Your Current and Final Won-Lost Record

 

              I intended to run this research two or three weeks ago.   The research is most interesting at the start of the season and gets less interesting as the season goes on, so I apologize for the delay; should have done it earlier.   With a little luck (and a few of you reminding me) I’ll run it again next April.

              Let us suppose that your team, which you thought during Spring Training was a very good team, loses on opening day.    Suppose that they start the season 1-3; suppose that they start 2-5, and 3-7, and 4-9.   At some point you know that this is becoming a serious problem, but where exactly is that point?

              The question I am really trying to get to is, obviously 3-1 teams are better than 1-3 teams, but just as obviously, four games doesn’t mean much of anything.   To what extent are 3-1 teams three and one because they have caught a few breaks early, and to what extent is 3 and 1 legitimately encouraging if you are trying to stay out of the basement?

              I took 50-some years worth of major league baseball, and sorted teams by their won-lost record as of the end of that game.   Let’s say 40 games, since that is about where we are in the schedule right now.     In my data I had 101 teams which were 16-24, 111 teams that were 17-23 after 40 games, 124 teams that were 18-22, 156 that were 19-21, 156 that were 20-20, 144 that were 21-19, 137 that were 22-18, and 134 that were 23-17.      Let’s take.. .let’s say a four-game difference, the difference between teams that are 18-22 and those which are 22-18.   To what extent are the 22-18 teams just better than the 18-22 teams?

              To a pretty large extent, actually.    Of the teams which were 22-18 after forty games, 70% finished the season with winning records, whereas of the teams which were 18-22, only 32% finished the season with winning records.   (If a team finished the season exactly .500, I counted that as one-half of a winning record.)     Anyway:

              Only 19% of teams which were 16-24 managed to finish the season with a winning record,

              25% of teams which were 17-23,

              32% of teams which were 18-22,

              42% of teams which were 19-21,

              51% of teams which were 20-20,

              58% of teams which were 21-19,

              70% of teams which were 22-18, and

              79% of teams which were 23-17. 

             

              Each win after the 40-game mark represents about an 8 to 9% gain in the likelihood of finishing the season with a winning record.     But what would this data be if it did not tell us anything about the underlying quality of the team?

              If the actual quality of the team was not a factor in their won-lost record through 40 games—that is, if the 22-18 teams were in reality no better than the 18-22 teams; they were all .500 teams, but some had been a little bit luckier than others—then

              24% of 16-24 teams would go on to finish over .500,

              29% of 17-23 teams,

              36% of 18-22 teams,

              43% of 19-21 teams,

              50% of 20-20 teams,

              57% of 21-19 teams,

              64% of 22-18 teams, and

              71% of 23-17 teams. 

              Hmm.   Well, that data isn’t all that different from the other data.   In other words:

              1)  If your team is 23-17, then you can probably cruise to a winning record by season’s end, not necessarily because you’re good but because even a .500 team isn’t that likely to be 6 games under .500 in 122 games.  

              2)  If your team is 21-19, that indicates almost nothing about the quality of your team.   Your chances of finishing over .500 are 58%--57% because you are two games over .500 so far, and 1% because you are actually good.   

              That’s mathematically miss-stated, but perhaps you will forgive me.   It miss-states the biases in the data.     Let’s go back to the beginning of the season.    In my data there were 1,530 teams, of which 755 started the season 0-1, and 775 started 1-0.  

              There is an imbalance there because the schedule-makers like to juggle the schedule to maximize the number of team which start the season at home.    More teams start the season at home than on the road, so more start the season 1-0 than 0-1.  

              Anyway, or those teams which start the season 0-1, 45% will finish the season with winning records, while of those teams which start 1-0, 57% will finish the season with winning records.   It’s kind of mathematically deceptive.   The one game (80-81 versus 81-80) occupies about 6% of the space on the random-outcomes won-lost distribution, so starting 1-0 vs. 0-1 has a pretty significant impact on the team’s chance of finishing the season over .500.   (There’s another imbalance there, caused by the fact that slightly more teams finish the season with a winning record than a losing record.)

