Doing the Math
So in my last blog I said that the Wolves had exactly a 0% chance of winning the title. For those of you who are math-oriented, you realized that that was a lie. It was just one of the many lies I tell every day either in person or in print. But like all lies that I tell, I don't allow the person to believe my lies for too long before telling the truth.
So I got to thinking about the Wolves and what their actual chances of winning it all are at this point. The answer, as you may guess, is not good. It's hard to try and calculate what the Wolves chances of even making the playoffs are at this point, so first we'll just look at their chances if they do manage to make the playoffs. To test this, I wrote a script in Python (I've been learning that language lately, so it seemed a logical choice).
To figure out the approximate chance of a team with winning percentage A beating a team with winning percentage B, we use can use the formula:
I'm not sure where this formula came from or who derived it, but I've seen it used before and it seems to be fairly accurate. We can also use home and road records to get a more accurate approximation of how teams will do.
Next, we can apply this formula repeatedly to determine the chances of one team beating another in a seven-game series. In order to simplify these calculations, I didn't actually calculate out every possible scenario, rather, I gave the home team a winning percentage equal to (4*home winning + 3*road winning)/7. Similarly, for the road team, I assigned them a winning percentage of (3*home winning + 4*road winning)/7.
Before I go any further, I have to point out that these are only estimates based on team records up to this point in the season. They don't take into account that some teams will play better during the playoffs. They don't take into account the fact that some teams will likely have better or worse records due to having a unbalanced number of home and road games. And they certainly don't take into account the distinct possibility that Timmy Duncan might get arrested for inciting a riot and be unavailable for the playoffs. They simply predict the results of future games based on what has happened so far.
When I applied this, Here's what I got for the Timberwolves chances in a road series against other teams.
Next, I took these calculations, and was able to predict each teams probability of winning it all based on who they might play at each point during the playoffs. For instance, if the Wolves have a 3.41% chance of beating the Spurs in the first round, then their second round opponent has a 3.41% chance of facing the Wolves and a 96.59% chance of playing the Spurs. Then, you can further calculate probabilities based on this information. You can continue doing this all the way to the top to determine each teams approximate chance of getting there. For this, I assumed current playoff seedings would hold, except that I took out Houston and inserted the Wolves into the 8-seed. Here are the results:
Anybody want to bet against the Spurs? Of course, the Spurs chances might be slightly over inflated due to the fact that they've won 23 out of 24 home games, and that they would have home court advantage for every series. Even for a team as good as the Spurs, this seems a little high, so I took a bit off of their percentage and increased their road winning percentage slightly to compensate. Here are the modified probabilities:
Still pretty dominant, although you may now notice that the Wolves chances have skyrocketed to slightly over 1/10,000. Also, for those of you who are curious, here's what would happen if you rightfully put the Rockets in the 8-seed instead of the Wolves:
And finally, the Rockets with the reduced home winning percentage for the Spurs:
Some interesting things to notice are that despite being the current 3-seed in the east, Boston falls 3rd or 4th from the bottom in all lists.
Also, notice that the Rockets fall ahead of the Lakers in both lists, despite being a lower seed. I ran similar test with the Wolves as the 6- or 7-seed and found that their chances actually went down with a higher seed. This is due to the fact that the 8-seed will likely face the 1-,2-, and 4-seeds, while the 6- and 7-seeds will likely have to face the 1-,2-, and 3-seeds in most scenarios to win the championship.
So we can now return to the original question. Assuming the Wolves continue to play in a way similar to how they've played so far this season, what are their chances of winning it all. I'll generously assume the Wolves have a 50/50 chance of making the playoffs. Of that 50% that they make it, I'll assume that 30% will be in the 8-seed, and the other 20% in the 6- or 7-seed. I'll also assume that the 6- or 7-seed has the chance to win consistent with the Wolves percentage in the first chart, and the 8-seed with the second chart. This gives the Wolves a 0.00506% chance of winning an NBA championship this season, or about 19,750:1 against.
This, of course assumes that nothing dramatic changes for the Wolves. They could make a trade which could possibly help them jump up as high as the 5-seed. But even looking at the Mavs, who are the current 5-seed, their chances are less than 2% in all estimates. Therefore, I conclude that the Wolves should not make any hasty moves in a desperate attempt to win the championship this season. Instead, any moves they make should be based on considerations for future seasons.
So I got to thinking about the Wolves and what their actual chances of winning it all are at this point. The answer, as you may guess, is not good. It's hard to try and calculate what the Wolves chances of even making the playoffs are at this point, so first we'll just look at their chances if they do manage to make the playoffs. To test this, I wrote a script in Python (I've been learning that language lately, so it seemed a logical choice).
To figure out the approximate chance of a team with winning percentage A beating a team with winning percentage B, we use can use the formula:
(A-A*B)/(A+B-2*A*B)
I'm not sure where this formula came from or who derived it, but I've seen it used before and it seems to be fairly accurate. We can also use home and road records to get a more accurate approximation of how teams will do.
Next, we can apply this formula repeatedly to determine the chances of one team beating another in a seven-game series. In order to simplify these calculations, I didn't actually calculate out every possible scenario, rather, I gave the home team a winning percentage equal to (4*home winning + 3*road winning)/7. Similarly, for the road team, I assigned them a winning percentage of (3*home winning + 4*road winning)/7.
Before I go any further, I have to point out that these are only estimates based on team records up to this point in the season. They don't take into account that some teams will play better during the playoffs. They don't take into account the fact that some teams will likely have better or worse records due to having a unbalanced number of home and road games. And they certainly don't take into account the distinct possibility that Timmy Duncan might get arrested for inciting a riot and be unavailable for the playoffs. They simply predict the results of future games based on what has happened so far.
