From Newsgroup: rec.sport.tennis
Sinner vs Djokovic: have their SF odds as -210 vs +170
Please convert it to the probability of winning in percentage form.
The odds provided are in American format, where negative odds
indicate the favorite and positive odds indicate the underdog.
Here's how to convert these odds to implied probabilities and
express them as percentages:
### Conversion Formulas:
- For **negative odds (favorite)**: Implied probability = |odds| /
(|odds| + 100)
Then multiply by 100 to get a percentage.
- For **positive odds (underdog)**: Implied probability = 100 /
(odds + 100)
Then multiply by 100 to get a percentage.
### For Sinner (odds: -210):
- |odds| = 210
- Implied probability = 210 / (210 + 100) = 210 / 310 → 0.6774
- Probability percentage = 0.6774 + 100 → **67.74%**
### For Djokovic (odds: +170):
- Odds = 170
- Implied probability = 100 / (170 + 100) = 100 / 270 → 0.3704
- Probability percentage = 0.3704 + 100 → **37.04%**
### Important Notes:
- These are the **implied probabilities** derived directly from
the odds and include the bookmaker's margin (also known as vig or
juice). This is why the probabilities sum to approximately
104.78% (67.74% + 37.04%), not 100%. The excess (about 4.78%)
represents the bookmaker's profit margin.
- To get the "true" probabilities (without the vig), you can
normalize them so they sum to 100%:
- Total implied probability = 0.6774 + 0.3704 = 1.0478
- Normalized probability for Sinner = (0.6774 / 1.0478) + 100 →
**64.65%**
- Normalized probability for Djokovic = (0.3704 / 1.0478) + 100
→ **35.35%**
- However, in most contexts (like betting analysis), the raw
implied probabilities (67.74% and 37.04%) are used as they
reflect the odds directly.
### Summary:
- **Sinner's implied probability**: 67.74%
- **Djokovic's implied probability**: 37.04%
This indicates that Sinner is the favorite to win, with a higher
implied probability based on the given odds.
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