shin

A Python implementation of Shin's method [1, 2] for calculating implied probabilities from bookmaker odds.

Probabilities calculated in this way have been shown to be more accurate than those obtained by the standard approach of dividing the inverse odds by the booksum [3].

Installation

Requires Python 3.9 or above.

pip install shin

Usage

import shin

shin.calculate_implied_probabilities([2.6, 2.4, 4.3])

[0.37299406033208965, 0.4047794109200184, 0.2222265287474275]

Shin's method assumes there is some unknown proportion of bettors that are insiders, z, and this proportion along with the implied probabilities can be estimated using an iterative procedure described in [4].

Diagnostic information from the iterative procedure can be obtained by setting the full_output argument to True:

import shin

shin.calculate_implied_probabilities([2.6, 2.4, 4.3], full_output=True)

ShinOptimisationDetails(
    implied_probabilities=[0.37299406033208965, 0.4047794109200184, 0.2222265287474275],
    iterations=426,
    delta=9.667822098435863e-13,
    z=0.01694251276407055
)

The returned object contains the following fields:

• implied_probablities
• iterations - compare this value to the max_iterations argument (default = 1000) to check for failed convergence
• delta - the final change in z for the final iteration. Compare with the convergence_threshold argument (default = 1e-12) to assess convergence
• z - the estimated proportion of theoretical betting volume coming from insider traders

When there are only two outcomes, z can be calculated analytically [3]. In this case, the iterations and delta fields of the returned dict are 0 to reflect this:

import shin

shin.calculate_implied_probabilities([1.5, 2.74], full_output=True)

ShinOptimisationDetails(
    implied_probabilities=[0.6508515815085157, 0.3491484184914841],
    iterations=0.0,
    delta=0.0,
    z=0.03172728540646625
)

Note that with two outcomes, Shin's method is equivalent to the Additive Method of [5].

What's New in Version 0.2.0?

The latest version improves support for static typing and includes a breaking change.

Breaking Change To calculate_implied_probabilities() Signature

All arguments to calculate_implied_probabilities() other than odds are now keyword only arguments. This change simplified declaration of overloads to support typing the function's return value and will allow for more flexibility in the API.

from shin import calculate_implied_probabilities

# still works
calculate_implied_probabilities([2.0, 2.0])
calculate_implied_probabilities(odds=[2.0, 2.0])
calculate_implied_probabilities([2.0, 2.0], full_output=True)
## also any other combination of passing arguments as keyword args remains the same

# passing any arg other than `odds` as positional is now an error
calculate_implied_probabilibies([2.0, 2.0], 1000)  # Error
calculate_implied_probabilities([2.0, 2.0], max_iterations=1000)  # OK


calculate_impolied_probabilities([2.0, 2.0], 1000, 1e-12, True) # Error
calculate_implied_probabilities([2.0, 2.0], max_iterations=1000, convergence_threshold=1e-12, full_output=True)  # OK

See this commit for more details.

Full Output Type

The full_output argument now returns a ShinOptimisationDetails object instead of a dict. This object is a dataclass with the same fields as the dict that was previously returned.

For the read-only case, the ShinOptimisationDetails object can be used as a drop-in replacement for the dict that was previously returned as it supports __getitem__().

This change was introduced to support generic typing of the implied_probabilities, currently not supported by TypedDict in versions of Python < 3.11.

See this and this for more details.

What's New in Version 0.1.0?

The latest version introduces some substantial changes and breaking API changes.

Default Return Value Behaviour

Previously shin.calculate_implied_probabilities would return a dict that contained convergence details of the iterative fitting procedure along with the implied probabilities:

import shin

shin.calculate_implied_probabilities([2.6, 2.4, 4.3])

{'implied_probabilities': [0.37299406033208965,
  0.4047794109200184,
  0.2222265287474275],
 'iterations': 425,
 'delta': 9.667822098435863e-13,
 'z': 0.01694251276407055}

The default behaviour now is for the function to only return the implied probabilities:

import shin

shin.calculate_implied_probabilities([2.6, 2.4, 4.3])

[0.37299406033208965, 0.4047794109200184, 0.2222265287474275]

The full output can still be had by setting the full_output argument to True:

import shin

shin.calculate_implied_probabilities([2.6, 2.4, 4.3], full_output=True)

{'implied_probabilities': [0.37299406033208965,
  0.4047794109200184,
  0.2222265287474275],
 'iterations': 425,
 'delta': 9.667822098435863e-13,
 'z': 0.01694251276407055}

Passing Mappings

A common scenario is to have a mapping between some selection identifiers and their odds. You can now pass such mappings to shin.calculate_implied_probabilities and have a new dict mapping between the selection identifiers and their probabilities returned:

import shin

shin.calculate_implied_probabilities({"HOME": 2.6, "AWAY": 2.4, "DRAW": 4.3})

{'HOME': 0.37299406033208965,
 'AWAY': 0.4047794109200184,
 'DRAW': 0.2222265287474275}

This also works when asking for the full output to be returned:

import shin

shin.calculate_implied_probabilities({"HOME": 2.6, "AWAY": 2.4, "DRAW": 4.3}, full_output=True)

{'implied_probabilities': {'HOME': 0.37299406033208965,
  'AWAY': 0.4047794109200184,
  'DRAW': 0.2222265287474275},
 'iterations': 426,
 'delta': 9.667822098435863e-13,
 'z': 0.01694251276407055}

Controlling the Optimiser

Starting in version 0.1.0, the iterative procedure is implemented in Rust which provides a considerable performance boost. If you would like to use the old Python based optimiser use the force_python_optimiser argument:

import timeit
timeit.timeit(
    "shin.calculate_implied_probabilities([2.6, 2.4, 4.3], force_python_optimiser=True)",
    setup="import shin",
    number=10000
)

3.9101167659973726

import timeit
timeit.timeit(
    "shin.calculate_implied_probabilities([2.6, 2.4, 4.3])",
    setup="import shin",
    number=10000
)

0.14442387002054602

References

[1] H. S. Shin, “Prices of State Contingent Claims with Insider traders, and the Favorite-Longshot Bias”. The Economic Journal, 1992, 102, pp. 426-435.

[2] H. S. Shin, “Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims”. The Economic Journal, 1993, 103(420), pp. 1141-1153.

[3] E. Štrumbelj, "On determining probability forecasts from betting odds". International Journal of Forecasting, 2014, Volume 30, Issue 4, pp. 934-943.

[4] B. Jullien and B. Salanié, "Measuring the Incidence of Insider Trading: A Comment on Shin". The Economic Journal, 1994, 104(427), pp. 1418–1419

[5] S. Clarke, S. Kovalchik, M. Ingram, "Adjusting bookmaker’s odds to allow for overround". American Journal of Sports Science, 2017, Volume 5, Issue 6, pp. 45-49.