projects 36 hits and 71 doubles/triples, which is clearly nonsensical!

[injury log]

Originally Posted by Charlie Hough

What about other rating scales? I imagine it would be pointless to try to compute this for a 1-10 rating scale, because the results would probably vary too much. But I play with the 1-10 scale, and it would be interesting to know.

Zeyes recently posted a conversion between the various ratings scales used by the game (and some don't convert as you might expect). If you can't find the thread via a search, I can try to dig it up- it was within the last 2-3 weeks.

[jar2574]

This post was incorrect, and so I am deleting it. That way people following the thread won't get confused.

[injury log]

First, I've figured out why you're seeing some odd results at various Gap ratings. The game works out the number of doubles, and the number of triples (using Speed), and then rounds off both. At, say, Gap = 20, it may be that the game is supposed to produce 5.7 2Bs/3Bs. At some low speed, you might get 0.4 3Bs and 5.3 2Bs, which will round to 5 2Bs, 0 3Bs. At a different speed, you might get 0.6 3Bs and 5.1 2Bs, rounding to 5 2Bs and 1 3B. So the unusual results you see at certain Gap ratings are a kind of compounded rounding error, and if you adjust speed while leaving Gap alone, you'll see that 2Bs+3Bs can change by 1. Normalized to 550 ABs, the number of 2Bs+3Bs appears to be 0.285*Gap.

I agree you can adjust BABIP and Avoid K independently, and the resulting number of hits remains the same for given Contact rating. However, in my Editor, if I change Power, the Contact rating will change. For example:

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

The Contact rating determines the total number of hits, not the total number of singles. Do you see something different in your Editor?

Originally Posted by jar2574

From what I saw, you can adjust Avoid K and BABIP to get the contact rating you want. At any given contract rating, it didn't really matter how you adjusted Avoid K and BABIP. It didn't matter whether the dude struck out all the time and had a great BABIP or whether he never struck out but didn't have a great BABIP. The contact rating of 10 produced the same amount of singles regardless of how you arrived at it.

I did not notice any affect on the Contact rating based on the Power rating. The Contact rating didn't go up when I increased or decreased Power.

The batting average expected would go up when I increased the Power rating. The Power rating affects batting average independently of Contact rating, from what I saw. It adds home runs to the singles from Contact rating and the doubles/triples of Gap rating.

But from what I saw, the contact rating ONLY affected singles. It did not affect doubles or triples or home runs.

To get an expected batting average we'd add up the HR, doubles, triples, and singles to get total hits, and then divide total hits by at bats.

So Power Rating, Gap Rating, and Contact Rating all play a role in batting average, but they all play that role independently of one another.

As an aside, I noticed some of the aburd results as well. The 250 Gap, 1 Contact player produces incoherent expected results. But in general, I think that the expected results are fairly accurate because the game doesn't produce players with 25 Gap, 1 Contact.

I think a lot of varience will come from the league and the quality of competition. As an example, I played out a season where Kiner won the batting title with a .356 average, even though he has a 12 contact rating (or at least that's what my scouts said.) He hit 56 HR or so, so those HR really jacked up his batting average.

Meanwhile a singles hitter had better have a really high contact rating if he can't get doubles from Gap or home runs from Power. Otherwise his batting average will be a lot lower than you'd expect. Walker for the Cardinals in 1947 comes to mind. His contact is like 19, but he hasn't led the league in any of the seasons I've played out. This is possibly because he doesn't hit many homers.

[jar2574]

Originally Posted by injury log

First, I've figured out why you're seeing some odd results at various Gap ratings. The game works out the number of doubles, and the number of triples (using Speed), and then rounds off both. At, say, Gap = 20, it may be that the game is supposed to produce 5.7 2Bs/3Bs. At some low speed, you might get 0.4 3Bs and 5.3 2Bs, which will round to 5 2Bs, 0 3Bs. At a different speed, you might get 0.6 3Bs and 5.1 2Bs, rounding to 5 2Bs and 1 3B. So the unusual results you see at certain Gap ratings are a kind of compounded rounding error, and if you adjust speed while leaving Gap alone, you'll see that 2Bs+3Bs can change by 1. Normalized to 550 ABs, the number of 2Bs+3Bs appears to be 0.285*Gap.

I agree you can adjust BABIP and Avoid K independently, and the resulting number of hits remains the same for given Contact rating. However, in my Editor, if I change Power, the Contact rating will change. For example:

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

The Contact rating determines the total number of hits, not the total number of singles. Do you see something different in your Editor?

Crap, you're right. I don't know how I missed that.

Power does affect Contact. It doesn't seem like Gap does though.

[jar2574]

So contact will determine the total number of hits, not just singles. Thanks so much to injury log for showing me that.

So that affects how we calculate total bases, but I don't think my research was for naught.

1) I think my calculations regarding expected "singles" will need to be converted into expected "hits."

2) Take expected hits; subtract expected HR and expected doubles and expected triples. Now we've got expected singles. Each single represents one total base.

3) Multiply expected HR by 4 to get total bases expected from HR.

4) Add expected doubles and triples and then multiply that number by the appropriate amount, found through the batter's Speed Rating. Now we'd have total bases for doubles and triples.

Add up total bases from singles, HR, doubles and triples, and we'd have "total expected bases."

