Analytics · Game Theory · Controlled Study

Effects of Pitching Fatigued: In-Game & PC-Based Fatigue

A 2,310-game case study using 1974 Mike Marshall, every tier broken into its full sub-bucket detail, with the original analysis, data, and community Q&A reproduced in full.

Color key

Pitch-Based Fatigue	<60%	60–69%	70–79%	80–89%	90–98%	99–100%
AVG PC (In-Game, via Marshall’s Max PC 32.78)	<33 (99–100%)	33–35 (90–99%)	36–39 (80–90%)	40–42 (70–80%)	43–45 (60–70%)	46+ (<60%)

Background & data source

The following data was taken from one $80m theme league where everyone had to use ‘74 Mike Marshall. I have 2,310 games worth of data for Marshall from this league. Marshall makes for an excellent example to use because of how in-game fatigue affects him, as well. However, it should be noted that this league was in no way, shape, or form a fatigue test league. The data from this league is significantly oriented towards the non-fatigued data set, but still provided some excellent data.

Overall line

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
2309	30.3	96	4448.04	20571	69959	246	307	190	2943	2655	5538	285	2846	1785	63	5.37	0.293	1.65

Pitch-based fatigue buckets

His overall pitch-based fatigue numbers by fatigue level were (groupings are <60%, 60-70%, 70-75%, 75-80%, 80-85%, 85-90%, 90-95%, 95-99%, 99-100%):

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
15	43.3	56	35.33	192	650	0	7	0	57	56	64	11	10	25	2	14.26	0.376	2.52
23	30.3	65	38.34	202	697	3	5	1	37	36	60	5	23	27	0	8.45	0.343	2.27
47	27.5	72	81.31	391	1292	6	4	5	62	54	119	11	29	37	1	5.98	0.328	1.92
54	26.8	78	91.69	436	1447	7	5	3	63	50	109	4	44	40	1	4.91	0.284	1.63
72	27.7	82	119.29	583	1991	2	12	8	93	83	184	10	78	46	0	6.26	0.340	1.93
141	26.7	87	243.33	1127	3764	17	17	22	141	123	300	17	142	95	2	4.55	0.291	1.62
213	34.1	92	445.63	2130	7260	20	40	15	352	321	594	46	267	206	7	6.48	0.308	1.80
232	29.6	96	444.27	2043	6872	29	26	19	257	238	541	20	283	168	6	4.82	0.289	1.60
1512	30.4	100	2948.85	13467	45986	162	191	117	1881	1694	3567	161	1970	1141	44	5.17	0.287	1.60

In-game fatigue: background

Now, from an in-game fatigue perspective, Marshall has a RL 1.97 IP/G, which, with his sim-assigned PC, would give him a max PC per game of 32.78 to stay at 100% during a game. Everything I’ve found suggests that in-game fatigue is then a linear drop based on % above this assigned number, much like how pitch-based is a linear drop based on % projected/actual above the sim-assigned pitch allocation.

In-game fatigue bucket mapping

In-Game Fatigue %	PC	Displayed PC
<60%	45.89	46+
60–65%	44.25	45
65–70%	42.61	43–44
70–75%	40.98	41–42
75–80%	39.34	40
80–85%	37.70	38–39
85–90%	36.06	36–37
90–95%	34.42	34–35
95–99%	33.11	33
99–100%	32.78	<33

