Through 60 games:

Team	Park	Games	PA	H	HR	3B	2B	XBH	1B
90 Ft from Home	AFCS	60	2230	479	35	25	82	142	337
AFCS Project	AFCS	60	2210	468	37	26	74	137	331
Pythagorean Triples	AFCS	60	2257	540	46	27	78	151	389
She's So Ugly	AFCS	60	2325	589	51	50	92	193	396
SpottieOttie	AFCS	60	2344	557	39	37	80	156	401
The Trouble With Triples	AFCS	60	2262	491	38	21	69	128	363
Three Men on Third	AFCS	60	2268	540	45	29	86	160	380
Triples in AFC	AFCS	60	2275	501	41	33	61	135	366
Born on Third Base	Petco	60	2343	530	26	63	94	183	347
Magda, Zsa Zsa, and Eva	Petco	60	2255	472	27	52	68	147	325
MH Will Prob Trip	Petco	60	2236	466	16	55	62	133	333
Petco Project	Petco	60	2251	472	20	73	66	159	313
Petco's Festival of Triples	Petco	60	2228	441	25	52	68	145	296
Roustabouts@Petco	Petco	60	2226	467	22	63	67	152	315
Run Run Run	Petco	60	2223	457	25	57	57	139	318
Sliding Headfirst Into Third	Petco	60	2270	470	19	50	62	131	339
Totals			36203	7940	512	713	1166	2391	5549
Averages			2262.6875	496.25	32	44.5625	72.875	149.438	346.813
Total AFCS			18171	4165	332	248	622	1202	2963
Average AFCS			2271.375	520.625	41.5	31	77.75	150.25	370.375
Total Petco			18032	3775	180	465	544	1189	2586
Average Petco			2254	471.875	22.5	58.125	68	148.625	323.25

Team	Park	H/PA	HR/PA	3B/PA	2B/PA	XBH/PA	1B/PA
90 Ft from Home	AFCS	0.215	0.016	0.011	0.037	0.064	0.151
AFCS Project	AFCS	0.212	0.017	0.012	0.033	0.062	0.150
Pythagorean Triples	AFCS	0.239	0.020	0.012	0.035	0.067	0.172
She's So Ugly	AFCS	0.253	0.022	0.022	0.040	0.083	0.170
SpottieOttie	AFCS	0.238	0.017	0.016	0.034	0.067	0.171
The Trouble With Triples	AFCS	0.217	0.017	0.009	0.031	0.057	0.160
Three Men on Third	AFCS	0.238	0.020	0.013	0.038	0.071	0.168
Triples in AFC	AFCS	0.220	0.018	0.015	0.027	0.059	0.161
Born on Third Base	Petco	0.226	0.011	0.027	0.040	0.078	0.148
Magda, Zsa Zsa, and Eva	Petco	0.209	0.012	0.023	0.030	0.065	0.144
MH Will Prob Trip	Petco	0.208	0.007	0.025	0.028	0.059	0.149
Petco Project	Petco	0.210	0.009	0.032	0.029	0.071	0.139
Petco's Festival of Triples	Petco	0.198	0.011	0.023	0.031	0.065	0.133
Roustabouts@Petco	Petco	0.210	0.010	0.028	0.030	0.068	0.142
Run Run Run	Petco	0.206	0.011	0.026	0.026	0.063	0.143
Sliding Headfirst Into Third	Petco	0.207	0.008	0.022	0.027	0.058	0.149
Totals
Averages		0.219	0.014	0.020	0.032	0.066	0.153
Total AFCS
Average AFCS		0.229	0.018	0.014	0.034	0.066	0.163
Total Petco
Average Petco		0.209	0.010	0.026	0.030	0.066	0.143

