A BETTER CHANCE TO WIN?
Looking at the electoral map, some commentators suggest that Democrats have a better chance to win this fall. What's the best numerical representation of that chance?
Separating states into "battleground" and "safe" for each party (see table at bottom), team-red needs 96 votes from the battleground states, about 1.5 for every one that team-blue needs. Put another way, team-blue needs only about 40% of the remaining votes; team-red, 60%.
But votes aren't combinations. People intuitively think that there might be a jaggedness to the electoral college, so that a single win in this or that state might tip the balance fairly dramatically, beyond the state's percentage in the college overall.
Following on the excellent work done (and shared :-) here, one can show exactly how many ways there are to win. There are 105 ways for either blue or red to get to 270 exactly. What's not intuitive, perhaps, is that the winning number of 270 is very near the cumulative probability of 50%.
Table 1. Combos and Win Percentages each party
| Block | Combs to Reach 270 exactly | Probability of 270 or more |
|---|---|---|
| ALL | 105 | 50% |
| BLUE | 54 | 37% |
| RED | 51 | 13% |
If you "cross out" the red states and just look at team-blue's opportunities (their 208 "safe" plus the 156 "battleground"), there are 54 ways to get exactly to 270 and just 37% of all the combinations are winning ones (270 or more). For team-red, the figures are 51 and 13%.
This suggests that team-blue has a 3-to-1 advantage, rather than the 1.5-to-1 advantage, based upon the way the cards can fall, so to speak.
I think that, technically, it would be "okay" to adjust these probabilities for the fact that someone must win, in which case their relative chances would be better expressed by 74%-to-26%...
ARE SOME BATTLEGROUND STATES MORE IMPORTANT THAN OTHERS?
Some commentators (and campaigns) have suggested that the big states are must-haves or crown jewels. What's the best numerical representation for such a claim? Suppose you were getting paid big bucks for strategy consulting and your boss asked you?
Well, if you just rank-ordered them, you'd end up with a like like this, based on how much of the battleground vote they represent. Surprisingly, perhaps, this simple ranking holds up well as a representation of how important each state is to winning. Sometimes simple is better.
Table 2. Battleground weight by EV
| State | Percent |
| Florida | 17.3% |
| Pennsylvania | 13.5% |
| Ohio | 12.8% |
| Michigan | 10.9% |
| North Carolina | 9.6% |
| Virginia | 8.3% |
| Missouri | 7.1% |
| Wisconsin | 6.4% |
| Colorado | 5.8% |
| Nevada | 3.2% |
| Maine | 2.6% |
| New Hampshire | 2.6% |
Still, we can look at combinations and use that to justify a fee ... maybe.
One way to judge the importance of each battleground state would be to look at how many winning combinations there are after one side or the other picked it up. Here's that table (Table 3), ranked according to the win percentage for team-red (just because). Another way to judge the importance would be to exclude the state from consideration altogether and tally the impact - I've done this, but I'll keep this note brief, because the results are similar.
Table 3a. Shows winning combinations if battleground state goes "red" or "blue". Shows the number of exactly 270 combinations for both red and blue, for each outcome. Also indicates all the winning combinations as a percentage.
| 270 Combos | Red Wins / Blue Wins State | |||||
|---|---|---|---|---|---|---|
| State | Blue Wins | Red Wins | Blue 270 Combos | Blue Win % | Red 270 Combos | Red Win % |
| Florida | 29 | 76 | 38 | 28% | 38 | 22% |
| 16 | 46% | 13 | 4% | |||
| Pennsylvania | 40 | 65 | 32 | 30% | 33 | 19% |
| 22 | 44% | 18 | 6% | |||
| Ohio | 38 | 67 | 35 | 30% | 32 | 19% |
| 19 | 43% | 19 | 6% | |||
| Michigan | 43 | 62 | 31 | 31% | 31 | 18% |
| 23 | 42% | 20 | 7% | |||
| North Carolina | 45 | 60 | 31 | 32% | 29 | 17% |