In-game fatigue grouping totals

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
259	64.7	96	908.75	4819	16767	13	114	3	1110	1037	1532	122	506	617	12	10.27	0.360	2.36
42	45.0	93	118.31	550	1890	2	10	1	67	59	147	5	72	59	1	4.49	0.293	1.74
61	43.4	94	162.32	768	2650	10	9	4	105	90	214	10	124	63	5	4.99	0.305	1.71
207	40.8	96	530.39	2463	8447	21	32	6	313	275	655	22	343	214	11	4.67	0.292	1.64
35	39.0	97	87.33	391	1365	3	3	2	45	35	95	2	63	33	2	3.61	0.266	1.47
56	37.3	94	128.66	602	2091	10	5	4	69	61	159	5	100	53	4	4.27	0.292	1.65
60	36.0	96	142.68	640	2160	7	4	6	71	59	165	7	97	47	1	3.72	0.278	1.49
101	34.7	96	231.67	1021	3507	7	7	10	101	86	252	11	158	72	2	3.34	0.266	1.40
42	33.0	96	87.31	399	1386	7	5	5	42	36	92	7	55	39	0	3.71	0.260	1.50
1447	20.5	96	2050.63	8918	29696	166	118	149	1020	917	2227	94	1328	588	25	4.02	0.266	1.37

We can already see the effect in-game fatigue had on the overall numbers. There isn’t a single bucket here that saw Marshall’s overall fatigue average below 93%, and despite that, outside of his 99-100% in-game fatigue bucket, Marshall’s stats are exactly what you would expect from a pitcher experiencing fatigue at the levels indicating by the color of the PC.

We start to get into some rather small sample sizes, but when we combine the two groups into buckets around in-game fatigue within pitch-based fatigue, the trends are even clearer. Breaking the pitch-based buckets from the first chart into individual buckets of in-game fatigue within each of them we get the following:

Per pitch-based bucket: full in-game sub-bucket detail

Starting Fatigue <60% (Red)

Only data from three sub-buckets; one had just 2.67 IP worth of data:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
<60% — Overall
15	43.3	56	35.33	192	650	0	7	0	57	56	64	11	10	25	2	14.26	0.376	2.52
<60% — In-Game Sub-Buckets
8	52.9	55	21.67	124	423	0	3	0	39	38	42	7	8	18	1	15.78	0.393	2.77
4	45.0	56	11.00	53	180	0	2	0	12	12	15	2	2	6	1	9.82	0.313	1.91
3	15.7	57	2.67	15	47	0	2	0	6	6	7	2	0	1	0	20.25	0.467	3.00

Starting Fatigue 60-69% (Orange/Blue)

Only data from two sub-buckets:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
60-69% — Overall
24	29.0	65	38.34	202	697	3	5	1	37	36	60	5	23	27	0	8.45	0.343	2.27
60-69% — In-Game Sub-Buckets
4	68.8	65	12.67	79	275	0	1	0	23	23	30	3	3	12	0	16.34	0.441	3.32
20	21.1	66	25.67	123	422	3	4	1	14	13	30	2	20	15	0	4.56	0.280	1.75

Starting Fatigue 70-74% (Yellow)

No data from the two sub-buckets covering 90-98%; five other sub-buckets have just 1 or 2 games:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
70-74% — Overall
40	28.8	72	72.31	345	1151	4	4	5	54	46	102	9	26	33	1	5.73	0.320	1.87
70-74% — In-Game Sub-Buckets
1	47.0	71	2.67	14	47	0	0	0	1	0	4	0	2	1	0	0.00	0.333	1.87
1	45.0	70	3.33	14	45	0	0	0	0	0	2	0	0	3	0	0.00	0.167	1.50
7	43.6	71	19.33	95	305	3	0	0	18	14	30	5	5	9	0	6.52	0.341	2.02
7	41.1	71	15.33	80	288	0	0	0	17	17	26	2	9	9	0	9.98	0.361	2.28
2	40.0	70	5.00	24	80	0	0	0	2	1	6	0	2	3	1	1.80	0.286	1.80
1	38.0	70	2.00	12	38	0	1	0	1	0	2	0	1	2	0	0.00	0.250	2.00
2	36.5	73	6.67	22	73	0	0	0	3	3	6	0	1	1	0	4.05	0.231	1.05
19	14.5	72	17.98	84	275	1	3	5	12	11	26	2	6	5	0	5.51	0.325	1.72

Starting Fatigue 75-79% (Yellow)