Team	Park	HR/H	3B/H	2B/H	XBH/H	1B/H
90 Ft from Home	AFCS	0.073	0.052	0.171	0.296	0.704
AFCS Project	AFCS	0.079	0.056	0.158	0.293	0.707
Pythagorean Triples	AFCS	0.085	0.050	0.144	0.280	0.720
She's So Ugly	AFCS	0.087	0.085	0.156	0.328	0.672
SpottieOttie	AFCS	0.070	0.066	0.144	0.280	0.720
The Trouble With Triples	AFCS	0.077	0.043	0.141	0.261	0.739
Three Men on Third	AFCS	0.083	0.054	0.159	0.296	0.704
Triples in AFC	AFCS	0.082	0.066	0.122	0.269	0.731
Born on Third Base	Petco	0.049	0.119	0.177	0.345	0.655
Magda, Zsa Zsa, and Eva	Petco	0.057	0.110	0.144	0.311	0.689
MH Will Prob Trip	Petco	0.034	0.118	0.133	0.285	0.715
Petco Project	Petco	0.042	0.155	0.140	0.337	0.663
Petco's Festival of Triples	Petco	0.057	0.118	0.154	0.329	0.671
Roustabouts@Petco	Petco	0.047	0.135	0.143	0.325	0.675
Run Run Run	Petco	0.055	0.125	0.125	0.304	0.696
Sliding Headfirst Into Third	Petco	0.040	0.106	0.132	0.279	0.721
Totals
Averages		0.064	0.091	0.146	0.301	0.699
Total AFCS
Average AFCS		0.080	0.059	0.149	0.288	0.712
Total Petco
Average Petco		0.048	0.123	0.144	0.315	0.685

I understand about 25% of what's in this thread. I have to read it like seven more times to have it sink in fully.

Relative to how you've all been able to dissect the math behind the game, I'm still playing "hit ball good, miss ball bad" over here.

I found some of the info on the actual modifiers used (the ratings, i.e., -2/+4 are just UI placeholders to categorize the actual modifiers). There was often speculation as to whether they were rounded or truncated, and it turns out it’s neither.

I’m on mobile now, but next time on my PC, I’ll post the data. Each event (1B, 2B, 3B, HR) appears to be on a different scale. Just a quick estimate from eyeballing it, it looks like for 1B, each +/- 1 adds or subtracts roughly .033 to the modifier. So, after running through the batter/pitcher matchup and normalization, the HIT calculation for the 1,000 sided die is multiplied by 1, +/- .033 per 1. So if in a +2 1B park the result of the batter/pitcher log5 is multiplied by 1.066 or for a -2 park multiplied by .934. Again, this was from a quick eyeball estimate, but I’ll post actual data within next couple of days.

Posted by just4me on 4/29/2020 6:36:00 PM (view original):
I found some of the info on the actual modifiers used (the ratings, i.e., -2/+4 are just UI placeholders to categorize the actual modifiers). There was often speculation as to whether they were rounded or truncated, and it turns out it’s neither.

I’m on mobile now, but next time on my PC, I’ll post the data. Each event (1B, 2B, 3B, HR) appears to be on a different scale. Just a quick estimate from eyeballing it, it looks like for 1B, each +/- 1 adds or subtracts roughly .033 to the modifier. So, after running through the batter/pitcher matchup and normalization, the HIT calculation for the 1,000 sided die is multiplied by 1, +/- .033 per 1. So if in a +2 1B park the result of the batter/pitcher log5 is multiplied by 1.066 or for a -2 park multiplied by .934. Again, this was from a quick eyeball estimate, but I’ll post actual data within next couple of days.

So here's what I've got: during one of the infamous Paul Bessire presentations there was a slide for ballpark effects and it showed a number of effects and the modifiers used in the calculations of the slide on page 2 of this thread. Those numbers are represented in the top chart. The second chart would be the bounds for each rating on the ballpark effect scale for that hit event. Obviously these are estimated bounds, but these should give a VERY ACCURATE estimation if you were to plug these into the log5 formula for your batter/pitcher matchup as described in the slide from page 2.