              Teams which started the season 1-0 had an overall winning percentage, for the season, of .509.   Those which started 0-1 had an overall winning percentage of .491.    But taking the first game out of it, the teams which started the season 1-0 had a REST OF SEASON winning percentage of .506, while those which started 0-1 had a rest-of-season winning percentage of .494.  

              That’s pretty meaningless, of course, but bear with me; that category won’t remain meaningless as we get further into the chart.    Let’s put all the data for one game in one chart.

 

Won	Lost	Pct	ROS WPct	Count	W Record	Pct
1	0	.509	.506	775	442.5	57%
0	1	.491	.494	755	336.5	45%

 

              To keep this clear. . . teams which had a 1-0 record in my study had a .506 winning percentage for the rest of the season, giving them a .509 final winning percentage.  442.5 of the 775 teams had winning records for the season, which is 57%.   

              This is the same data after 40 games, for all levels of success that we have covered by at least 50 games:

 

Won	Lost	Pct	ROS WPct	Count	W Record	Pct
26	14	.564	.534	55	48.5	88%
25	15	.564	.543	73	69	95%
24	16	.554	.538	87	74	85%
23	17	.542	.531	134	106	79%
22	18	.525	.516	137	95.5	70%
21	19	.514	.510	144	83.5	58%
20	20	.503	.504	156	79	51%
19	21	.491	.496	156	66	42%
18	22	.476	.485	124	39.5	32%
17	23	.465	.478	111	28	25%
16	24	.449	.465	101	19.5	19%
15	25	.429	.447	68	5	7%

 

              Fifty games is kind of a low standard for inclusion, and you get some unreliable data included when you get under 100 games, under 150 games really.   Anyway, if your team is 25-15, you’ve probably got a 90+% chance of having a winning season—not only because you’ve got a ten-game head start, but also because you probably have a good team.   Teams which were 25-15 had a rest-of-season winning percentage of .543, whereas teams that were 15-25 had a rest-of-season winning percentage of .447.  

              There’s a lot of charts here. . . .I’ll run the charts up to twenty games, and then we’ll take a little break.  

 