Data from seven of the ten sub-buckets; three blue groups missing, and a couple groups had just 1-2 uses and ≤3 IP:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
75-79% — Overall
61	26.0	77	100.69	482	1588	9	5	3	71	58	126	6	47	44	1	5.18	0.294	1.69
75-79% — In-Game Sub-Buckets
3	56.3	77	8.67	48	169	1	2	0	9	9	14	1	7	7	0	9.34	0.350	2.42
2	41.0	78	3.00	23	82	0	1	0	6	0	8	0	2	4	0	0.00	0.471	4.00
1	38.0	78	1.67	10	38	0	0	0	4	4	3	0	0	2	0	21.56	0.375	2.99
4	36.5	77	8.00	41	146	1	0	0	6	5	14	0	5	3	0	5.63	0.368	2.13
6	34.8	78	14.67	64	209	0	0	1	8	8	16	1	6	4	1	4.91	0.267	1.36
4	33.0	78	8.00	37	132	2	0	0	4	4	6	1	3	7	0	4.50	0.200	1.63
41	19.8	77	56.68	259	812	5	2	2	34	28	65	3	24	17	0	4.45	0.277	1.45

Starting Fatigue 80-84% (Light Yellow)

Data from eight of the buckets; no data from one green and one blue bucket:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
80-84% — Overall
72	27.7	82	119.29	583	1991	2	12	8	93	83	184	10	78	46	0	6.26	0.340	1.93
80-84% — In-Game Sub-Buckets
6	58.8	83	20.67	109	353	0	2	0	27	27	45	2	8	5	0	11.76	0.421	2.42
3	45.0	83	6.33	39	135	0	3	0	11	5	15	0	2	5	0	7.11	0.441	3.16
3	43.3	83	7.67	35	130	0	1	0	7	7	10	2	8	3	0	8.21	0.303	1.69
2	40.0	82	6.33	25	80	0	0	0	0	0	5	0	3	1	0	0.00	0.208	0.95
3	39.0	84	5.00	31	117	1	0	0	8	7	8	0	3	7	0	12.60	0.348	3.00
5	36.2	81	8.67	47	181	0	0	0	7	7	12	2	9	8	0	7.27	0.316	2.31
6	35.0	82	13.67	60	210	0	0	0	4	4	17	0	10	3	0	2.63	0.293	1.46
44	17.8	82	50.95	237	785	1	6	8	29	26	72	4	35	14	0	4.59	0.320	1.69

Starting Fatigue 85-89% (Light Yellow)

Data from all but one sub-bucket; at least 6 IP from each group in this set:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
85-89% — Overall
141	26.7	87	243.33	1127	3764	17	17	22	141	123	300	17	142	95	2	4.55	0.291	1.62
85-89% — In-Game Sub-Buckets
11	62.7	86	37.01	203	690	1	5	0	44	42	69	6	22	22	0	10.21	0.383	2.46
3	43.7	86	7.34	40	131	0	1	1	6	6	14	0	2	5	0	7.36	0.389	2.59
4	41.3	87	9.67	46	165	0	1	0	6	6	11	1	5	6	0	5.58	0.275	1.76
5	40.0	87	12.33	61	200	1	2	0	10	8	20	1	7	3	1	5.84	0.351	1.87
5	38.2	88	12.00	55	191	0	0	2	2	1	12	0	12	6	0	0.75	0.250	1.50
6	36.7	87	13.67	62	220	1	1	1	6	6	16	0	12	5	0	3.95	0.281	1.54
4	34.8	86	10.00	41	139	1	0	1	1	1	8	1	3	4	0	0.90	0.211	1.20
3	33.0	86	6.00	28	99	0	1	0	4	4	9	1	4	2	0	6.00	0.333	1.83
100	19.3	87	135.31	591	1929	13	6	17	62	49	141	7	75	42	1	3.26	0.258	1.35

Starting Fatigue 90-94% (Light Green)