I plugged everything exactly as you'd see it with the exception of Petco's hit modifier. In the original presentation this was a -2 and Petco had a Park Factor (Runs) of .830, now it is a -3 and Petco is displaying a Park Factor of .820. So, I have the extreme negative hit factor displayed in -2 instead of -3. This also helped keep the bounds for chart 2 tangible, as if the .908 was a -3, then all the other bounds would've been linear, but the hit (1B) factor would have been exponential and that wouldn't make sense. This shift to accommodate the change in Petco's rating over the first few seasons of its existence made everything else fit exceptionally well.

Hope these charts help understand the effect each modifier has on your batters performance for each ballpark in conjunction with the slide from the previous page and I'm happy to answer any questions or lay out a specific batter/pitcher/ballpark scenario to see how this works in practice.

	-4	-3	-2	-1	0	+1	+2	+3	+4
1B	x	x	0.908	x	1.000	x	x	1.182
2B	0.795	x	x	x	1.000	x	x	x	1.291
3B	x	0.523	x	x	1.000	x	x	x	1.868
HR/L	0.634	x	x	x	1.000	x	x	x	1.385
HR/R	0.636	x	x	x	1.000	x	x	x	1.374
PF		0.820	x	x	1.000	x	x	x	1.370
	-4	-3	-2	-1	0	+1	+2	+3	+4
1B	0.816	0.862	0.908	0.954	1.000	1.046	1.092	1.138	1.184
2B	0.800	0.850	0.900	0.950	1.000	1.050	1.100	1.150	1.200
3B	0.400	0.550	0.700	0.850	1.000	1.150	1.300	1.450	1.700
HR/L	0.640	0.760	0.840	0.920	1.000	1.080	1.160	1.240	1.320
HR/R	0.640	0.760	0.840	0.920	1.000	1.080	1.160	1.240	1.320
PF	0.800	0.850	0.900	0.950	1.000	1.050	1.100	1.150	1.200

I for one would love for you to walk through an example. And if you can clarify, based on your understanding, is the 1B multiplier for hits overall, or just for singles. I have always understood that it applies to hits overall (and mathematically I can't understand any other way for the numbers to make sense) but I recognize there is some disagreement on this point.

thats great stuff just4me, I would also love to see an example

	-4	-3	-2	-1	0	+1	+2	+3	+4
1B	x	x	0.908	x	1.000	x	x	1.182
2B	0.795	x	x	x	1.000	x	x	x	1.291
3B	x	0.523	x	x	1.000	x	x	x	1.868
HR/L	0.634	x	x	x	1.000	x	x	x	1.385
HR/R	0.636	x	x	x	1.000	x	x	x	1.374
PF		0.820	x	x	1.000	x	x	x	1.370
	-4	-3	-2	-1	0	+1	+2	+3	+4
1B	0.816	0.862	0.908	0.954	1.000	1.046	1.092	1.138	1.184
2B	0.800	0.850	0.900	0.950	1.000	1.050	1.100	1.150	1.200
3B	0.400	0.550	0.700	0.850	1.000	1.150	1.300	1.450	1.700
HR/L	0.640	0.760	0.840	0.920	1.000	1.080	1.160	1.240	1.320
HR/R	0.640	0.760	0.840	0.920	1.000	1.080	1.160	1.240	1.320
PF	0.800	0.850	0.900	0.950	1.000	1.050	1.100	1.150	1.200

I'm going to use the same example Paul used in his presentation, then add in the modifiers.

2000 Pedro Martinez vs 1923 Babe Ruth:
[H/AB=((AVG*OAV)/Lgavg)/((AVG*OAV)/LgAVG+(1-AVG)*(1-OAV)/(1-LGAVG))
Where, LgAVG=(PLgAVG+BLgAVG)/2]
Thus: H/AB=((.393*.167)/.2791)/((.393*.167)/.2791+(1-.393)*(1-.167)/(1-.2791))
Where, LgAVG=(.283+.276)/2], or .2791

Log5 result = .2504 This is the expected AVG for Ruth or OAV for Pedro in this matchup including normalization. If they had both been lefties or righties we then would've used the handedness modifier (new result would have been .2379, but that doesn't apply here). So in this case we apply the hit modifier (1B effect). For Coors that's a multiplier of 1.182, and the new result is .2959, for a -3 Park, like Petco, our modifier range is .862-.908, so in a worst case, that would be the original .2504*.862, or .2158. The next step if it is a hit is to determine what type of hit. WIS works backwards and starts with HR. The HR/H rate is calculated the same way as the H/AB but instead of AVG, OAV, LgAVG we use bHR/H, pHR/H, and LHR/H.