Won	Lost	Pct	ROS WPct	Count	W Record	Pct
1	0	.509	.506	775	442.5	57%
0	1	.491	.494	755	336.5	45%
2	0	.522	.516	394	253	64%
1	1	.499	.499	750	373.5	50%
0	2	.480	.487	392	156	40%
3	0	.534	.525	197	139	71%
2	1	.506	.503	574	311.5	54%
1	2	.490	.493	567	259	46%
0	3	.476	.485	192	69.5	36%
4	0	.545	.533	102	78.5	77%
3	1	.515	.509	385	227.5	59%
2	2	.498	.498	569	289.5	51%
1	3	.487	.493	368	150.5	41%
0	4	.460	.473	109	35.5	33%
5	0	.555	.540	50	41.5	83%
4	1	.526	.517	252	161.5	64%
3	2	.508	.505	455	257	56%
2	3	.491	.494	506	229.5	45%
1	4	.478	.487	206	70.5	34%
0	5	.445	.460	64	21	33%
5	1	.535	.523	161	112	70%
4	2	.518	.512	324	200	62%
3	3	.502	.502	510	266.5	52%
2	4	.479	.485	344	129	38%
1	5	.467	.479	131	40	31%
6	1	.545	.530	104	79.5	76%
5	2	.527	.519	238	157	66%
4	3	.510	.507	395	228.5	58%
3	4	.494	.497	431	200	46%
2	5	.471	.480	245	76.5	31%
1	6	.453	.468	85	22	26%
7	1	.563	.546	64	56	88%
6	2	.531	.519	157	110	70%
5	3	.519	.514	333	207	62%
4	4	.501	.501	402	209.5	52%
3	5	.482	.488	342	130.5	38%
2	6	.465	.477	151	42.5	28%
1	7	.439	.456	60	12	20%
7	2	.544	.530	114	89	78%
6	3	.523	.514	239	154	64%
5	4	.515	.512	370	219.5	59%
4	5	.489	.492	367	161	44%
3	6	.474	.482	248	81	33%
2	7	.457	.471	103	27	26%
8	2	.559	.543	60	51.5	86%
7	3	.535	.524	190	141	74%
6	4	.520	.514	312	190.5	61%
5	5	.502	.502	344	178.5	52%
4	6	.480	.486	332	129	39%
3	7	.460	.471	155	37	24%
2	8	.456	.474	81	22.5	28%
8	3	.552	.540	118	97.5	83%
7	4	.522	.514	257	163.5	64%
6	5	.508	.506	347	195	56%
5	6	.494	.497	332	149.5	45%
4	7	.471	.479	232	81	35%
3	8	.452	.465	111	21.5	19%
2	9	.449	.469	50	14.5	29%
9	3	.559	.544	86	75.5	88%
8	4	.534	.523	185	133.5	72%
7	5	.514	.508	302	173.5	57%
6	6	.505	.506	332	180	54%
5	7	.482	.487	275	111	40%
4	8	.461	.472	171	44	26%
3	9	.450	.467	92	21	23%
10	3	.564	.545	54	48	89%
9	4	.543	.530	130	104.5	80%
8	5	.526	.518	251	159	63%
7	6	.509	.506	323	182.5	57%
6	7	.494	.497	278	130	47%
5	8	.474	.482	239	82	34%
4	9	.452	.465	125	30	24%
3	10	.445	.465	67	13	19%
10	4	.551	.535	99	86.5	87%
9	5	.531	.521	191	122	64%
8	6	.520	.515	292	188	64%
7	7	.503	.503	275	146	53%
6	8	.481	.486	266	99	37%
5	9	.467	.478	181	58	32%
4	10	.449	.465	101	20	20%
11	4	.552	.533	71	60.5	85%
10	5	.548	.535	141	109.5	78%
9	6	.525	.517	255	168.5	66%
8	7	.510	.507	263	148	56%
7	8	.492	.495	270	120	44%
6	9	.479	.487	227	84.5	37%
5	10	.451	.463	145	34.5	24%
4	11	.440	.458	79	11.5	15%
12	4	.552	.530	56	48.5	87%
11	5	.555	.540	119	96	81%
10	6	.534	.523	180	134.5	75%
9	7	.519	.514	261	160	61%
8	8	.500	.500	256	129	50%
7	9	.488	.494	248	102	41%
6	10	.463	.473	195	56	29%
5	11	.443	.458	115	20.5	18%
12	5	.561	.543	98	84	86%
11	6	.542	.529	140	105	75%
10	7	.526	.519	209	148.5	71%
9	8	.512	.510	268	149	56%
8	9	.494	.496	244	113.5	47%
7	10	.476	.484	224	74.5	33%
6	11	.455	.467	157	40	25%
5	12	.432	.449	86	10.5	12%
13	5	.562	.541	83	71	86%
12	6	.553	.539	108	90.5	84%
11	7	.533	.523	184	139	76%
10	8	.520	.515	233	140.5	60%
9	9	.501	.501	237	115	49%
8	10	.487	.492	251	107	43%
7	11	.473	.484	188	59.5	32%
6	12	.436	.449	119	20.5	17%
5	13	.429	.449	60	6	10%
14	5	.569	.546	55	51	93%
13	6	.559	.542	89	74.5	84%
12	7	.540	.527	158	123.5	78%
11	8	.526	.519	212	143.5	68%
10	9	.511	.509	224	124.5	56%
9	10	.490	.493	244	105.5	43%
8	11	.486	.495	229	92	40%
7	12	.446	.457	142	30	21%
6	13	.440	.458	88	14	16%
14	6	.565	.545	74	67	91%
13	7	.550	.535	137	114.5	84%
12	8	.529	.519	154	106.5	69%
11	9	.521	.517	225	141.5	63%
10	10	.502	.503	233	119.5	51%
9	11	.486	.491	232	98	42%
8	12	.471	.482	192	60	31%
7	13	.440	.453	119	19	16%
6	14	.427	.446	64	5	8%

 

              By the 20-game mark, if you are at the margins of the won-lost chart, something significant has happened.   If your team is 14-6 or better, you have a 90% chance of having a winning season.   If you are 6-14 or worse, you’re under 10%.   

