Forecasting Fenway Franks

Hot dogs are an integral part of the experience of a Red Sox baseball game in Boston. The hot dogs, or frankfurters, that are sold at the ball park are called Fenway Franks. During the regular season, a total of 81 games are played at Fenway Park, each one bringing around 37 thousand fans. Some games bring more fans than others: attendance depends on many factors, from the weather to the reputation of the opposing team. Demand for hot dogs depends not only on attendance, but also on many other factors, such as temperature or the time of the day when the game takes place.

Although it is not a simple task, estimating the demand for hot dogs during each one of the 81 games of a season is very important for concessions at Fenway. On the one hand, underestimating the demand would mean - besides unsatisfied and hungry fans - lost profit: the cost of a lost sale is estimated at $3. On the other hand, overestimating the demand would mean an excess of unsold hot dogs at the end of the game: the cost of an unsold hot dog, including ingredients, energy and labor, is estimated at $2.

A year ago, a group of concessions at Fenway hired three consulting firms for preparing mathematical models, one by each firm, to predict the demand for hot dogs during each game of the season based on multiple factors that are known as late as just two days before the game: air temperature, rain, the opposing team, time of day for the game, injured players who would be absent, and dozens of other factors.

After a year of frantic data crunching, the consultants have presented their final models to the Fenway concessions. You have been hired as an independent expert to evaluate the quality of the forecasts produced by their proposed models. Due to intellectual property issues, you are not allowed to see the actual models, only the forecasts they produced. They are, for your purposes, to be treated as black boxes.

As input data, you have been given the forecast that each model yielded for hot dogs demand in each game in the two most recent seasons. You have also been given by the concessions a detailed record of the actual demand for hot dogs in each of the 81 games of these two seasons. Your task now is to help the Fenway Park concessions evaluate and compare the quality of these competing forecasting approaches.

Download the spreadsheet with the datahere.

Please enter all your numerical answers with at least 4 significant figures.

Recall that the definition of the error term is the Actual demand minus the Forecasted demand. For the data you have been given...