Thus: HR/H=((.200*.132)/.0805)/((.200*.132)/.0805+(1-.200)*(1-.132)/(1-.0805))
Where, LgHR/H=(.124+.037)/2], or .0805
Log5 result = .3027 (roughly 30% of the hits Ruth gets off of Pedro will be HRs. Now, in Coors, this wold be multiplied by the HR/RF (Sim assumes pull for hitter in calculations), so we take the .3027 and multiply the HR modifier of 1.374 to get a park adjusted rate of .4159 or roughly 41 HR per 100 hits off of Pedro in Coors.

This is HR/H, not HR/AB. The HR/AB for this matchup is simply multiplying the H/AB rate by the HR/H rate. (.2959*.4159) for a HR/AB of .1230 in Coors. In Petco we'd start with the -3 modifier (which puts us somewhere between .64-.76, so we'll use .7 for our estimate) and multiply the original outcome of .3027 by .7 to get the park adjusted HR/H rate of .2118 or roughly 21 HR per 100 hits or a (.2158*.2118) .0457 HR/AB in Petco (12.3 HR/AB in Coors & 4.57 HR/AB in Petco for this particular Batter/Pitcher matchup (7.58 HR/AB in neutral park)).

If it's not a HR, then using a regression from the pitcher ERA and the batters 3B/H and 2B/H, the SIM works to see if it's a + play on defense , or a triple or double the same as the HR above and uses the park effects the same way. Any hits that didn't become HR, + play, 3B, or 2B are singles.

Excellent. Thank you.

OK, assuming just4me's descriptions are correct, then it is clear that the Park 1B rating affects overall hits, NOT singles.

Posted by contrarian23 on 4/30/2020 12:41:00 PM (view original):
Excellent. Thank you.

OK, assuming just4me's descriptions are correct, then it is clear that the Park 1B rating affects overall hits, NOT singles.

For me, the clearest indicator of this being correct is that the 1B modifier on park effects is applied at the beginning of Decision Tree Step 3 and no modifier is applied at the 1B point of the Decision Tree Step 3.

I have always wondered why Rogers Center is at 1.03 with -2/+2/0/+1/+1 while Riverfront is 0.90 with the same -2/+2/0/+1/+1.

Any insight?

none whatsoever

Posted by FatDad on 4/30/2020 2:25:00 PM (view original):
I have always wondered why Rogers Center is at 1.03 with -2/+2/0/+1/+1 while Riverfront is 0.90 with the same -2/+2/0/+1/+1.

Any insight?

Two questions from that:

1. Could it be that they are reflecting that each of those +/- numbers actually is a range so one of those parks has more at one edge of the ranges and is therefore pulling the overall rating there?

2. Is there somewhere on the decision tree where that single park factor number factors in? Or is it just a representation of the cumulative effect of all the individual 1B/2B/3B/HR ratings?

Posted by FatDad on 4/30/2020 2:25:00 PM (view original):
I have always wondered why Rogers Center is at 1.03 with -2/+2/0/+1/+1 while Riverfront is 0.90 with the same -2/+2/0/+1/+1.

Any insight?

The Park Effect deal with the run scoring environment and the ratings deal with the modifiers above for each hit type event. Those ratings could be on opposite sides of the respective bounds with Riverfront on the least hitter friendly variant of each modifier within the rating (i.e., .908 1B modifier for Riverfront and .954 for Rogers).

Ultimately the Park Factor isn’t used at all in the sim, but is a reflection of the overall run scoring environment for the ballpark. Essentially, Riverfront suppresses run scoring by roughly 10% and Rogers sees about a 3% gain in run scoring over neutral parks.