When I applied this, Here's what I got for the Timberwolves chances in a road series against other teams.
- Chances of Wolves Beating Spurs in a 7-game series: 3.41%
- Chances of Wolves Beating Suns in a 7-game series: 5.42%
- Chances of Wolves Beating Sonics in a 7-game series: 13.29%
- Chances of Wolves Beating Kings in a 7-game series: 15.27%
- Chances of Wolves Beating Mavs in a 7-game series: 17.10%
- Chances of Wolves Beating Grizzlies in a 7-game series: 34.83%
- Chances of Wolves Beating Lakers in a 7-game series: 42.45%
- Chances of Wolves Beating Heat in a 7-game series: 12.21%
Next, I took these calculations, and was able to predict each teams probability of winning it all based on who they might play at each point during the playoffs. For instance, if the Wolves have a 3.41% chance of beating the Spurs in the first round, then their second round opponent has a 3.41% chance of facing the Wolves and a 96.59% chance of playing the Spurs. Then, you can further calculate probabilities based on this information. You can continue doing this all the way to the top to determine each teams approximate chance of getting there. For this, I assumed current playoff seedings would hold, except that I took out Houston and inserted the Wolves into the 8-seed. Here are the results:
| Team | Chance to Win |
| Spurs: | 45.9781% |
| Suns: | 25.6755% |
| Heat: | 16.3335% |
| Sonics: | 4.6669% |
| Pistons: | 2.0922% |
| Kings: | 1.6339% |
| Mavs: | 1.6057% |
| Wizards: | 0.7156% |
| Cavs: | 0.6743% |
| Magic: | 0.4832% |
| Grizzlies: | 0.0541% |
| Bulls: | 0.0372% |
| Celtics: | 0.0151% |
| 76ers: | 0.0135% |
| Lakers: | 0.0122% |
| Wolves: | 0.0091% |
Anybody want to bet against the Spurs? Of course, the Spurs chances might be slightly over inflated due to the fact that they've won 23 out of 24 home games, and that they would have home court advantage for every series. Even for a team as good as the Spurs, this seems a little high, so I took a bit off of their percentage and increased their road winning percentage slightly to compensate. Here are the modified probabilities:
| Team | Chance to Win |
| Spurs: | 41.3044% |
| Suns: | 27.7913% |
| Heat: | 17.5551% |
| Sonics: | 5.1682% |
| Pistons: | 2.2854% |
| Kings: | 1.8599% |
| Mavs: | 1.8224% |
| Wizards: | 0.7844% |
| Cavs: | 0.7381% |
| Magic: | 0.5314% |
| Grizzlies: | 0.0617% |
| Bulls: | 0.0412% |
| Celtics: | 0.0167% |
| 76ers: | 0.0150% |
| Lakers: | 0.0140% |
| Wolves: | 0.0108% |
Still pretty dominant, although you may now notice that the Wolves chances have skyrocketed to slightly over 1/10,000. Also, for those of you who are curious, here's what would happen if you rightfully put the Rockets in the 8-seed instead of the Wolves:
| Team | Chance to Win |
| Spurs: | 45.2957% |
| Suns: | 25.9687% |
| Heat: | 16.4510% |
| Sonics: | 4.7519% |
| Pistons: | 2.1143% |
| Kings: | 1.6985% |
| Mavs: | 1.6613% |
| Wizards: | 0.7240% |
| Cavs: | 0.6821% |
| Magic: | 0.4896% |
| Grizzlies: | 0.0561% |
| Bulls: | 0.0378% |
| Rockets: | 0.0275% |
| Celtics: | 0.0153% |
| 76ers: | 0.0137% |
| Lakers: | 0.0127% |
And finally, the Rockets with the reduced home winning percentage for the Spurs:
| Team | Chance to Win |
| Spurs: | 40.5888% |
| Suns: | 28.0971% |
| Heat: | 17.6711% |
| Sonics: | 5.2587% |
| Pistons: | 2.3079% |
| Kings: | 1.9311% |
| Mavs: | 1.8832% |
| Wizards: | 0.7930% |
| Cavs: | 0.7462% |
| Magic: | 0.5382% |
| Grizzlies: | 0.0638% |
| Bulls: | 0.0417% |
| Rockets: | 0.0325% |
| Celtics: | 0.0170% |
| 76ers: | 0.0152% |
| Lakers: | 0.0146% |
Some interesting things to notice are that despite being the current 3-seed in the east, Boston falls 3rd or 4th from the bottom in all lists.
Also, notice that the Rockets fall ahead of the Lakers in both lists, despite being a lower seed. I ran similar test with the Wolves as the 6- or 7-seed and found that their chances actually went down with a higher seed. This is due to the fact that the 8-seed will likely face the 1-,2-, and 4-seeds, while the 6- and 7-seeds will likely have to face the 1-,2-, and 3-seeds in most scenarios to win the championship.
So we can now return to the original question. Assuming the Wolves continue to play in a way similar to how they've played so far this season, what are their chances of winning it all. I'll generously assume the Wolves have a 50/50 chance of making the playoffs. Of that 50% that they make it, I'll assume that 30% will be in the 8-seed, and the other 20% in the 6- or 7-seed. I'll also assume that the 6- or 7-seed has the chance to win consistent with the Wolves percentage in the first chart, and the 8-seed with the second chart. This gives the Wolves a 0.00506% chance of winning an NBA championship this season, or about 19,750:1 against.
This, of course assumes that nothing dramatic changes for the Wolves. They could make a trade which could possibly help them jump up as high as the 5-seed. But even looking at the Mavs, who are the current 5-seed, their chances are less than 2% in all estimates. Therefore, I conclude that the Wolves should not make any hasty moves in a desperate attempt to win the championship this season. Instead, any moves they make should be based on considerations for future seasons.
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