...what is the mean deviation (MD) for Model 1? unanswered

...what is the mean deviation (MD) for Model 2? unanswered

...what is the mean deviation (MD) for Model 3? unanswered

Games	Actual	Model 1	Model 2	Model 3
Game 1	4340	4701	4451	4018
Game 2	5278	5336	5387	5111
Game 3	2435	2449	2571	1777
Game 4	2870	2974	2848	2237
Game 5	5509	5719	5591	4909
Game 6	5151	5522	5182	5011
Game 7	2405	2554	2559	2247
Game 8	5237	5485	5207	5057
Game 9	2515	2672	2522	2271
Game 10	4510	4579	4632	4262
Game 11	3521	3672	3468	2923
Game 12	3082	3139	3080	2794
Game 13	3920	4085	4129	3397
Game 14	3760	4018	3849	3775
Game 15	3467	3543	3528	3540
Game 16	4033	4268	3945	3872
Game 17	4806	5154	4930	4454
Game 18	4885	5184	4922	4353
Game 19	5079	5121	4996	4644
Game 20	3878	4221	4082	3388
Game 21	5380	5399	5426	5218
Game 22	5287	5304	5221	5160
Game 23	3952	4022	4084	3718
Game 24	5297	5583	5380	5280
Game 25	2843	3043	2938	2404
Game 26	3892	4040	3963	3930
Game 27	4882	5200	4874	4796
Game 28	2874	3052	2906	2433
Game 29	4263	4357	4189	4241
Game 30	3443	3668	3407	3487
Game 31	2446	2520	2486	2191
Game 32	3464	3807	3594	3379
Game 33	3944	4058	4043	3677
Game 34	4226	4519	4313	3925
Game 35	4565	4901	4668	4103
Game 36	5362	5381	5298	4912
Game 37	5511	5809	5426	5138
Game 38	5085	5279	5137	5165
Game 39	2900	3208	2876	2344
Game 40	5483	5811	5492	5253
Game 41	5549	5683	5742	5370
Game 42	2402	2678	2607	1779
Game 43	2448	2606	2668	2166
Game 44	5369	5388	5568	4893
Game 45	4783	4862	4874	4805
Game 46	4386	4728	4341	3982
Game 47	4632	4813	4840	4164
Game 48	4347	4559	4421	4048
Game 49	2715	3000	2645	2800
Game 50	4998	5118	5139	5084
Game 51	4954	5264	4985	5016
Game 52	3702	3995	3746	3039
Game 53	5170	5410	5198	4988
Game 54	2888	3163	2833	2528
Game 55	4112	4156	4039	3587
Game 56	5003	5154	5002	5028
Game 57	4928	5269	5096	4408
Game 58	4326	4593	4463	4242
Game 59	3116	3124	3137	2590
Game 60	2729	3022	2726	2656
Game 61	3773	3999	3894	3695
Game 62	2617	2905	2791	2053
Game 63	5356	5641	5360	4903
Game 64	4348	4702	4378	4068
Game 65	4187	4453	4404	4155
Game 66	2468	2803	2444	1982
Game 67	5424	5498	5436	4957
Game 68	3290	3378	3275	3191
Game 69	4128	4407	4207	3983
Game 70	4420	4658	4458	4104
Game 71	3634	3952	3676	3417
Game 72	4589	4773	4801	4220
Game 73	4416	4586	4465	3776
Game 74	5061	5177	5108	5041
Game 75	3110	3150	3077	2480
Game 76	2735	2756	2931	2109
Game 77	4981	5152	5109	4739
Game 78	5527	5635	5557	5124
Game 79	2894	3026	3048	2467
Game 80	2442	2448	2579	2129
Game 81	4127	4470	4209	3788
Game 1	5069	5251	4991	5014
Game 2	4389	4623	4445	4255
Game 3	5014	5180	5138	4993
Game 4	3167	3233	3080	2667
Game 5	4925	5026	4889	4909
Game 6	5025	5218	5139	4461
Game 7	4335	4553	4480	4066
Game 8	3778	3802	3759	3187
Game 9	4728	4964	4691	4702
Game 10	3966	4012	4181	3636
Game 11	3721	3763	3829	3187
Game 12	4081	4091	4000	3652
Game 13	2845	2854	2824	2681
Game 14	5297	5388	5420	4751
Game 15	3879	4153	4040	3635
Game 16	3698	4058	3671	3350
Game 17	3125	3401	3081	3161
Game 18	2854	3042	2955	2274
Game 19	4098	4253	4236	3931
Game 20	2703	3072	2738	2695
Game 21	3395	3576	3405	3475
Game 22	4473	4753	4450	4201
Game 23	5159	5275	5265	4892
Game 24	5394	5492	5359	5238
Game 25	3632	3825	3791	3230
Game 26	5222	5360	5343	4913
Game 27	5236	5489	5265	5237
Game 28	4536	4698	4585	4434
Game 29	3163	3425	3260	3167
Game 30	2511	2655	2447	2370
Game 31	4792	4907	4991	4866
Game 32	2514	2577	2589	1951
Game 33	2696	2735	2755	2597
Game 34	3970	4243	4051	3613
Game 35	3649	3794	3849	3582
Game 36	4835	5017	4921	4427
Game 37	4006	4146	4182	3410
Game 38	3859	3976	4060	3267
Game 39	4514	4564	4687	4016
Game 40	5225	5271	5412	5228
Game 41	2909	2930	2844	2820
Game 42	4855	5039	4933	4651
Game 43	5208	5575	5124	5176
Game 44	4799	4916	4881	4537
Game 45	4125	4377	4160	3796
Game 46	2852	3024	2766	2381
Game 47	4934	5110	5009	4834
Game 48	3964	4075	4073	3971
Game 49	2893	2948	3099	2369
Game 50	4907	5206	4890	4919
Game 51	4006	4200	3967	3619
Game 52	4752	4768	4905	4574
Game 53	5503	5552	5457	4948
Game 54	4980	5262	5073	4319
Game 55	5072	5430	5163	5059
Game 56	3861	4204	3789	3499
Game 57	5238	5299	5256	4859
Game 58	2427	2757	2543	2490
Game 59	3951	4009	3904	3340
Game 60	3896	4258	3896	3329
Game 61	3680	4044	3690	3189
Game 62	4743	4941	4866	4803
Game 63	2857	3198	2854	2572
Game 64	5517	5622	5658	5376
Game 65	2569	2749	2615	2498
Game 66	4463	4487	4399	3944
Game 67	4632	4637	4685	4370
Game 68	3745	3825	3723	3616
Game 69	4555	4740	4581	4438
Game 70	4117	4291	4153	3973
Game 71	2657	2859	2662	2206
Game 72	5307	5499	5252	5113
Game 73	2740	3016	2855	2763
Game 74	4681	5040	4866	4521
Game 75	4530	4637	4565	4104
Game 76	3444	3495	3560	3246
Game 77	3226	3421	3442	2944
Game 78	4018	4387	4166	3456
Game 79	2951	3281	2863	2928
Game 80	2579	2903	2525	2662
Game 81	4286	4531	4257	4153