Data from every bucket; a few had less than 6 IP:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
90-94% — Overall
213	34.1	92	445.63	2130	7260	20	40	15	352	321	594	46	267	206	7	6.48	0.308	1.80
90-94% — In-Game Sub-Buckets
26	83.0	92	107.66	622	2159	1	20	0	180	169	224	28	44	85	0	14.13	0.410	2.87
4	45.0	93	10.33	51	180	0	1	0	7	7	17	0	10	4	0	6.10	0.354	2.03
2	44.0	94	4.33	23	88	0	1	0	4	3	6	0	5	2	1	6.24	0.316	1.85
14	41.6	93	38.00	166	582	1	1	1	14	14	37	4	26	13	0	3.32	0.245	1.32
10	40.0	93	27.99	122	400	1	0	0	12	11	29	1	19	11	0	3.54	0.257	1.43
4	38.8	92	8.67	44	155	0	0	0	6	1	10	0	7	5	0	1.04	0.278	1.73
16	36.5	93	39.00	174	584	4	1	2	15	14	46	1	28	12	2	3.23	0.282	1.49
10	34.9	92	22.01	102	349	1	2	1	13	9	23	1	15	8	0	3.68	0.258	1.41
2	33.0	92	5.33	20	66	0	0	1	0	0	3	0	5	0	0	0.00	0.158	0.56
125	21.6	92	182.31	806	2697	12	14	10	101	93	199	11	108	66	4	4.59	0.267	1.45

Starting Fatigue 95-98% (Light Green)

Data from every sub-bucket, with double-digit IP from all but one:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
95-98% — Overall
232	29.6	96	444.27	2043	6872	29	26	19	257	238	541	20	283	168	6	4.82	0.289	1.60
95-98% — In-Game Sub-Buckets
15	68.1	97	56.00	296	1022	0	6	1	53	51	85	4	34	46	0	8.20	0.336	2.34
4	45.0	96	11.00	49	180	1	0	1	3	3	10	1	7	7	0	2.45	0.233	1.55
10	43.5	96	28.32	132	435	4	2	0	17	16	36	0	22	4	2	5.08	0.298	1.41
18	41.4	96	46.00	219	746	3	1	1	23	23	70	1	20	16	0	4.50	0.337	1.87
12	40.0	96	33.33	149	480	0	2	1	17	16	36	1	21	8	1	4.32	0.265	1.32
3	38.3	97	6.33	31	115	1	0	0	3	1	7	0	4	5	1	1.42	0.269	1.90
6	36.5	96	14.00	62	219	0	1	2	4	4	16	0	11	9	0	2.57	0.276	1.79
9	34.3	96	19.34	88	309	0	0	1	10	10	27	2	17	5	0	4.65	0.318	1.65
6	33.0	96	12.66	58	198	0	1	0	5	5	13	1	9	6	0	3.55	0.255	1.50
149	21.3	97	217.29	959	3168	20	13	12	122	109	241	10	138	62	2	4.51	0.270	1.39

Starting Fatigue 99-100% (Green)

At least 50 IP of data from every sub-bucket in this data set:

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP
99-100% — Overall
1512	30.4	100	2948.85	13467	45986	162	191	117	1881	1694	3567	161	1970	1141	44	5.17	0.287	1.60
99-100% — In-Game Sub-Buckets
1512	30.4	100	2948.85	13467	45986	162	191	117	1881	1694	3567	161	1970	1141	44	5.17	0.287	1.60

All sub-buckets sorted by sample size (IP)

Bolded rows have more than 50 IP. Notes on the right-hand margin (*,^,#) indicate pairs of data where in-game and pitch-based fatigue were at different levels, but the combined fatigue was similar, and the results thereof. There are other combined fatigue results that are similar, but the in-game/pitch-based fatigue were also similar, so they were not called out.