[jar2574]

Originally Posted by injury log

First, I've figured out why you're seeing some odd results at various Gap ratings. The game works out the number of doubles, and the number of triples (using Speed), and then rounds off both. At, say, Gap = 20, it may be that the game is supposed to produce 5.7 2Bs/3Bs. At some low speed, you might get 0.4 3Bs and 5.3 2Bs, which will round to 5 2Bs, 0 3Bs. At a different speed, you might get 0.6 3Bs and 5.1 2Bs, rounding to 5 2Bs and 1 3B. So the unusual results you see at certain Gap ratings are a kind of compounded rounding error, and if you adjust speed while leaving Gap alone, you'll see that 2Bs+3Bs can change by 1. Normalized to 550 ABs, the number of 2Bs+3Bs appears to be 0.285*Gap.

Thanks for figuring out the rounding problem.

I think our .285 or 5.2 calculations are basically two ways of arriving at the same number. And unfortunately, I think that sometimes we will remain a little off because of the rounding.

When I checked 250 Gap in the editor led to 71 or 72 doubles and triples in 550 AB depending on batting's speed. 250 x .285 would be 71.25.

So I think we're right there, but the rounding problems will prevent us from being totally correct all of the time.

I think I'll leave the multiplier at 5.2 for now, since I'm using the 25 Gap rating from the screen, rather than the 250 Gap rating in the editor.

[injury log]

Definitely true that Gap is completely independent of the other ratings. The interplay between Power and Contact complicates matters, but with Power set to 1 (minimum, i.e. 0 HRs), the numbers work out very nicely to work out expected hits. It all seems to be 'normalized' around 550 ABs, so using that as a benchmark:

Avoid Ks determines how many balls are in play (if no HRs), as follows:
BIP = 350+AK

(AK determines Ks by: Ks = 200-AK)

[ EDIT: this is slightly off; Avoid K also has a 'break' at 100, though not a pronounced one, and I didn't notice it the first time round. For Avoid K less than 100, the above is correct. For Avoid K above 100, expected Ks = 180 - 0.8*AK. The below needs to be accordingly adjusted for AK > 100 ]

BABIP determines the PCT of balls in play which are hits (again, ignoring HRs). BABIP is another rating which has a 'break' at 100:

For BABIP under 100:
Projected Hits = (0.1 + 0.002B)*(350 + AK)

For BABIP over 100:
Projected Hits = (0.2 + 0.001B)*(350 + AK)

The Contact rating is correlated with batting average. Adding 10 points of Contact corresponds to adding about 20 points of BA for Contact ratings below 100, and 10 points of BA for Contact above 100. A 1 Contact produces a .065 BA; 100 Contact produces .264; 200 Contact produces .364, from which the relationship is easy to produce.

I haven't looked at Power at all yet, so will see if that's easy to work out.

[injury log]

So I think Power works as follows:

Work out projected number of HRs using Power, as you've done;

Balls in Play = 350 + AK - projected HRs;

Use BABIP, which tells you the % of balls in play which are hits, to work out the number of hits on Balls in Play, as in my post above;

Add HRs to get total number of hits.

You could use the three ratings (Avoid K, BABIP, Power) to get a formula for Contact, though I think it would be a bit messy. Maybe something I'll look at tomorrow...

[Prodigal Son]

Does the avoid k rating actually produce any more hits independent of the contact ratings? Will a player with 10 avoid k and 10 contact get more hits than a player with 1 avoid k and 10 contact?

[jar2574]

Originally Posted by Prodigal Son

Does the avoid k rating actually produce any more hits independent of the contact ratings? Will a player with 10 avoid k and 10 contact get more hits than a player with 1 avoid k and 10 contact?

No. I don't think so. Hits will be the result of his contact rating. The Avoid K plays a role in creating the contact rating, but it does not affect hits directly.

I completely ignored Avoid K for that reason. But lately I've been paying slightly more attention since I'm in a 1901 league. There are so many more errors that it pays off to get guys who put the ball in play more consistently.

[RonCo]

Hits consist of either balls hit out of the park (controlled by HR/Movement) or hits on balls hit inside the park (controlled by BABIP).

"Contact" is the result of BABIP (average on balls in play) and AB-K-HR (balls in play), strikeouts (outs on balls not in play), and HR (hits on balls not in play). Its intention is to provide an idea of what a player's batting average should be. So, a very low contact rating when teamed with a really high avoid K rating means that the batter's BABIP and Power ratings are probably very low.

[RonCo]

Originally Posted by jar2574

No. I don't think so. Hits will be the result of his contact rating. The Avoid K plays a role in creating the contact rating, but it does not affect hits directly.

I completely ignored Avoid K for that reason. But lately I've been paying slightly more attention since I'm in a 1901 league. There are so many more errors that it pays off to get guys who put the ball in play more consistently.

Technically, hits are not the result of the contact rating. hits are the result of the BABIP rating and the HR rating and are limited (or enabled) but the AvoidK rating.

[jar2574]

Originally Posted by RonCo

Technically, hits are not the result of the contact rating. hits are the result of the BABIP rating and the HR rating and are limited (or enabled) but the AvoidK rating.

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.

e.g. If one guy has a 15 contact rating via a high BABIP + high power + a low Avoid K, and another guy has a 15 contact rating via a lower BABIP + lower power + a much higher Avoid K, as long as their contact rating is the same, their expected hits should be the same.

[Prodigal Son]

If avoid K does not affect hits independent of the contact rating (e.g. if the contact rating already accounts for the avoid K ability), it seems rather odd to display avoid K but not display BABIP, as they function similarly.