              At the ten-game mark. . .well, probably nothing too meaningful has happened unless you’re 9-1 or 10-0.     Let’s move ahead now to about the point of the season where we are now. . .let’s say 40 to 60 games in:

 

Won	Lost	Pct	ROS WPct	Count	W Record	Pct
26	14	.564	.534	55	48.5	88%
25	15	.564	.543	73	69	95%
24	16	.554	.538	87	74	85%
23	17	.542	.531	134	106	79%
22	18	.525	.516	137	95.5	70%
21	19	.514	.510	144	83.5	58%
20	20	.503	.504	156	79	51%
19	21	.491	.496	156	66	42%
18	22	.476	.485	124	39.5	32%
17	23	.465	.478	111	28	25%
16	24	.449	.465	101	19.5	19%
15	25	.429	.447	68	5	7%
26	15	.564	.539	64	57	89%
25	16	.558	.540	73	67	92%
24	17	.548	.535	118	96	81%
23	18	.535	.525	134	103	77%
22	19	.519	.512	132	81	61%
21	20	.506	.504	164	88.5	54%
20	21	.498	.502	154	76.5	50%
19	22	.482	.488	121	39	32%
18	23	.472	.484	128	38.5	30%
17	24	.460	.475	113	25.5	23%
16	25	.436	.452	76	9	12%
15	26	.421	.440	57	3	5%
27	15	.566	.538	59	53	90%
26	16	.563	.542	62	56.5	91%
25	17	.551	.534	100	86	86%
24	18	.544	.533	127	101	80%
23	19	.525	.517	132	90	68%
22	20	.513	.509	145	86	59%
21	21	.499	.499	150	76	51%
20	22	.494	.500	150	64	43%
19	23	.474	.482	128	37.5	29%
18	24	.466	.479	99	28	28%
17	25	.451	.468	98	16	16%
16	26	.429	.447	67	6	9%
15	27	.414	.434	55	3	5%
27	16	.565	.541	56	51	91%
26	17	.555	.536	84	71.5	85%
25	18	.545	.532	117	95.5	82%
24	19	.538	.530	123	94	76%
23	20	.517	.511	146	94	64%
22	21	.511	.510	143	80.5	56%
21	22	.491	.493	144	63.5	44%
20	23	.488	.497	148	57	39%
19	24	.468	.477	115	29.5	26%
18	25	.460	.475	93	20.5	22%
17	26	.442	.460	77	12	16%
16	27	.419	.436	66	3	5%
Won	Lost	Pct	ROS WPct	Count	W Record	Pct
27	17	.561	.540	67	59	88%
26	18	.549	.532	104	86	83%
25	19	.545	.536	128	106	83%
24	20	.522	.514	123	83	67%
23	21	.520	.519	152	99	65%
22	22	.492	.489	138	58.5	42%
21	23	.489	.494	145	59.5	41%
20	24	.480	.490	131	46	35%
19	25	.466	.479	99	23	23%
18	26	.456	.474	93	21	23%
17	27	.429	.446	67	4	6%
16	28	.416	.435	59	3	5%
29	16	.574	.545	52	48	92%
28	17	.559	.534	59	53	90%
27	18	.555	.537	83	73	88%
26	19	.547	.535	112	91.5	82%
25	20	.533	.525	136	105	77%
24	21	.518	.512	127	77	61%
23	22	.512	.512	142	84	59%
22	23	.492	.494	139	61	44%
21	24	.480	.486	144	49.5	34%
20	25	.476	.489	114	34	30%
19	26	.457	.471	86	18.5	22%
18	27	.449	.468	83	13.5	16%
17	28	.423	.441	62	5	8%
16	29	.409	.430	51	2	4%
29	17	.568	.542	53	49.5	93%
28	18	.560	.540	66	61	92%
27	19	.552	.537	109	91	83%