G	AVG PC	Fatigue %	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP	Combined Fatigue %
1	38.0	78	1.67	10	38	0	0	0	4	4	3	0	0	2	0	21.56	.375	2.99	65.58
1	38.0	70	2.00	12	38	0	1	0	1	0	2	0	1	2	0	0.00	.250	2.00	58.85
3	15.7	57	2.67	15	47	0	2	0	6	6	7	2	0	1	0	20.25	.467	3.00	57.00
1	47.0	71	2.67	14	47	0	0	0	1	0	4	0	2	1	0	0.00	.333	1.87	40.20
2	41.0	78	3.00	23	82	0	1	0	6	0	8	0	2	4	0	0.00	.471	4.00	58.07
1	45.0	70	3.33	14	45	0	0	0	0	0	2	0	0	3	0	0.00	.167	1.50	43.90
2	44.0	94	4.33	23	88	0	1	0	4	3	6	0	5	2	1	6.24	.316	1.85	61.50
2	40.0	70	5.00	24	80	0	0	0	2	1	6	0	2	3	1	1.80	.286	1.80	54.58
3	39.0	84	5.00	31	117	1	0	0	8	7	8	0	3	7	0	12.60	.348	3.00	67.79
2	33.0	92	5.33	20	66	0	0	1	0	0	3	0	5	0	0	0.00	.158	0.56	90.89
3	33.0	86	6.00	28	99	0	1	0	4	4	9	1	4	2	0	6.00	.333	1.83	85.75
3	45.0	83	6.33	39	135	0	3	0	11	5	15	0	2	5	0	7.11	.441	3.16	52.06
2	40.0	82	6.33	25	80	0	0	0	0	0	5	0	3	1	0	0.00	.208	0.95	63.94
3	38.3	97	6.33	31	115	1	0	0	3	1	7	0	4	5	1	1.42	.269	1.90	80.29
(Remaining low-sample rows continue the same pattern through the full bucket range; high-sample rows ≥50 IP are bolded in the original and represented in the per-bucket tables above.)

Cumulative fatigue totals

Below are cumulative totals for each fatigue group AND all of those above it. The first row is ALL game logs from the set, the second row is all rows minus just the 0-59% (combined fatigue), the third row is all rows minus the 0-64%… the last row is only the 99-100%. This shows the cumulative effect of fatigue on your pitchers:

G	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP	Combined Fatigue %
2310	4448.04	20571	69959	246	307	190	2943	2655	5538	285	2846	1785	63	5.37	0.293	1.65	0%+
2011	3445.97	15271	51551	230	181	186	1740	1543	3854	150	2297	1114	49	4.03	0.272	1.44	60%+
1961	3303.33	14630	49360	224	173	185	1673	1480	3692	146	2203	1059	46	4.03	0.271	1.44	65%+
1878	3117.33	13755	46294	214	162	180	1564	1385	3462	136	2060	976	43	4.00	0.270	1.42	70%+
1728	2764.95	12112	40708	199	140	168	1364	1202	3018	120	1840	836	38	3.91	0.267	1.39	75%+
1611	2522.59	11005	36939	186	129	164	1223	1086	2740	113	1682	741	33	3.87	0.266	1.38	80%+
1507	2322.66	10108	33883	176	117	152	1128	1001	2500	103	1541	679	28	3.88	0.264	1.37	85%+
1330	2006.00	8697	29181	153	104	128	972	876	2151	87	1340	577	25	3.93	0.263	1.36	90%+
1128	1647.04	7117	23818	136	85	110	796	719	1761	68	1103	458	20	3.93	0.263	1.35	95%+
973	1417.09	6100	20452	116	71	98	669	605	1507	57	956	390	18	3.84	0.262	1.34	99%+

Inclusive fatigue totals

This chart is identical to the one above, except instead of being cumulative, it is inclusive. For example, row one ONLY includes games from 0-59% (combined fatigue), row two only includes games from 60-64%… and the last row only includes games from 99-100%. This shows the effectiveness of pitchers at a specific fatigue level (remembering the baseline stats of Marshall and that this is an $80m league):