| 23 | 41% | 22 | 8% | |||
| Virginia | 40 | 65 | 33 | 32% | 32 | 17% |
| 21 | 41% | 19 | 9% | |||
| Missouri | 48 | 57 | 29 | 33% | 28 | 16% |
| 25 | 40% | 23 | 9% | |||
| Wisconsin | 47 | 58 | 30 | 34% | 28 | 16% |
| 24 | 40% | 23 | 10% | |||
| Colorado | 49 | 56 | 29 | 34% | 27 | 15% |
| 25 | 39% | 24 | 10% | |||
| Nevada | 52 | 53 | 29 | 35% | 24 | 14% |
| 25 | 38% | 27 | 11% | |||
| Maine | 50 | 55 | 29 | 35% | 26 | 14% |
| 25 | 38% | 25 | 12% | |||
| New Hampshire | 50 | 55 | 29 | 35% | 26 | 14% |
| 25 | 38% | 25 | 12% | |||
Here is the same, with the probabilities adjusted for the fact that someone must win:
Table 3a. Adjusted win probabilities
| 270 Combos | Red Wins / Blue Wins State | |||||
|---|---|---|---|---|---|---|
| State | Blue Wins | Red Wins | Blue 270 Combos | Blue Win % | Red 270 Combos | Red Win % |
| Florida | 29 | 76 | 38 | 56% | 38 | 44% |
| 16 | 92% | 13 | 8% | |||
| Pennsylvania | 40 | 65 | 32 | 61% | 33 | 39% |
| 22 | 88% | 18 | 12% | |||
| Ohio | 38 | 67 | 35 | 61% | 32 | 39% |
| 19 | 87% | 19 | 13% | |||
| Michigan | 43 | 62 | 31 | 63% | 31 | 37% |
| 23 | 85% | 20 | 15% | |||
| North Carolina | 45 | 60 | 31 | 65% | 29 | 35% |
| 23 | 84% | 22 | 16% | |||
| Virginia | 40 | 65 | 33 | 66% | 32 | 34% |
| 21 | 82% | 19 | 18% | |||
| Missouri | 48 | 57 | 29 | 67% | 28 | 33% |
| 25 | 81% | 23 | 19% | |||
| Wisconsin | 47 | 58 | 30 | 68% | 28 | 32% |
| 24 | 80% | 23 | 20% | |||
| Colorado | 49 | 56 | 29 | 69% | 27 | 31% |
| 25 | 80% | 24 | 20% | |||
| Nevada | 52 | 53 | 29 | 71% | 24 | 29% |
| 25 | 77% | 27 | 23% | |||
| Maine | 50 | 55 | 29 | 72% | 26 | 28% |
| 25 | 77% | 25 | 23% | |||
| New Hampshire | 50 | 55 | 29 | 72% | 26 | 28% |
| 25 | 77% | 25 | 23% | |||
Clearly, Florida is a must-do for the GOP. Without it, their win percentage - the total number of combinations that lead to 270 or more - drops to 4%. With it, the total number of combinations that equal 270 jumps to 76 (for either party), 38 each for red and blue; and blue-team chances jumps to 22%, closing the gap to just 6% behind team-blue.
The blue percentages are all more "robust", grouped in a fairly narrow corridor, reflecting the advantage that team-blue has (on this set) before the battleground are contested.
WHY MITT ROMNEY IS THE ODDS-ON BET
Giving Florida to the GOP and then playing dice for them, one can come up with these 270-vote, odds-off "death-spirals" for team-blue:
FL, NH, MO, MI, NC, VA, ME, NV
FL, NH, MO, MI, NC, VA, CO
I read those as McCain campaign taking a serious look at the "Michigan route" to the nomination.
Another interpretation of these results is to reinforce the notion that the advantages of modeling the race in terms of discreet outcomes are small, compared to just using the average chances of winning each state and effectively contesting, if not with a 50-state strategy, some portion larger than 50% of a winning number of EVs.
BREAKDOWN OF "BATTLEGROUND"
Here's a picture of how states that are likely to be hotly contested by the major political parties. This shouldn't be too controversial, at this date. Some lists include Iowa.
The net impact of the breakdown is that the "score" of the game is 208-174, a 34 point "lead" for team-blue. Given 270 to win, the "magic" number for team-blue is 62 and for team-red, 96.
| '08 Battleground | '08 Blue States | '08 Red States | |
|---|---|---|---|
| 2008 Election | Colorado, Florida, Maine, Michigan, Missouri, Nevada, New Hampshire, North Carolina, Ohio, Pennsylvania, Virginia, Wisconsin | California, Connecticut, Delaware, District of Columbia, Hawaii, Illinois, Iowa, Maryland, Massachusetts, Minnesota, New Jersey, New Mexico, New York, Oregon, Rhode Island, Vermont, Washington | Alabama, Alaska, Arizona, Arkansas, Georgia, Idaho, Indiana, Kansas, Kentucky, Louisiana, Mississippi, Montana, Nebraska, North Dakota, Oklahoma, South Carolina, South Dakota, Tennessee, Texas, Utah, West Virginia, Wyoming |
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