26	20	.539	.528	126	100	79%
25	21	.527	.520	132	92	70%
24	22	.516	.514	126	79.5	63%
23	23	.500	.500	131	64	49%
22	24	.486	.489	153	60	39%
21	25	.480	.490	129	41.5	32%
20	26	.464	.475	93	18	19%
19	27	.458	.476	88	20	23%
18	28	.438	.457	70	8	11%
17	29	.415	.433	62	4	6%
29	18	.573	.554	58	55	95%
28	19	.554	.536	85	75.5	89%
27	20	.547	.536	122	102.5	84%
26	21	.534	.526	133	97.5	73%
25	22	.516	.510	114	76	67%
24	23	.509	.509	143	75.5	53%
23	24	.492	.493	136	63	46%
22	25	.483	.490	128	43.5	34%
21	26	.475	.487	122	34.5	28%
20	27	.463	.479	87	18.5	21%
19	28	.446	.463	79	13.5	17%
18	29	.422	.439	66	4	6%
17	30	.413	.435	51	3	6%
Won	Lost	Pct	ROS WPct	Count	W Record	Pct
30	18	.568	.542	52	47	90%
29	19	.563	.545	77	71	92%
28	20	.553	.539	103	88	85%
27	21	.535	.522	133	104.5	79%
26	22	.537	.535	112	89.5	80%
25	23	.509	.504	129	70	54%
24	24	.499	.499	151	74	49%
23	25	.488	.492	125	45	36%
22	26	.479	.488	127	44	35%
21	27	.466	.478	98	21.5	22%
20	28	.454	.471	95	18	19%
19	29	.435	.452	67	8	12%
18	30	.420	.439	63	3	5%
30	19	.573	.555	74	70	95%
29	20	.555	.538	90	76.5	85%
28	21	.547	.536	104	88	85%
27	22	.531	.521	130	101.5	78%
26	23	.526	.523	117	77	66%
25	24	.505	.503	153	83	54%
24	25	.498	.501	128	56	44%
23	26	.478	.482	123	38.5	31%
22	27	.470	.480	117	34	29%
21	28	.462	.477	93	20	22%
20	29	.445	.461	76	11.5	15%
19	30	.431	.451	59	6	10%
18	31	.417	.439	57	2	4%
31	19	.575	.554	64	59	92%
30	20	.560	.541	85	78	92%
29	21	.552	.538	97	79.5	82%
28	22	.540	.530	115	100.5	87%
27	23	.528	.523	133	91.5	69%
26	24	.514	.511	127	77	61%
25	25	.503	.505	139	68	49%
24	26	.487	.490	113	41.5	37%
23	27	.475	.482	134	43	32%
22	28	.463	.474	97	22.5	23%
21	29	.457	.474	89	15	17%
20	30	.433	.448	67	9.5	14%
19	31	.424	.445	53	2	4%
31	20	.566	.546	80	74	93%
30	21	.552	.535	90	76	84%
29	22	.549	.539	108	96	89%
28	23	.534	.527	113	87.5	77%
27	24	.519	.514	131	81	62%
26	25	.510	.510	135	78	58%
25	26	.494	.496	121	46.5	38%
24	27	.483	.489	130	52	40%
23	28	.461	.466	109	21.5	20%
22	29	.467	.484	99	27	27%
21	30	.445	.461	71	8.5	12%
20	31	.426	.443	64	5	8%
Won	Lost	Pct	ROS WPct	Count	W Record	Pct
32	20	.572	.551	52	48	92%
31	21	.559	.540	80	72	90%
30	22	.550	.536	115	100.5	87%
29	23	.545	.539	104	88	85%
28	24	.524	.517	126	86	68%
27	25	.514	.512	132	82	62%
26	26	.501	.502	128	58.5	46%
25	27	.486	.489	125	46.5	37%
24	28	.469	.472	115	32	28%
23	29	.471	.485	84	23	27%
22	30	.454	.470	101	20	20%