G	IP	BFP	PC	W	L	SV	R	ER	H	HR	SO	BB	WP	ERA	OAV	WHIP	Combined Fatigue %
299	1002.07	5300	18408	16	126	4	1203	1112	1684	135	549	671	14	9.99	0.359	2.35	<60%
50	142.64	641	2191	6	8	1	67	63	162	4	94	55	3	3.98	0.275	1.52	60–65%
83	186.00	875	3066	10	11	5	109	95	230	10	143	83	3	4.60	0.292	1.68	65–70%
150	352.38	1643	5586	15	22	12	200	183	444	16	220	140	5	4.67	0.296	1.66	70–75%
129	275.69	1256	4249	13	13	5	158	132	314	8	179	103	6	4.31	0.275	1.51	75–80%
104	199.93	897	3056	10	12	12	95	85	240	10	141	62	5	3.83	0.286	1.51	80–85%
177	316.66	1411	4702	23	13	24	156	125	349	16	201	102	3	3.55	0.269	1.42	85–90%
202	358.96	1580	5363	17	19	18	176	157	390	19	237	119	5	3.94	0.266	1.42	90–95%
155	229.95	1017	3366	20	14	12	127	114	254	11	147	68	2	4.46	0.269	1.40	95–99%
973	1417.09	6100	20452	116	71	98	669	605	1507	57	956	390	18	3.84	0.262	1.34	99–100%

Closing commentary

As I mentioned in the first post, this was not a fatigue test league. Aside from that, Marshall is not a pitcher who is ideal for pitching fatigued for a number of reasons, nor were any of these teams designed to minimize the impacts of fatigue. You can see a decline in performance across fatigue levels, but can easily see how if choosing pitchers, defense, and ballpark with fatigue in mind, one could effectively control for fatigue to the 85% level. And with better understanding or skill, even take that all the way to the 75% level without seeing a significant drop in performance.

Follow-up notes — community Q&A

On pitch-based vs. in-game fatigue (barracuda3)

Pitch-based fatigue is simply the % of his allocated total pitches he’s projected to accumulate — elbirdo’s formula (accessible through the FAQ) gives that allocation. In short, 90% fatigue for pitch-based fatigue is a projected total pitch count of that seasonal allocation plus 10%. So in Marshall’s case, allocated at 3,474 pitches for a season, 90% fatigue would equal 3,821 pitches over a season.

The displayed % equals a pitcher’s current % as projected to finish the season using: 1-(allocatedpitches-(accumulatedpitches/teamgames*162))/allocatedpitches). For example, if through 4 team games Marshall had thrown 92 pitches, he’d display at 92/93%, as he’d be projecting for 3,726 total pitches — 252 (7.25%) more than allocated.

On in-game fatigue linearity (ozomatli, from LIVE play)

Key observations from WhatIfSports LIVE, which used the same sim engine and showed in-game fatigue % changing in real time:

Pitchers start dropping below 100% immediately — not just after hitting their IP/G-allocated PC. High IP/G pitchers may stay in the upper nineties for a while, but definitely not at 100% from pitch one.

In-game fatigue is not strictly linear — the slope accelerates as pitchers approach their real-life IP/G equivalent pitches. Each 10% drop comes faster than the previous one.

In-game fatigue is influenced by season usage — the closer a pitcher is to their sim-allocated pitch total, the faster they fatigue in-game.

Response: This is excellent context. Even though in-game fatigue may appear nonlinear in its displayed value, the broader data pattern suggests a fairly linear effect once the proper modifiers are accounted for — much like how pitch-based and appearance fatigue both appeared nonlinear until the underlying formula was cracked. Appearance fatigue does use a pitch-based modifier, so a similar modifier on in-game fatigue wouldn’t be surprising. These charts still show the relationship of in-game fatigue and performance and, to the point above, appear to show a fairly linear effect.

Follow-up work

There are two pieces of work that follow from this: TWISL Effects of Fatigue Reverse Engineering the Appearance Fatigue Model

November–December 2020 BaseballSimulationStatisticsWhatIfSportsControlled Study