21	31	.437	.453	62	5.5	9%
20	32	.429	.450	60	6	10%
32	21	.562	.541	58	53	91%
31	22	.561	.548	103	93	90%
30	23	.543	.531	121	104	86%
29	24	.536	.531	102	81.5	80%
28	25	.521	.517	130	83	64%
27	26	.506	.504	124	64	52%
26	27	.493	.495	136	58.5	43%
25	28	.477	.479	114	35.5	31%
24	29	.471	.480	108	31	29%
23	30	.463	.477	85	20.5	24%
22	31	.442	.456	85	9	11%
21	32	.438	.459	53	5	9%
20	33	.420	.441	61	5	8%
Won	Lost	Pct	ROS WPct	Count	W Record	Pct
33	21	.563	.537	58	53	91%
32	22	.564	.550	81	74	91%
31	23	.546	.532	107	91.5	86%
30	24	.543	.536	116	101	87%
29	25	.528	.523	108	76.5	71%
28	26	.512	.508	133	77.5	58%
27	27	.498	.497	125	54	43%
26	28	.484	.485	121	46	38%
25	29	.483	.493	116	41.5	36%
24	30	.460	.469	98	20.5	21%
23	31	.449	.462	77	11.5	15%
22	32	.441	.459	72	9	13%
21	33	.433	.456	61	4	7%
20	34	.414	.436	50	2	4%
33	22	.566	.547	71	63	89%
32	23	.554	.539	103	91.5	89%
31	24	.543	.532	112	98	88%
30	25	.538	.534	110	89	81%
29	26	.518	.512	106	68.5	65%
28	27	.502	.498	134	60.5	45%
27	28	.496	.499	125	57	46%
26	29	.479	.482	114	40.5	36%
25	30	.472	.481	113	31.5	28%
24	31	.459	.471	81	15.5	19%
23	32	.442	.455	81	10	12%
22	33	.441	.463	51	7	14%
21	34	.424	.447	63	2	3%
34	22	.573	.554	64	59	92%
33	23	.559	.543	77	70.5	92%
32	24	.549	.537	109	95.5	88%
31	25	.539	.531	119	102	86%
30	26	.527	.523	104	75	72%
29	27	.507	.502	118	63	53%
28	28	.502	.504	131	58.5	45%
27	29	.489	.493	117	51	44%
26	30	.474	.480	117	36	31%
25	31	.473	.488	88	22	25%
24	32	.446	.456	82	11.5	14%
23	33	.440	.456	69	8	12%
22	34	.431	.452	57	4	7%
35	22	.572	.547	53	51	96%
34	23	.572	.557	63	57.5	91%
33	24	.551	.535	99	86	87%
32	25	.545	.536	111	101.5	91%
31	26	.532	.526	121	93	77%
30	27	.514	.508	109	64.5	59%
29	28	.505	.503	112	54.5	49%
28	29	.499	.504	136	65	48%
27	30	.478	.480	107	37	35%
26	31	.476	.488	97	31	32%
25	32	.462	.475	93	17	18%
24	33	.439	.449	73	9	12%
23	34	.433	.451	72	5	7%
Won	Lost	Pct	ROS WPct	Count	W Record	Pct
35	23	.572	.553	63	60	95%
34	24	.559	.543	84	72.5	86%
33	25	.548	.536	100	92.5	93%
32	26	.537	.529	125	104.5	84%
31	27	.524	.518	107	72	67%
30	28	.510	.506	114	61.5	54%
29	29	.498	.497	113	51.5	46%
28	30	.492	.498	121	52.5	43%
27	31	.478	.485	101	34.5	34%
26	32	.467	.478	95	21.5	23%
25	33	.457	.472	84	15.5	18%
24	34	.441	.457	69	6.5	9%
23	35	.421	.435	74	3	4%
36	23	.575	.554	51	49	96%
35	24	.565	.548	73	66	90%
34	25	.553	.540	96	87.5	91%
33	26	.540	.529	99	88	89%
32	27	.532	.526	131	99.5	76%
31	28